【C++】LeetCode 85. Maximal Rectangle

题目：

Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.

For example, given the following matrix:

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

Return 6.

思路：

这一题参考84题（http://blog.youkuaiyun.com/lv1224/article/details/72461540）的思路。矩形每一列可以看做一个柱状图。

用动态规划，每一行调用84题程序，即可求解。

代码：

/*参考84题 LeetCode 84. Largest Rectangle in Histogram*/
class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        stack<int> index;
        int maxarea=0;
        int i=0;
        while(!index.empty()||i<heights.size())
        {
            if(index.empty()||(i<heights.size()&&heights[i]>heights[index.top()]))
            {
                index.push(i++);
            }
            else
            {
                int temp=heights[index.top()];
                index.pop();
                maxarea=max(maxarea,temp*(i-(index.empty()?0:index.top()+1)));
            }
        }
        return maxarea;
    }

    int maximalRectangle(vector<vector<char>>& matrix) {
        if(matrix.size()==0||matrix[0].size()==0)return 0;
        vector<int> heights(matrix[0].size(),0);
        int res=0;
        for(int i=0;i<matrix.size();i++)
        {
            for(int j=0;j<matrix[0].size();j++)
            {
                if(matrix[i][j]=='0')heights[j]=0;
                else heights[j]+=1;
            }
            res=max(res,largestRectangleArea(heights));
        }
        return res;
    }
};