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[leetcode]Largest Rectangle in Histogram

问题描述:

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.

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

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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.

基本思想:

最基本的方法是穷举所有可能的左右边界组合,复杂度为O(n^2);

现在考虑如果左边界固定,右边界h[k]>h[k-1],那么右边界为k时的面接一定大于等于右边界为k-1;所以对于连续递增的一段区间,我们可以暂时不考虑其作为右边界的情况。当出现h[k]<h[k-1]时,穷举左边界,找到最大的面积。这对上面穷举法做了剪枝。


更简单的一种方法是:当遇到h[k]<h[k-1]时,回退计算前面比h[k]更高的挡板组成的矩形面积,并更新最大的面积,直到前一个挡板比h[k]小。可以结合代码理解。

代码:

int largestRectangleArea(vector<int> &height) {  //c++
        if(height.size() == 0)
            return 0;
        height.push_back(0);
        
        int max = 0;
        vector<int> stack;
        
        for(int i = 0; i < height.size(); i++)
        {
            while(stack.size() >0&&height[stack.back()]>height[i])
            {
                int h = height[stack.back()];
                stack.pop_back();
                
                int left = stack.size()>0?stack.back():-1;
                if(h*(i-1-left)>max)
                    max = h*(i-1-left);
            }
            stack.push_back(i);
        }
        return max;
    }


[leetcode]Largest Rectangle in Histogram