medium array/string questions

backend/data/questions/container-with-most-water.yaml

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+title: Container With Most Water
+slug: container-with-most-water
+difficulty: medium
+leetcode_id: 11
+leetcode_url: https://leetcode.com/problems/container-with-most-water/
+categories:
+  - arrays
+  - two-pointers
+patterns:
+  - two-pointers
+  - greedy
+
+description: |
+  You are given an integer array `height` of length n. There are n vertical lines drawn such
+  that the two endpoints of the ith line are (i, 0) and (i, height[i]).
+
+  Find two lines that together with the x-axis form a container, such that the container
+  contains the most water.
+
+  Return the maximum amount of water a container can store.
+
+constraints: |
+  - n == height.length
+  - 2 <= n <= 10^5
+  - 0 <= height[i] <= 10^4
+
+examples:
+  - input: "height = [1,8,6,2,5,4,8,3,7]"
+    output: "49"
+    explanation: "Lines at index 1 (height 8) and 8 (height 7) form container with area 7 * 7 = 49."
+  - input: "height = [1,1]"
+    output: "1"
+    explanation: "Only container possible has area 1 * 1 = 1."
+
+explanation:
+  approach: |
+    1. Start with two pointers at the far left and far right
+    2. Calculate the area formed by the two lines
+    3. Move the pointer pointing to the shorter line inward
+    4. Track maximum area seen
+    5. Continue until pointers meet
+
+  intuition: |
+    Area = width × height. The height is limited by the shorter line.
+
+    Starting with maximum width (endpoints), we can only improve by finding taller lines.
+    If we move the taller pointer, width decreases and height can't increase beyond the
+    shorter line — so area can only decrease or stay the same.
+
+    Moving the shorter pointer gives us a chance to find a taller line that could
+    increase the height enough to compensate for the reduced width.
+
+  common_pitfalls:
+    - title: Moving the wrong pointer
+      description: |
+        Always move the pointer pointing to the shorter line. Moving the taller one
+        cannot possibly increase the area since height is constrained by the shorter.
+      wrong_approach: "Moving left pointer always or randomly"
+      correct_approach: "Move the pointer with smaller height[i]"
+
+    - title: Using nested loops
+      description: |
+        O(n²) brute force is unnecessary. Two pointers achieve O(n) by eliminating
+        suboptimal pairs without checking them.
+
+  key_takeaways:
+    - Two pointers from opposite ends is powerful for optimization
+    - Moving the limiting factor gives the best chance of improvement
+    - Greedy choice (move shorter) is provably optimal here
+    - Width × min(heights) is the key formula
+
+  time_complexity: "O(n)"
+  space_complexity: "O(1)"
+  complexity_explanation: |
+    Time: Each pointer moves at most n times total.
+    Space: Only a few variables for pointers and max area.
+
+solutions:
+  - approach_name: Two Pointers (Optimal)
+    is_optimal: true
+    code: |
+      def max_area(height: list[int]) -> int:
+          left, right = 0, len(height) - 1
+          max_water = 0
+
+          while left < right:
+              width = right - left
+              h = min(height[left], height[right])
+              max_water = max(max_water, width * h)
+
+              if height[left] < height[right]:
+                  left += 1
+              else:
+                  right -= 1
+
+          return max_water
+    explanation: |
+      Start from both ends and move the shorter line inward.
+      Track maximum area found during traversal.

backend/data/questions/longest-substring-without-repeating.yaml

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+title: Longest Substring Without Repeating Characters
+slug: longest-substring-without-repeating
+difficulty: medium
+leetcode_id: 3
+leetcode_url: https://leetcode.com/problems/longest-substring-without-repeating-characters/
+categories:
+  - strings
+  - hash-tables
+patterns:
+  - sliding-window
+
+description: |
+  Given a string `s`, find the length of the longest substring without repeating characters.
+
+constraints: |
+  - 0 <= s.length <= 5 * 10^4
+  - s consists of English letters, digits, symbols and spaces
+
+examples:
+  - input: 's = "abcabcbb"'
+    output: "3"
+    explanation: "The answer is 'abc', with length 3."
+  - input: 's = "bbbbb"'
+    output: "1"
+    explanation: "The answer is 'b', with length 1."
+  - input: 's = "pwwkew"'
+    output: "3"
+    explanation: "The answer is 'wke', with length 3."
+
+explanation:
+  approach: |
+    1. Use a sliding window with left and right pointers
+    2. Maintain a set of characters in the current window
+    3. Expand right pointer, adding characters to the set
+    4. When a duplicate is found, shrink from left until duplicate is removed
+    5. Track maximum window size throughout
+
+  intuition: |
+    We're looking for the longest contiguous substring where all characters are unique.
+    A sliding window naturally represents a substring.
+
+    When we encounter a duplicate, the current window is invalid. Instead of restarting
+    from scratch, we shrink the window from the left until the duplicate is removed.
+    This way, we never revisit characters unnecessarily.
+
+  common_pitfalls:
+    - title: Resetting the window incorrectly
+      description: |
+        When finding a duplicate, don't start over from the next character.
+        Instead, shrink from the left until the duplicate is removed.
+      wrong_approach: "left = right when duplicate found"
+      correct_approach: "Increment left until duplicate is out of window"
+
+    - title: Not handling empty string
+      description: |
+        An empty string should return 0. Make sure the algorithm handles this.
+
+    - title: Off-by-one in length calculation
+      description: |
+        Window length is right - left + 1, or just track max before removing.
+
+  key_takeaways:
+    - Sliding window is ideal for substring problems with constraints
+    - Use a set or map to track elements in current window
+    - Shrinking from one end maintains the contiguous property
+    - This pattern appears in many "longest/shortest with constraint" problems
+
+  time_complexity: "O(n)"
+  space_complexity: "O(min(m, n))"
+  complexity_explanation: |
+    Time: Each character is visited at most twice (once by right, once by left).
+    Space: The set holds at most min(n, m) characters where m is the charset size.
+
+solutions:
+  - approach_name: Sliding Window with Set (Optimal)
+    is_optimal: true
+    code: |
+      def length_of_longest_substring(s: str) -> int:
+          char_set = set()
+          left = 0
+          max_length = 0
+
+          for right in range(len(s)):
+              while s[right] in char_set:
+                  char_set.remove(s[left])
+                  left += 1
+
+              char_set.add(s[right])
+              max_length = max(max_length, right - left + 1)
+
+          return max_length
+    explanation: |
+      Expand window by moving right pointer.
+      When duplicate found, shrink from left until window is valid again.
+
+  - approach_name: Optimized with Hash Map
+    is_optimal: true
+    code: |
+      def length_of_longest_substring(s: str) -> int:
+          char_index = {}
+          left = 0
+          max_length = 0
+
+          for right, char in enumerate(s):
+              if char in char_index and char_index[char] >= left:
+                  left = char_index[char] + 1
+
+              char_index[char] = right
+              max_length = max(max_length, right - left + 1)
+
+          return max_length
+    explanation: |
+      Store the last index of each character.
+      Jump left pointer directly past the duplicate instead of shrinking one by one.

