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26. Trapping Rain Water

hardAsked at Udemy

Compute how much water is trapped between elevation bars — Udemy uses this two-pointer classic to test candidates' ability to reason about prefix/suffix max arrays for data-bucketing problems.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an array of non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.

Constraints

  • 1 <= height.length <= 2 * 10^4
  • 0 <= height[i] <= 10^5

Examples

Example 1

Input
height = [0,1,0,2,1,0,1,3,2,1,2,1]
Output
6

Example 2

Input
height = [4,2,0,3,2,5]
Output
9

Approaches

1. Prefix and suffix max arrays

Precompute leftMax[i] and rightMax[i] arrays; water at i = min(leftMax[i], rightMax[i]) - height[i].

Time
O(n)
Space
O(n)
function trap(height) {
  const n = height.length;
  const lMax = new Array(n), rMax = new Array(n);
  lMax[0] = height[0]; rMax[n-1] = height[n-1];
  for (let i = 1; i < n; i++) lMax[i] = Math.max(lMax[i-1], height[i]);
  for (let i = n-2; i >= 0; i--) rMax[i] = Math.max(rMax[i+1], height[i]);
  let water = 0;
  for (let i = 0; i < n; i++) water += Math.min(lMax[i], rMax[i]) - height[i];
  return water;
}

Tradeoff:

2. Two-pointer O(1) space

Use left and right pointers; move the pointer with the smaller max inward, accumulating water based on the known max from that side — eliminates the auxiliary arrays entirely.

Time
O(n)
Space
O(1)
function trap(height) {
  let left = 0, right = height.length - 1;
  let lMax = 0, rMax = 0, water = 0;
  while (left < right) {
    if (height[left] < height[right]) {
      if (height[left] >= lMax) lMax = height[left];
      else water += lMax - height[left];
      left++;
    } else {
      if (height[right] >= rMax) rMax = height[right];
      else water += rMax - height[right];
      right--;
    }
  }
  return water;
}

Tradeoff:

Udemy-specific tips

Udemy asks about e-learning recommendation systems, content search, and marketplace algorithms — balanced mix of arrays, hash maps, and dynamic programming problems.

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