feat(viz): trie visualisation
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'use client';
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import { useVisualization } from '@/lib/visualizations/use-visualization';
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import type { AlgorithmDefinition } from '@/lib/visualizations/types';
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import { VisualizationContainer } from '../core/visualization-container';
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import { TrieView } from '../data-structures/trie-view';
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interface TrieVisualizationProps {
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algorithm: AlgorithmDefinition;
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className?: string;
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}
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export function TrieVisualization({
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algorithm,
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className,
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}: TrieVisualizationProps) {
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const {
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currentStep,
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currentStepIndex,
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totalSteps,
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playback,
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controls,
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currentPhase,
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progress,
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} = useVisualization(algorithm);
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const { dataState } = currentStep;
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const trie = dataState.tries?.[0] ?? null;
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return (
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<VisualizationContainer
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title={algorithm.title}
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pattern={algorithm.pattern}
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code={algorithm.code}
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currentLine={currentStep.codeLine}
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highlightLines={currentStep.codeHighlightLines}
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explanation={currentStep.explanation}
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decision={currentStep.decision}
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phase={currentPhase}
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variables={dataState.variables}
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currentStepIndex={currentStepIndex}
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totalSteps={totalSteps}
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isPlaying={playback.isPlaying}
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speed={playback.speed}
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controls={controls}
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progress={progress}
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className={className}
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>
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<div className="flex items-start justify-center">
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{trie && <TrieView trie={trie} />}
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</div>
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</VisualizationContainer>
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);
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}
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'use client';
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import { useMemo } from 'react';
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import { motion } from 'framer-motion';
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import { cn } from '@/lib/utils';
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import type { TrieState, TrieNodeState } from '@/lib/visualizations/types';
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import { TrieNode } from '../primitives/trie-node';
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interface TrieViewProps {
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trie: TrieState;
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className?: string;
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}
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const NODE_RADIUS = 20;
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const LEVEL_HEIGHT = 64;
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const MIN_NODE_SPACING = 48;
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const SVG_PADDING = 40;
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interface NodePosition {
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node: TrieNodeState;
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x: number;
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y: number;
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parentX?: number;
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parentY?: number;
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}
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function buildNodeMap(nodes: TrieNodeState[]): Map<string, TrieNodeState> {
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const map = new Map<string, TrieNodeState>();
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for (const node of nodes) {
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map.set(node.id, node);
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}
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return map;
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}
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/**
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* Calculate the width needed for a subtree rooted at the given node.
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* Leaf nodes need MIN_NODE_SPACING, internal nodes need sum of children widths.
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*/
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function calculateSubtreeWidth(
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nodeId: string,
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nodeMap: Map<string, TrieNodeState>
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): number {
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const node = nodeMap.get(nodeId);
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if (!node) return MIN_NODE_SPACING;
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if (node.children.length === 0) {
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return MIN_NODE_SPACING;
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}
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let totalWidth = 0;
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for (const childId of node.children) {
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totalWidth += calculateSubtreeWidth(childId, nodeMap);
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}
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return Math.max(totalWidth, MIN_NODE_SPACING);
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}
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/**
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* Calculate the maximum depth of the trie.
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*/
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function calculateTrieDepth(
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nodeId: string,
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nodeMap: Map<string, TrieNodeState>
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): number {
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const node = nodeMap.get(nodeId);
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if (!node) return 0;
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if (node.children.length === 0) {
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return 1;
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}
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let maxChildDepth = 0;
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for (const childId of node.children) {
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const childDepth = calculateTrieDepth(childId, nodeMap);
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maxChildDepth = Math.max(maxChildDepth, childDepth);
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}
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return 1 + maxChildDepth;
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}
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/**
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* Calculate positions for all nodes using N-ary tree layout.
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* Each node is centered above its children.
