LeetCode-in-All

84. Largest Rectangle in Histogram

Hard

Given an array of integers heights representing the histogram’s bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.

Example 1:

Input: heights = [2,1,5,6,2,3]

Output: 10

Explanation: The above is a histogram where width of each bar is 1.

The largest rectangle is shown in the red area, which has an area = 10 units.

Example 2:

Input: heights = [2,4]

Output: 4

Constraints:

• 1 <= heights.length <= 105
• 0 <= heights[i] <= 104

Solution

import "math"

func largestRectangleArea(heights []int) int {
	return largestArea(heights, 0, len(heights))
}

func largestArea(a []int, start, limit int) int {
	if len(a) == 0 {
		return 0
	}
	if start == limit {
		return 0
	}
	if limit-start == 1 {
		return a[start]
	}
	if limit-start == 2 {
		maxOfTwoBars := max(a[start], a[start+1])
		areaFromTwo := min(a[start], a[start+1]) * 2
		return max(maxOfTwoBars, areaFromTwo)
	}
	if checkIfSorted(a, start, limit) {
		maxWhenSorted := 0
		for i := start; i < limit; i++ {
			if a[i]*(limit-i) > maxWhenSorted {
				maxWhenSorted = a[i] * (limit - i)
			}
		}
		return maxWhenSorted
	} else {
		minInd := findMinInArray(a, start, limit)
		return maxOfThreeNums(
			largestArea(a, start, minInd),
			a[minInd]*(limit-start),
			largestArea(a, minInd+1, limit),
		)
	}
}

func findMinInArray(a []int, start, limit int) int {
	min := math.MaxInt32
	minIndex := -1
	for index := start; index < limit; index++ {
		if a[index] < min {
			min = a[index]
			minIndex = index
		}
	}
	return minIndex
}

func checkIfSorted(a []int, start, limit int) bool {
	for i := start + 1; i < limit; i++ {
		if a[i] < a[i-1] {
			return false
		}
	}
	return true
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func maxOfThreeNums(x, y, z int) int {
	return max(max(x, y), z)
}

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