[Leetcode] Largest Rectangle in Histogram

最新推荐文章于 2019-04-10 21:02:20 发布

原创最新推荐文章于 2019-04-10 21:02:20 发布 · 584 阅读

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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和宽度，该算法能够在O(n)的时间复杂度内找到具有最大面积的矩形。

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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.

For example,
Given height = [2,1,5,6,2,3],
return 10.

class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        stack<int> heightIndex;
        stack<int> widthIndex;
        int maxSum = 0;
        int width;
        int lastIndex;
        int i = 0;
        
        for(i = 0;i<height.size();i++)
        {
            lastIndex = i;
            while(!heightIndex.empty() && height[i]<height[heightIndex.top()] )
            {
                width = i - widthIndex.top();
                lastIndex = widthIndex.top();
                maxSum = max(maxSum,width*height[heightIndex.top()]);
                heightIndex.pop();
                widthIndex.pop();
            }
            widthIndex.push(lastIndex);
            heightIndex.push(i);        
        }
        
        while(!heightIndex.empty())
        {
            width = i - widthIndex.top();
            maxSum = max(maxSum,width*height[heightIndex.top()]);
            heightIndex.pop();
            widthIndex.pop();
        }
        
        return maxSum;
    }
};