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*/
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function calculatePositions(
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trie: TrieState,
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totalWidth: number
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): NodePosition[] {
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const nodeMap = buildNodeMap(trie.nodes);
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const positions: NodePosition[] = [];
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// Pre-calculate subtree widths for all nodes
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const subtreeWidths = new Map<string, number>();
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for (const node of trie.nodes) {
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subtreeWidths.set(node.id, calculateSubtreeWidth(node.id, nodeMap));
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}
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function traverse(
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nodeId: string,
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level: number,
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left: number,
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right: number,
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parentX?: number,
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parentY?: number
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) {
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const node = nodeMap.get(nodeId);
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if (!node) return;
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const x = (left + right) / 2;
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const y = SVG_PADDING + level * LEVEL_HEIGHT + NODE_RADIUS;
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positions.push({ node, x, y, parentX, parentY });
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if (node.children.length > 0) {
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// Calculate total children width
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const childrenWidth = node.children.reduce(
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(sum, childId) => sum + (subtreeWidths.get(childId) ?? MIN_NODE_SPACING),
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0
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);
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// Start position for first child
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let childLeft = x - childrenWidth / 2;
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for (const childId of node.children) {
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const childWidth = subtreeWidths.get(childId) ?? MIN_NODE_SPACING;
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traverse(
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childId,
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level + 1,
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childLeft,
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childLeft + childWidth,
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x,
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y
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);
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childLeft += childWidth;
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}
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}
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}
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traverse(trie.rootId, 0, 0, totalWidth);
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return positions;
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}
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export function TrieView({ trie, className }: TrieViewProps) {
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const { positions, svgWidth, svgHeight } = useMemo(() => {
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const nodeMap = buildNodeMap(trie.nodes);
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const depth = calculateTrieDepth(trie.rootId, nodeMap);
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const rootWidth = calculateSubtreeWidth(trie.rootId, nodeMap);
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const width = Math.max(rootWidth + SVG_PADDING * 2, 200);
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const height = depth * LEVEL_HEIGHT + SVG_PADDING * 2;
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const pos = calculatePositions(trie, width);
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return { positions: pos, svgWidth: width, svgHeight: height };
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}, [trie]);
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// Build a set of highlighted path nodes for edge styling
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const pathNodeIds = new Set(trie.currentPath ?? []);
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return (
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<div className={cn('flex flex-col items-center', className)}>
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{trie.label && (
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<span className="mb-2 text-sm font-medium text-[var(--muted-foreground)]">
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{trie.label}
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</span>
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)}
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<svg
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width={svgWidth}
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height={svgHeight}
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viewBox={`0 0 ${svgWidth} ${svgHeight}`}
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className="overflow-visible"
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>
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{/* Draw edges first (behind nodes) */}
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{positions.map(({ node, x, y, parentX, parentY }) => {
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if (parentX === undefined || parentY === undefined) return null;
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// Determine if this edge is on the current path
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const isOnPath = pathNodeIds.has(node.id);
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// Calculate midpoint for character label
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const midX = (parentX + x) / 2;
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const midY = (parentY + NODE_RADIUS + y - NODE_RADIUS) / 2;
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return (
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<g key={`edge-${node.id}`}>
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<motion.line
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x1={parentX}
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y1={parentY + NODE_RADIUS}
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x2={x}
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y2={y - NODE_RADIUS}
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className={cn(
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'stroke-[var(--border)]',
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isOnPath && 'stroke-[var(--primary)]'
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)}
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strokeWidth={isOnPath ? 2.5 : 2}
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initial={false}
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animate={{
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opacity: node.state === 'notfound' ? 0.3 : 1,
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}}
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transition={{ duration: 0.2 }}
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/>
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{/* Edge character label */}
