[LeetCode] Largest Rectangle in Histogram

最新推荐文章于 2022-09-26 09:37:37 发布

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本文介绍了一种求解直方图中最大矩形面积的高效算法。通过使用栈来跟踪直方图条的高度，该算法能够在线性时间内找到最大矩形区域。举例说明了如何实现这一算法并给出了具体的代码实现。

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.

For example,
Given height = [2,1,5,6,2,3],

return 10.

class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        int ans = 0,area;
        stack<int> s;
        height.push_back(0);
        for(int i = 0;i < height.size();i ++){
            if(s.empty() || !s.empty() && height[i] > height[s.top()])
                s.push(i);
            else{
                while(!s.empty() && height[s.top()] > height[i]){
                    int idx = s.top();
                    s.pop();
                    int width = s.empty() ? i : i - s.top() - 1;
                    area = height[idx]*width;
                    ans = max(ans,area);
                }
                s.push(i);
            }
        }
        return ans;
    }
};