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 scala.util.control.Breaks.{break, breakable}

object Solution {
    def largestRectangleArea(heights: Array[Int]): Int = {
        largestArea(heights, 0, heights.length)
    }

    private def largestArea(a: Array[Int], start: Int, limit: Int): Int = {
        if (a == null || a.isEmpty) {
            return 0
        }
        if (start == limit) {
            return 0
        }
        if (limit - start == 1) {
            return a(start)
        }
        if (limit - start == 2) {
            val maxOfTwoBars = math.max(a(start), a(start + 1))
            val areaFromTwo = math.min(a(start), a(start + 1)) * 2
            return math.max(maxOfTwoBars, areaFromTwo)
        }
        if (checkIfSorted(a, start, limit)) {
            var maxWhenSorted = 0
            for (i <- start until limit) {
                if (a(i) * (limit - i) > maxWhenSorted) {
                    maxWhenSorted = a(i) * (limit - i)
                }
            }
            return maxWhenSorted
        } else {
            val minInd = findMinInArray(a, start, limit)
            maxOfThreeNums(
                largestArea(a, start, minInd),
                a(minInd) * (limit - start),
                largestArea(a, minInd + 1, limit)
            )
        }
    }

    private def findMinInArray(a: Array[Int], start: Int, limit: Int): Int = {
        var min = Int.MaxValue
        var minIndex = -1
        for (index <- start until limit) {
            if (a(index) < min) {
                min = a(index)
                minIndex = index
            }
        }
        minIndex
    }

    private def checkIfSorted(a: Array[Int], start: Int, limit: Int): Boolean = {
        var sorted = true
        breakable {
            for (i <- start + 1 until limit) {
                if (a(i) < a(i - 1)) {
                    sorted = false
                    break
                }
            }
        }
        sorted
    }

    private def maxOfThreeNums(a: Int, b: Int, c: Int): Int = {
        math.max(math.max(a, b), c)
    }
}

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