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<motion.text
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x={midX}
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y={midY}
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textAnchor="middle"
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dominantBaseline="central"
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className={cn(
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'pointer-events-none select-none font-mono text-xs font-medium',
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isOnPath ? 'fill-[var(--primary)]' : 'fill-[var(--muted-foreground)]'
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)}
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initial={false}
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animate={{
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opacity: node.state === 'notfound' ? 0.3 : 1,
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}}
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transition={{ duration: 0.2 }}
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>
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{node.char}
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</motion.text>
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</g>
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);
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})}
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{/* Draw nodes */}
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{positions.map(({ node, x, y }) => (
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<TrieNode
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key={node.id}
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node={node}
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x={x}
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y={y}
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radius={NODE_RADIUS}
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/>
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))}
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{/* Current operation indicator */}
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{trie.searchWord && (
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<g>
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<text
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x={svgWidth / 2}
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y={svgHeight - 10}
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textAnchor="middle"
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className="fill-[var(--muted-foreground)] text-xs"
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>
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{trie.searchIndex !== undefined
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? `"${trie.searchWord}" [${trie.searchIndex}/${trie.searchWord.length}]`
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: `"${trie.searchWord}"`}
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</text>
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</g>
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)}
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</svg>
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</div>
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);
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}
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@@ -0,0 +1,107 @@
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'use client';
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import { motion } from 'framer-motion';
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import { cn } from '@/lib/utils';
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import type { TrieNodeState } from '@/lib/visualizations/types';
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interface TrieNodeProps {
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node: TrieNodeState;
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x: number;
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y: number;
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radius?: number;
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className?: string;
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}
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const STATE_CLASSES = {
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normal: 'fill-[var(--surface-variant)] stroke-[var(--border)]',
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current: 'fill-[var(--primary)]/20 stroke-[var(--primary)]',
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found: 'fill-[var(--success)]/20 stroke-[var(--success)]',
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notfound: 'fill-[var(--error)]/20 stroke-[var(--error)]',
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highlighted: 'fill-[var(--primary)]/30 stroke-[var(--primary)]',
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creating: 'fill-[var(--info)]/20 stroke-[var(--info)]',
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} as const;
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const TEXT_CLASSES = {
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normal: 'fill-[var(--foreground)]',
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current: 'fill-[var(--primary)]',
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found: 'fill-[var(--success)]',
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notfound: 'fill-[var(--error)]',
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highlighted: 'fill-[var(--primary)]',
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creating: 'fill-[var(--info)]',
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} as const;
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export function TrieNode({
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node,
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x,
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y,
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radius = 20,
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className,
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}: TrieNodeProps) {
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const isActive = node.state === 'current' || node.state === 'highlighted' || node.state === 'creating';
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const isRoot = node.char === '';
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return (
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<motion.g
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initial={false}
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animate={{
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scale: isActive ? 1.1 : 1,
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}}
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transition={{
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type: 'spring',
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stiffness: 300,
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damping: 30,
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}}
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style={{ transformOrigin: `${x}px ${y}px` }}
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className={cn(className)}
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>
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{/* Main circle */}
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<motion.circle
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cx={x}
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cy={y}
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r={radius}
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strokeWidth={2}
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className={cn(
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'transition-colors duration-200',
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STATE_CLASSES[node.state]
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)}
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initial={false}
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animate={{
