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

class Solution {
    /**
     * @param Integer[] $heights
     * @return Integer
     */
    public function largestRectangleArea($heights) {
        return $this->largestArea($heights, 0, count($heights));
    }

    private function largestArea($a, $start, $limit) {
        if ($a == null || empty($a)) {
            return 0;
        }
        if ($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, $areaFromTwo);
        }
        if ($this->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 = $this->findMinInArray($a, $start, $limit);
            return $this->maxOfThreeNums(
                $this->largestArea($a, $start, $minInd),
                $a[$minInd] * ($limit - $start),
                $this->largestArea($a, $minInd + 1, $limit));
        }
    }

    private function findMinInArray($a, $start, $limit) {
        $min = PHP_INT_MAX;
        $minIndex = -1;
        for ($index = $start; $index < $limit; $index++) {
            if ($a[$index] < $min) {
                $min = $a[$index];
                $minIndex = $index;
            }
        }
        return $minIndex;
    }

    private function checkIfSorted($a, $start, $limit) {
        for ($i = $start + 1; $i < $limit; $i++) {
            if ($a[$i] < $a[$i - 1]) {
                return false;
            }
        }
        return true;
    }

    private function maxOfThreeNums($a, $b, $c) {
        return max(max($a, $b), $c);
    }
}

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