Maximum Water Trapped Between Walls

mediumcodingAlgorithmsTwo PointersArrays~25 min

Asked at Google, Meta, Stripe

Overview

Given n non-negative integers representing wall heights where the width of each wall is 1, find two walls that together with the x-axis form a container that holds the most water.

Return the maximum amount of water the container can store.

Constraints

2 <= height.length <= 100,000
0 <= height[i] <= 10,000
Must run in O(n) time.
You may not slant the container.

Examples

maxArea([1, 8, 6, 2, 5, 4, 8, 3, 7]);
// => 49  (walls at index 1 and 8: min(8,7) * 7 = 49)

maxArea([1, 1]);
// => 1

maxArea([4, 3, 2, 1, 4]);
// => 16  (walls at index 0 and 4: min(4,4) * 4 = 16)

Solution

Reveal solution

function maxArea(height) {
  let left = 0, right = height.length - 1;
  let max = 0;

  while (left < right) {
    const area = Math.min(height[left], height[right]) * (right - left);
    max = Math.max(max, area);

    if (height[left] < height[right]) left++;
    else right--;
  }

  return max;
}

Two pointers start at opposite ends. The area is limited by the shorter wall, so move the shorter pointer inward. O(n) time, O(1) space.

Resources

max-water-trapped.js

Maximum Water Trapped Between Walls

mediumcodingAlgorithmsTwo Pointers

Overview

Given n non-negative integers representing wall heights where the width of each wall is 1, find two walls that together with the x-axis form a container that holds the most water.

Return the maximum amount of water the container can store.

Constraints

2 <= height.length <= 100,000
0 <= height[i] <= 10,000
Must run in O(n) time.
You may not slant the container.

Examples

maxArea([1, 8, 6, 2, 5, 4, 8, 3, 7]);
// => 49  (walls at index 1 and 8: min(8,7) * 7 = 49)

maxArea([1, 1]);
// => 1

maxArea([4, 3, 2, 1, 4]);
// => 16  (walls at index 0 and 4: min(4,4) * 4 = 16)

Solution

Reveal solution

function maxArea(height) {
  let left = 0, right = height.length - 1;
  let max = 0;

  while (left < right) {
    const area = Math.min(height[left], height[right]) * (right - left);
    max = Math.max(max, area);

    if (height[left] < height[right]) left++;
    else right--;
  }

  return max;
}

Two pointers start at opposite ends. The area is limited by the shorter wall, so move the shorter pointer inward. O(n) time, O(1) space.

Resources

NameTopicDifficulty

Add BinaryAlgorithmseasy Balanced Binary TreeAlgorithmseasy Balanced BracketsAlgorithmseasy Binary SearchAlgorithmseasy Binary Search Tree Lowest Common AncestorAlgorithmseasy Binary Tree Maximum DepthAlgorithmseasy Binary Tree SubtreeAlgorithmseasy Bit CountingAlgorithmseasy Bit ReversalAlgorithmseasy Count Set Bits in a Binary NumberAlgorithmseasy Diameter of Binary TreeAlgorithmseasy Find Duplicates in ArrayAlgorithmseasy First Bad VersionAlgorithmseasy Flip Binary TreeAlgorithmseasy Flood FillAlgorithmseasy Linked List Detect CycleAlgorithmseasy Linked List ReversalAlgorithmseasy Linked Lists Combine Two SortedAlgorithmseasy Longest PalindromeAlgorithmseasy Middle of the Linked ListAlgorithmseasy Most Common ElementsAlgorithmseasy Optimal Stock TradingAlgorithmseasy Pair SumAlgorithmseasy Ransom NoteAlgorithmseasy Staircase Climbing CombinationsAlgorithmseasy String AnagramAlgorithmseasy String PalindromeAlgorithmseasy 01 MatrixAlgorithmsmedium Accounts MergeAlgorithmsmedium Array Product Excluding CurrentAlgorithmsmedium Binary Search Tree Kth Smallest ElementAlgorithmsmedium Binary Tree Level Order TraversalAlgorithmsmedium Binary Tree Rebuilding from Preorder and Inorder TraversalsAlgorithmsmedium Binary Tree Right Side ViewAlgorithmsmedium Combinations for Target SumAlgorithmsmedium Count Islands in a GridAlgorithmsmedium Course DependencyAlgorithmsmedium Decode MessageAlgorithmsmedium Disjoint IntervalsAlgorithmsmedium Distinct Paths in GridAlgorithmsmedium Evaluate Reverse Polish NotationAlgorithmsmedium Find All Anagrams in a StringAlgorithmsmedium Find Element in Rotated ArrayAlgorithmsmedium Find the Longest Palindromic SubstringAlgorithmsmedium Find Word in GridAlgorithmsmedium Graph CloneAlgorithmsmedium Graph Count Connected ComponentsAlgorithmsmedium Is the Graph a TreeAlgorithmsmedium K Closest Points to OriginAlgorithmsmedium Letter Combinations of a Phone NumberAlgorithmsmedium Longest Increasing SubsequenceAlgorithmsmedium Longest Non-repeating SubstringAlgorithmsmedium Longest Repeating Substring After ReplacementsAlgorithmsmedium Lowest Common Ancestor of a Binary TreeAlgorithmsmedium Matrix RotationAlgorithmsmedium Matrix Spiral TraversalAlgorithmsmedium Matrix ZeroingAlgorithmsmedium Maximum Sum in Contiguous ArrayAlgorithmsmedium Maximum Water Trapped Between WallsAlgorithmsmedium Merge New IntervalAlgorithmsmedium Merge Overlapping IntervalsAlgorithmsmedium Minimum Coins for ChangeAlgorithmsmedium Minimum Height TreesAlgorithmsmedium Palindromic SubstringsAlgorithmsmedium Partition Equal Subset SumAlgorithmsmedium PermutationsAlgorithmsmedium Rotting OrangesAlgorithmsmedium Segment WordsAlgorithmsmedium Sort ColorsAlgorithmsmedium String Anagram GroupsAlgorithmsmedium String to Integer (atoi)Algorithmsmedium SubsetsAlgorithmsmedium Sum Without AdditionAlgorithmsmedium Task CoordinationAlgorithmsmedium Trie (Prefix Tree)Algorithmsmedium Triplet SumAlgorithmsmedium Validate Binary Search TreeAlgorithmsmedium Basic CalculatorAlgorithmshard Binary Tree EqualAlgorithmshard Binary Tree Maximum Total PathAlgorithmshard Delete Nth Node from End of Linked ListAlgorithmshard End of Array ReachableAlgorithmshard Extraterrestrial LanguageAlgorithmshard Find Missing Number in SequenceAlgorithmshard Find Words in GridAlgorithmshard Largest Rectangle in HistogramAlgorithmshard Linked Lists Combine K SortedAlgorithmshard Longest Common SubsequenceAlgorithmshard Longest Consecutive Number SequenceAlgorithmshard Maximum Product in Contiguous ArrayAlgorithmshard Maximum Profit in Job SchedulingAlgorithmshard Meeting CalendarAlgorithmshard Minimum Meeting Rooms NeededAlgorithmshard Neighborhood TheftAlgorithmshard Neighborhood Theft (Circular)Algorithmshard Number Stream MedianAlgorithmshard Ocean FlowAlgorithmshard Rearrange Linked ListAlgorithmshard Shortest Substring Containing CharactersAlgorithmshard Smallest Element in Rotated Sorted ArrayAlgorithmshard Trapping Rain WaterAlgorithmshard Word FinderAlgorithmshard Word LadderAlgorithmshard

103 of 103 problems