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filter: isActive ? 'drop-shadow(0 0 8px var(--primary))' : 'none',
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}}
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transition={{ duration: 0.2 }}
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/>
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{/* End-of-word indicator: inner circle */}
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{node.isEndOfWord && (
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<motion.circle
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cx={x}
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cy={y}
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r={radius - 5}
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strokeWidth={2}
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fill="none"
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className={cn(
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'transition-colors duration-200',
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STATE_CLASSES[node.state]
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)}
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initial={{ opacity: 0, scale: 0.8 }}
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animate={{ opacity: 1, scale: 1 }}
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transition={{ duration: 0.2 }}
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/>
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)}
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{/* Character label */}
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<text
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x={x}
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y={y}
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textAnchor="middle"
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dominantBaseline="central"
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className={cn(
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'pointer-events-none select-none font-mono text-sm font-medium',
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TEXT_CLASSES[node.state]
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)}
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>
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{isRoot ? '\u2205' : node.char}
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</text>
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</motion.g>
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);
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}
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701
frontend/src/content/algorithms/implement-trie.ts
Normal file
701
frontend/src/content/algorithms/implement-trie.ts
Normal file
@@ -0,0 +1,701 @@
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import type { AlgorithmDefinition, TrieNodeState, TrieState } from '@/lib/visualizations/types';
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/**
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* Implement Trie (Prefix Tree) - LeetCode 208
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*
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* Trie structure after inserting "app" and "apple":
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*
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* (root)
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* |
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* a
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* |
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* p
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* |
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* p* (* = end of word)
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* |
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* l
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* |
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* e*
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*/
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// Node IDs
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const ROOT = 'root';
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const NODE_A = 'a';
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const NODE_P1 = 'p1';
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const NODE_P2 = 'p2';
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const NODE_L = 'l';
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const NODE_E = 'e';
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type NodeState = 'normal' | 'current' | 'found' | 'notfound' | 'highlighted' | 'creating';
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// Helper to create a single trie node
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function createNode(
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id: string,
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char: string,
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state: NodeState,
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isEndOfWord: boolean,
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children: string[]
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): TrieNodeState {
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return { id, char, state, isEndOfWord, children };
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}
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// Helper to create trie state with given nodes
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function createTrieState(
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nodes: TrieNodeState[],
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currentPath?: string[],
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searchWord?: string,
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searchIndex?: number
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): TrieState {
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return {
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id: 'trie',
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nodes,
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rootId: ROOT,
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label: 'Trie',
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currentPath,
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searchWord,
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searchIndex,
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};
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}
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// Empty trie (just root)
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function emptyTrie(rootState: NodeState = 'normal'): TrieNodeState[] {
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return [createNode(ROOT, '', rootState, false, [])];
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}
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// Trie with just 'a' node
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function trieWithA(
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states: Partial<Record<string, NodeState>> = {},
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endOfWords: Partial<Record<string, boolean>> = {}
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): TrieNodeState[] {
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return [
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createNode(ROOT, '', states[ROOT] ?? 'normal', false, [NODE_A]),
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createNode(NODE_A, 'a', states[NODE_A] ?? 'normal', endOfWords[NODE_A] ?? false, []),
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];
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}
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// Trie with 'a' -> 'p'
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function trieWithAP(
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states: Partial<Record<string, NodeState>> = {},
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endOfWords: Partial<Record<string, boolean>> = {}
