Largest Rectangle in Histogram

hardcodingAlgorithmsStackArrays~35 min

Asked at Google, Meta

Overview

Given an array of integers heights representing a histogram where each bar has width 1, find the area of the largest rectangle in the histogram.

Constraints

1 <= heights.length <= 100,000
0 <= heights[i] <= 10,000

Examples

largestRectangleArea([2, 1, 5, 6, 2, 3]); // => 10 (bars 5,6 → 5×2)
largestRectangleArea([2, 4]);              // => 4

Solution

Reveal solution

function largestRectangleArea(heights) {
  const stack = [];
  let maxArea = 0;
  const n = heights.length;
  for (let i = 0; i <= n; i++) {
    const h = i === n ? 0 : heights[i];
    while (stack.length && heights[stack[stack.length - 1]] > h) {
      const height = heights[stack.pop()];
      const width = stack.length ? i - stack[stack.length - 1] - 1 : i;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

Monotonic stack: maintain ascending heights. On pop, compute the rectangle using the popped height and the width to the new stack top.

Resources

Largest Rectangle in Histogram — LeetCode

largest-rectangle-in-histogram.js

Largest Rectangle in Histogram

hardcodingAlgorithmsStack

Overview

Given an array of integers heights representing a histogram where each bar has width 1, find the area of the largest rectangle in the histogram.

Constraints

1 <= heights.length <= 100,000
0 <= heights[i] <= 10,000

Examples

largestRectangleArea([2, 1, 5, 6, 2, 3]); // => 10 (bars 5,6 → 5×2)
largestRectangleArea([2, 4]);              // => 4

Solution

Reveal solution

function largestRectangleArea(heights) {
  const stack = [];
  let maxArea = 0;
  const n = heights.length;
  for (let i = 0; i <= n; i++) {
    const h = i === n ? 0 : heights[i];
    while (stack.length && heights[stack[stack.length - 1]] > h) {
      const height = heights[stack.pop()];
      const width = stack.length ? i - stack[stack.length - 1] - 1 : i;
      maxArea = Math.max(maxArea, height * width);
    }
    stack.push(i);
  }
  return maxArea;
}

Monotonic stack: maintain ascending heights. On pop, compute the rectangle using the popped height and the width to the new stack top.

Resources

Largest Rectangle in Histogram — LeetCode

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