backend/data/questions/three-sum.yaml

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+title: 3Sum
+slug: three-sum
+difficulty: medium
+leetcode_id: 15
+leetcode_url: https://leetcode.com/problems/3sum/
+categories:
+  - arrays
+  - two-pointers
+  - sorting
+patterns:
+  - two-pointers
+
+description: |
+  Given an integer array `nums`, return all the triplets [nums[i], nums[j], nums[k]] such that
+  i != j, i != k, and j != k, and nums[i] + nums[j] + nums[k] == 0.
+
+  Notice that the solution set must not contain duplicate triplets.
+
+constraints: |
+  - 3 <= nums.length <= 3000
+  - -10^5 <= nums[i] <= 10^5
+
+examples:
+  - input: "nums = [-1,0,1,2,-1,-4]"
+    output: "[[-1,-1,2],[-1,0,1]]"
+    explanation: "The distinct triplets that sum to zero."
+  - input: "nums = [0,1,1]"
+    output: "[]"
+    explanation: "No triplet sums to zero."
+  - input: "nums = [0,0,0]"
+    output: "[[0,0,0]]"
+    explanation: "Only one triplet sums to zero."
+
+explanation:
+  approach: |
+    1. Sort the array
+    2. For each element nums[i], find pairs that sum to -nums[i]
+    3. Use two pointers (left, right) to find pairs in the remaining array
+    4. Skip duplicates at each level to avoid duplicate triplets
+
+  intuition: |
+    After sorting, for each fixed element nums[i], we need to find nums[j] + nums[k] = -nums[i].
+    This reduces to the Two Sum II problem on a sorted array, solvable with two pointers.
+
+    Sorting enables two things: efficient two-pointer search and easy duplicate skipping.
+    We skip duplicates by checking if current value equals previous value.
+
+  common_pitfalls:
+    - title: Not handling duplicates
+      description: |
+        Without duplicate skipping, you'll return duplicate triplets.
+        Skip at the outer loop and both pointers.
+      wrong_approach: "Not skipping when nums[i] == nums[i-1]"
+      correct_approach: "if i > 0 and nums[i] == nums[i-1]: continue"
+
+    - title: Wrong pointer skipping
+      description: |
+        After finding a valid triplet, skip duplicates for both left and right pointers
+        while maintaining left < right.
+
+    - title: Starting i too late
+      description: |
+        The outer loop should start at index 0. Also, skip if nums[i] > 0 since
+        sorted array means no valid triplet possible.
+
+  key_takeaways:
+    - Reduce N-sum to (N-1)-sum by fixing one element
+    - Sorting enables two-pointer approach and duplicate handling
+    - Duplicate skipping happens at multiple levels
+    - Time complexity is O(n²) — can't do better for returning all triplets
+
+  time_complexity: "O(n²)"
+  space_complexity: "O(log n) to O(n)"
+  complexity_explanation: |
+    Time: O(n log n) for sorting + O(n²) for the two-pointer search.
+    Space: Depends on sorting algorithm (log n for in-place, n for non-in-place).
+
+solutions:
+  - approach_name: Sort + Two Pointers (Optimal)
+    is_optimal: true
+    code: |
+      def three_sum(nums: list[int]) -> list[list[int]]:
+          nums.sort()
+          result = []
+
+          for i in range(len(nums) - 2):
+              # Skip duplicates for i
+              if i > 0 and nums[i] == nums[i - 1]:
+                  continue
+
+              # Early termination
+              if nums[i] > 0:
+                  break
+
+              left, right = i + 1, len(nums) - 1
+
+              while left < right:
+                  total = nums[i] + nums[left] + nums[right]
+
+                  if total < 0:
+                      left += 1
+                  elif total > 0:
+                      right -= 1
+                  else:
+                      result.append([nums[i], nums[left], nums[right]])
+
+                      # Skip duplicates for left and right
+                      while left < right and nums[left] == nums[left + 1]:
+                          left += 1
+                      while left < right and nums[right] == nums[right - 1]:
+                          right -= 1
+
+                      left += 1
+                      right -= 1
+
+          return result
+    explanation: |
+      Fix one element and use two pointers to find the other two.
+      Skip duplicates at all levels to avoid duplicate triplets.