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): TrieNodeState[] {
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return [
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createNode(ROOT, '', states[ROOT] ?? 'normal', false, [NODE_A]),
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createNode(NODE_A, 'a', states[NODE_A] ?? 'normal', endOfWords[NODE_A] ?? false, [NODE_P1]),
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createNode(NODE_P1, 'p', states[NODE_P1] ?? 'normal', endOfWords[NODE_P1] ?? false, []),
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];
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}
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// Trie with 'a' -> 'p' -> 'p' (for "app")
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function trieWithApp(
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states: Partial<Record<string, NodeState>> = {},
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endOfWords: Partial<Record<string, boolean>> = {}
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): TrieNodeState[] {
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return [
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createNode(ROOT, '', states[ROOT] ?? 'normal', false, [NODE_A]),
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createNode(NODE_A, 'a', states[NODE_A] ?? 'normal', endOfWords[NODE_A] ?? false, [NODE_P1]),
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createNode(NODE_P1, 'p', states[NODE_P1] ?? 'normal', endOfWords[NODE_P1] ?? false, [NODE_P2]),
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createNode(NODE_P2, 'p', states[NODE_P2] ?? 'normal', endOfWords[NODE_P2] ?? true, []),
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];
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}
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// Trie with 'a' -> 'p' -> 'p' -> 'l' -> 'e' (for "app" and "apple")
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function trieWithAppApple(
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states: Partial<Record<string, NodeState>> = {},
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endOfWords: Partial<Record<string, boolean>> = {}
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): TrieNodeState[] {
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return [
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createNode(ROOT, '', states[ROOT] ?? 'normal', false, [NODE_A]),
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createNode(NODE_A, 'a', states[NODE_A] ?? 'normal', endOfWords[NODE_A] ?? false, [NODE_P1]),
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createNode(NODE_P1, 'p', states[NODE_P1] ?? 'normal', endOfWords[NODE_P1] ?? false, [NODE_P2]),
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createNode(NODE_P2, 'p', states[NODE_P2] ?? 'normal', endOfWords[NODE_P2] ?? true, [NODE_L]),
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createNode(NODE_L, 'l', states[NODE_L] ?? 'normal', endOfWords[NODE_L] ?? false, [NODE_E]),
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createNode(NODE_E, 'e', states[NODE_E] ?? 'normal', endOfWords[NODE_E] ?? true, []),
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];
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}
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export const implementTrieAlgorithm: AlgorithmDefinition = {
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id: 'implement-trie',
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title: 'Implement Trie (Prefix Tree)',
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slug: 'implement-trie',
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pattern: {
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name: 'Trie',
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description:
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'A tree-like data structure for efficient prefix-based operations on strings, where each node represents a character and paths from root represent words or prefixes.',
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},
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problemStatement:
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'Implement a trie with insert, search, and startsWith methods. insert(word) inserts a word into the trie. search(word) returns true if the word exists. startsWith(prefix) returns true if any word starts with the given prefix.',
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intuition:
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'Think of a trie like a filing cabinet where each drawer is labeled with a letter. To find a word, you open drawers one letter at a time. Words sharing the same prefix share the same path through the drawers, making prefix operations very efficient.',
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code: {
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language: 'python',
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code: `class TrieNode:
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def __init__(self):
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self.children = {} # char -> TrieNode
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self.is_end = False
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class Trie:
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def __init__(self):
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self.root = TrieNode()
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def insert(self, word: str) -> None:
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node = self.root
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for char in word:
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if char not in node.children:
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node.children[char] = TrieNode()
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node = node.children[char]
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node.is_end = True
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def search(self, word: str) -> bool:
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node = self._traverse(word)
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return node is not None and node.is_end
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def startsWith(self, prefix: str) -> bool:
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return self._traverse(prefix) is not None
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def _traverse(self, s: str) -> TrieNode:
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node = self.root
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for char in s:
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if char not in node.children:
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return None
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node = node.children[char]
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return node`,
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},
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initialExample: {
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input: { operations: ['insert("app")', 'insert("apple")', 'search("app")', 'search("apple")', 'startsWith("ap")'] },
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expected: [null, null, true, true, true],
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},
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steps: [
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// ==========================================
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// Phase 1: Problem (2 steps)
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// ==========================================
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{
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id: 'problem-1',
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phase: 'problem',
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explanation:
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'We need to implement a Trie (prefix tree) that supports three operations: insert(word), search(word), and startsWith(prefix). Each operation should run in O(m) time where m is the length of the input string.',
