• Difficulty: Hard
• Related Topics: Array, Stack
• Link: https://leetcode.com/problems/largest-rectangle-in-histogram/

Description

Givennnon-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.
給定 n 各非負整數，表示直方圖中每個柱子的高度（所有柱子的寬度都是 1），找到該立方圖中面積最大的矩形的面積。

Above is a histogram where width of each bar is 1, given height =[2,1,5,6,2,3].
上圖中，每個柱子的高度是 1，高度為 [2, 1, 5, 6, 2, 3]。

The largest rectangle is shown in the shaded area, which has area =10unit.
上圖中面積最大的矩形為陰影所示，面積為 10 個單位。

Example

Input: [2,1,5,6,2,3]
Output: 10

Solution

對於每一個 heights[i]，其最大的矩形面積為以 heights[i]

import kotlin.math.max

class Solution {
    fun largestRectangleArea(heights: IntArray): Int {
        if (heights.isEmpty()) {
            return 0
        }

        val lessFromLeft = IntArray(heights.size)
        val lessFromRight = IntArray(heights.size)
        lessFromLeft[0] = -1
        lessFromRight[lessFromRight.lastIndex] = heights.size

        for (i in 1..heights.lastIndex) {
            var p = i - 1
            while (p >= 0 && heights[p] >= heights[i]) {
                p = lessFromLeft[p]
            }
            lessFromLeft[i] = p
        }

        for (i in (heights.lastIndex - 1) downTo 0) {
            var p = i + 1
            while (p < heights.size && heights[p] >= heights[i]) {
                p = lessFromRight[p]
            }
            lessFromRight[i] = p
        }

        var result = 0
        for (i in heights.indices) {
            result = max(result, heights[i] * (lessFromRight[i] - lessFromLeft[i] - 1))
        }

        return result
    }
}