84. Largest Rectangle in Histogram

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本文探讨了在给定的直方图中寻找最大矩形面积的问题，通过一个算法示例，展示了如何遍历直方图并计算局部峰值，以此找到最大的矩形面积。

84. Largest Rectangle in Histogram

Hard

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Given n non-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.

Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

The largest rectangle is shown in the shaded area, which has area = 10 unit.

Example:

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

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class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        int res = 0;
        for (int i = 0; i < height.size(); ++i) {
            if (i + 1 < height.size() && height[i] <= height[i + 1]) {
                continue;
            }
            int minH = height[i];//找到一个局部峰值
            for (int j = i; j >= 0; --j) {
                minH = min(minH, height[j]);
                int area = minH * (i - j + 1);//从当前位置往前依次计算可组成的矩形面积
                res = max(res, area);
            }
        }
        return res;
    }
};