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dataState: {
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arrays: [],
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pointers: [],
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variables: [],
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calculations: [],
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tries: [createTrieState(emptyTrie())],
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},
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},
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{
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id: 'problem-2',
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phase: 'problem',
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explanation:
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'We\'ll demonstrate with: insert("app"), insert("apple"), search("app"), search("apple"), and startsWith("ap"). Notice how "app" and "apple" share the prefix "app".',
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dataState: {
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arrays: [],
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pointers: [],
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variables: [
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{ id: 'ops', name: 'operations', value: '["app", "apple", ...]' },
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],
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calculations: [],
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tries: [createTrieState(emptyTrie('highlighted'))],
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},
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},
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// ==========================================
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// Phase 2: Intuition (3 steps)
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// ==========================================
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{
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id: 'intuition-1',
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phase: 'intuition',
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explanation:
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'Imagine a filing cabinet where each drawer is labeled with a single letter. To store the word "app", you open drawer "a", then find drawer "p" inside it, then drawer "p" inside that. The final drawer is marked as "end of word".',
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dataState: {
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arrays: [],
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pointers: [],
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variables: [],
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calculations: [],
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tries: [createTrieState(emptyTrie())],
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},
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},
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{
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id: 'intuition-2',
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phase: 'intuition',
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explanation:
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'When adding "apple" after "app", we reuse the existing path a→p→p and only create new drawers for "l" and "e". This sharing of prefixes is what makes tries efficient for dictionary operations.',
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dataState: {
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arrays: [],
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pointers: [],
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variables: [
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{ id: 'insight', name: 'Key Insight', value: 'Shared prefixes = shared nodes' },
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],
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calculations: [],
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tries: [createTrieState(emptyTrie())],
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},
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},
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{
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id: 'intuition-3',
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phase: 'intuition',
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explanation:
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'To search, we follow the path character by character. If we reach the end and the final node is marked "end of word", the word exists. For startsWith, we just need to confirm the path exists—no end-of-word check needed.',
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dataState: {
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arrays: [],
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pointers: [],
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variables: [],
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calculations: [],
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tries: [createTrieState(emptyTrie())],
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},
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},
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// ==========================================
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// Phase 3: Pattern (2 steps)
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// ==========================================
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{
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id: 'pattern-1',
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phase: 'pattern',
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explanation:
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'Each TrieNode has two properties: a dictionary mapping characters to child nodes, and a boolean is_end flag. The root node is always empty and serves as the starting point.',
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codeLine: 1,
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codeHighlightLines: [1, 2, 3, 4],
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dataState: {
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arrays: [],
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pointers: [],
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variables: [
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{ id: 'struct', name: 'TrieNode', value: '{children: {}, is_end: bool}' },
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],
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calculations: [],
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tries: [createTrieState(emptyTrie('highlighted'))],
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},
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},
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{
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id: 'pattern-2',
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phase: 'pattern',
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explanation:
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'All three operations share the same traversal pattern: start at root, follow character edges one by one. Insert creates missing nodes; search/startsWith just follow existing edges.',
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codeLine: 11,
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codeHighlightLines: [11, 12, 13, 14, 15, 16],
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dataState: {
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arrays: [],
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pointers: [],
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variables: [
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{ id: 'complexity', name: 'Time', value: 'O(m) per operation' },
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],
