LeetCode--Maximal Rectangle

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：这道题单独拿出来绝对是一道难题，但是有了上一题Largest Rectangle in Histogram的基础，再思考这个问题就变的简单了许多，可以考虑遍历矩阵的每一行，把每一行为1的部分当做直方图的高度，求得当前行以上构成的各个直方图的最大矩阵面积即可。

class Solution {public:    int maximalRectangle(vector<vector<char>>& matrix) {        int res=0;        vector<int>height;        for(int i=0;i<matrix.size();i++){            height.resize(matrix[i].size());            for(int j=0;j<matrix[i].size();j++){                height[j]=matrix[i][j]=='0'?0:(1+height[j]);            }            res=max(res,largestRectangleArea(height));        }        return res;    }    int largestRectangleArea(vector<int>&heights){        int w,h,area=0;        stack<int>index;        heights.push_back(0);        for(int i=0;i<heights.size();i++){            while(index.size()&&heights[index.top()]>heights[i]){                h=heights[index.top()];                index.pop();                if(index.size())                    w=i-1-index.top();                else                    w=i;                area=max(area,w*h);            }            index.push(i);        }        return area;    }};