24. Trapping Rain Water
hardAsked at CoinbaseCalculate total liquidity trapped between price-bar barriers — Coinbase uses this classic to evaluate whether engineers can reason about prefix/suffix maximums and then collapse the solution to a two-pointer scan without extra arrays.
By Alex Chen, Founder, InterviewChamp.AI · Last verified
Problem
Given n 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
n == height.length1 <= n <= 2 * 10^40 <= height[i] <= 10^5
Examples
Example 1
height = [0,1,0,2,1,0,1,3,2,1,2,1]6Explanation: 6 units of water are trapped between the bars.
Example 2
height = [4,2,0,3,2,5]9Approaches
1. Prefix/suffix max arrays
Precompute leftMax[i] and rightMax[i]. Water at each bar = min(leftMax[i], rightMax[i]) - height[i].
- Time
- O(n)
- Space
- O(n)
function trap(height) {
const n = height.length;
const leftMax = new Array(n).fill(0);
const rightMax = new Array(n).fill(0);
leftMax[0] = height[0];
for (let i = 1; i < n; i++) leftMax[i] = Math.max(leftMax[i - 1], height[i]);
rightMax[n - 1] = height[n - 1];
for (let i = n - 2; i >= 0; i--) rightMax[i] = Math.max(rightMax[i + 1], height[i]);
let water = 0;
for (let i = 0; i < n; i++) water += Math.min(leftMax[i], rightMax[i]) - height[i];
return water;
}Tradeoff:
2. Two-pointer (optimal)
Advance the pointer on the shorter-max side, accumulating water. Eliminates the extra arrays by computing max on the fly.
- Time
- O(n)
- Space
- O(1)
function trap(height) {
let left = 0, right = height.length - 1;
let leftMax = 0, rightMax = 0, water = 0;
while (left < right) {
if (height[left] < height[right]) {
if (height[left] >= leftMax) leftMax = height[left];
else water += leftMax - height[left];
left++;
} else {
if (height[right] >= rightMax) rightMax = height[right];
else water += rightMax - height[right];
right--;
}
}
return water;
}Tradeoff:
Coinbase-specific tips
Coinbase treats this as a liquidity-depth question: given a histogram of bid/ask volumes, how much liquidity is 'locked' between walls? They test whether you arrive at the two-pointer solution — constant space matters on their high-frequency data paths. Expect a follow-up asking you to prove why advancing the shorter side is always safe.
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