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calculations: [],
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tries: [createTrieState(emptyTrie())],
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},
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},
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// ==========================================
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// Phase 4: Code (3 steps)
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// ==========================================
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{
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id: 'code-1',
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phase: 'code',
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explanation:
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'Initialize the Trie with an empty root node. This root doesn\'t represent any character—it\'s just the starting point for all operations.',
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codeLine: 8,
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codeHighlightLines: [6, 7, 8],
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dataState: {
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arrays: [],
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pointers: [],
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variables: [
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{ id: 'root', name: 'root', value: 'TrieNode()' },
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],
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calculations: [],
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tries: [createTrieState(emptyTrie('current'))],
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},
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},
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{
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id: 'code-2',
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phase: 'code',
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explanation:
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'insert(word): Traverse from root, creating new nodes for characters that don\'t exist. After processing all characters, mark the final node as end-of-word.',
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codeLine: 11,
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codeHighlightLines: [10, 11, 12, 13, 14, 15, 16],
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dataState: {
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||||||
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arrays: [],
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pointers: [],
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||||||
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variables: [],
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||||||
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calculations: [],
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||||||
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tries: [createTrieState(emptyTrie())],
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},
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},
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{
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id: 'code-3',
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phase: 'code',
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explanation:
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'search and startsWith both use _traverse to follow the path. search additionally checks is_end; startsWith only checks if the path exists.',
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codeLine: 18,
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||||||
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codeHighlightLines: [18, 19, 20, 22, 23],
|
||||||
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dataState: {
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||||||
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arrays: [],
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||||||
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pointers: [],
|
||||||
|
variables: [],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(emptyTrie())],
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||||||
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},
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||||||
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},
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||||||
|
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||||||
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// ==========================================
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// Phase 5: Execution - insert("app") (4 steps)
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// ==========================================
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{
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||||||
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id: 'exec-insert-app-1',
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||||||
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phase: 'execution',
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||||||
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explanation:
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'insert("app"): Start at root. Character \'a\' not in children, so create new node for \'a\'.',
|
||||||
|
codeLine: 13,
|
||||||
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dataState: {
|
||||||
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arrays: [],
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||||||
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pointers: [],
|
||||||
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variables: [
|
||||||
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{ id: 'word', name: 'word', value: '"app"' },
|
||||||
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{ id: 'char', name: 'char', value: '"a"' },
|
||||||
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{ id: 'node', name: 'node', value: 'root' },
|
||||||
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],
|
||||||
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calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithA({ [ROOT]: 'current', [NODE_A]: 'creating' }),
|
||||||
|
[ROOT],
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'app',
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||||||
|
0
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)],
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||||||
|
},
|
||||||
|
},
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||||||
|
{
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||||||
|
id: 'exec-insert-app-2',
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||||||
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phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'Move to node \'a\'. Character \'p\' not in children, create new node for first \'p\'.',
|
||||||
|
codeLine: 13,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"app"' },
|
||||||
|
{ id: 'char', name: 'char', value: '"p"' },
|
||||||
|
{ id: 'node', name: 'node', value: 'node_a' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAP({ [NODE_A]: 'current', [NODE_P1]: 'creating' }),
|
||||||
|
[ROOT, NODE_A],
|
||||||
|
'app',
|
||||||
|
1
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-insert-app-3',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'Move to first \'p\' node. Character \'p\' not in children, create new node for second \'p\'.',
|
||||||
|
codeLine: 13,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"app"' },
|
||||||
|
{ id: 'char', name: 'char', value: '"p"' },
|
||||||
|
{ id: 'node', name: 'node', value: 'node_p1' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithApp({ [NODE_P1]: 'current', [NODE_P2]: 'creating' }, { [NODE_P2]: false }),
|
||||||
|
[ROOT, NODE_A, NODE_P1],
|
||||||
|
'app',
|
||||||
|
2
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-insert-app-4',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'All characters processed. Mark second \'p\' as end-of-word. "app" is now in the trie!',
|
||||||
|
codeLine: 16,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"app"' },
|
||||||
|
{ id: 'result', name: 'is_end', value: 'true' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithApp({ [NODE_P2]: 'found' }, { [NODE_P2]: true }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2],
|
||||||
|
'app',
|
||||||
|
3
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
|
||||||
|
// ==========================================
|
||||||
|
// Phase 5: Execution - insert("apple") (3 steps)
|
||||||
|
// ==========================================
|
||||||
|
{
|
||||||
|
id: 'exec-insert-apple-1',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'insert("apple"): Start at root. Traverse existing path a→p→p (nodes already exist from "app").',
|
||||||
|
codeLine: 15,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"apple"' },
|
||||||
|
{ id: 'node', name: 'node', value: 'node_p2' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithApp({ [ROOT]: 'highlighted', [NODE_A]: 'highlighted', [NODE_P1]: 'highlighted', [NODE_P2]: 'current' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2],
|
||||||
|
'apple',
|
||||||
|
2
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-insert-apple-2',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'At second \'p\'. Character \'l\' not in children, create node for \'l\'. Then \'e\' not in children, create node for \'e\'.',
|
||||||
|
codeLine: 13,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"apple"' },
|
||||||
|
{ id: 'char', name: 'char', value: '"l", "e"' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_P2]: 'highlighted', [NODE_L]: 'creating', [NODE_E]: 'creating' }, { [NODE_E]: false }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2],
|
||||||
|
'apple',
|
||||||
|
4
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-insert-apple-3',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'All characters processed. Mark \'e\' as end-of-word. "apple" is now in the trie! Notice "app" and "apple" share nodes a→p→p.',
|
||||||
|
codeLine: 16,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"apple"' },
|
||||||
|
{ id: 'result', name: 'is_end', value: 'true' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_E]: 'found' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2, NODE_L, NODE_E],
|
||||||
|
'apple',
|
||||||
|
5
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
|
||||||
|
// ==========================================
|
||||||
|
// Phase 5: Execution - search("app") (3 steps)
|
||||||
|
// ==========================================
|
||||||
|
{
|
||||||
|
id: 'exec-search-app-1',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'search("app"): Traverse path a→p→p. All characters exist in the trie.',
|
||||||
|
codeLine: 26,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"app"' },
|
||||||
|
{ id: 'node', name: 'node', value: 'traversing...' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [ROOT]: 'highlighted', [NODE_A]: 'highlighted', [NODE_P1]: 'highlighted', [NODE_P2]: 'current' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2],
|
||||||
|
'app',
|
||||||
|
2
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-search-app-2',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'Reached end of word. Check is_end on second \'p\': it\'s True (we marked it when inserting "app").',
|
||||||
|
codeLine: 19,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"app"' },
|
||||||
|
{ id: 'is_end', name: 'is_end', value: 'true' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_P2]: 'current' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2],
|
||||||
|
'app',
|
||||||
|
3
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-search-app-3',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'search("app") returns True. The word exists in the trie.',
|
||||||
|
codeLine: 19,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'result', name: 'return', value: 'True' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_P2]: 'found' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2],
|
||||||
|
'app'
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
|
||||||
|
// ==========================================
|
||||||
|
// Phase 5: Execution - search("apple") (3 steps)
|
||||||
|
// ==========================================
|
||||||
|
{
|
||||||
|
id: 'exec-search-apple-1',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'search("apple"): Traverse path a→p→p→l→e. All characters exist.',
|
||||||
|
codeLine: 26,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"apple"' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [ROOT]: 'highlighted', [NODE_A]: 'highlighted', [NODE_P1]: 'highlighted', [NODE_P2]: 'highlighted', [NODE_L]: 'highlighted', [NODE_E]: 'current' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2, NODE_L, NODE_E],
|
||||||
|
'apple',
|
||||||
|
4
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-search-apple-2',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'Check is_end on \'e\': it\'s True (we marked it when inserting "apple").',
|
||||||
|
codeLine: 19,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'word', name: 'word', value: '"apple"' },
|
||||||
|
{ id: 'is_end', name: 'is_end', value: 'true' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_E]: 'current' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2, NODE_L, NODE_E],
|
||||||
|
'apple',
|
||||||
|
5
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-search-apple-3',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'search("apple") returns True. The word exists in the trie.',
|
||||||
|
codeLine: 19,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'result', name: 'return', value: 'True' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_E]: 'found' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1, NODE_P2, NODE_L, NODE_E],
|
||||||
|
'apple'
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
|
||||||
|
// ==========================================
|
||||||
|
// Phase 5: Execution - startsWith("ap") (2 steps)
|
||||||
|
// ==========================================
|
||||||
|
{
|
||||||
|
id: 'exec-starts-ap-1',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'startsWith("ap"): Traverse path a→p. Both nodes exist.',
|
||||||
|
codeLine: 26,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'prefix', name: 'prefix', value: '"ap"' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [ROOT]: 'highlighted', [NODE_A]: 'highlighted', [NODE_P1]: 'current' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1],
|
||||||
|
'ap',
|
||||||
|
1
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
{
|
||||||
|
id: 'exec-starts-ap-2',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'startsWith("ap") returns True. We found the prefix—no need to check is_end. Both "app" and "apple" start with "ap".',
|
||||||
|
codeLine: 23,
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'prefix', name: 'prefix', value: '"ap"' },
|
||||||
|
{ id: 'result', name: 'return', value: 'True' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(
|
||||||
|
trieWithAppApple({ [NODE_P1]: 'found' }),
|
||||||
|
[ROOT, NODE_A, NODE_P1],
|
||||||
|
'ap'
|
||||||
|
)],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
|
||||||
|
// ==========================================
|
||||||
|
// Final Summary
|
||||||
|
// ==========================================
|
||||||
|
{
|
||||||
|
id: 'exec-done',
|
||||||
|
phase: 'execution',
|
||||||
|
explanation:
|
||||||
|
'Complete! The trie stores "app" and "apple" efficiently by sharing the prefix a→p→p. All operations run in O(m) time where m is the string length.',
|
||||||
|
dataState: {
|
||||||
|
arrays: [],
|
||||||
|
pointers: [],
|
||||||
|
variables: [
|
||||||
|
{ id: 'words', name: 'stored', value: '["app", "apple"]' },
|
||||||
|
{ id: 'time', name: 'complexity', value: 'O(m) per operation' },
|
||||||
|
{ id: 'space', name: 'space', value: 'O(total chars)' },
|
||||||
|
],
|
||||||
|
calculations: [],
|
||||||
|
tries: [createTrieState(trieWithAppApple())],
|
||||||
|
},
|
||||||
|
},
|
||||||
|
],
|
||||||
|
};
|
||||||
Reference in New Issue
Block a user