Maximal Rectangle

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两种方法，第一种参考 http://blog.csdn.net/fightforyourdream/article/details/17711893

Time O(n^3), Space O(n^2)

class Solution {public:    int maximalRectangle(vector<vector<char> > &matrix) {        int rows = matrix.size();        if(rows == 0) return 0;        int cols = matrix[0].size();                vector<vector<int> > ones(rows, vector<int>(cols, 0));        for(int i=0; i<rows; i++)        {            for(int j=0; j<cols; j++)            {                if(matrix[i][j] == '1')                {                    if(j == 0)                        ones[i][j] = 1;                    else                        ones[i][j] = ones[i][j-1]+1;                }            }        }                int max_area = 0;                for(int i=0; i<rows; i++)        {            for(int j=0; j<cols; j++)            {                if(ones[i][j] != 0)                {                    int minWidth = ones[i][j];                    int idx = i;                    while(idx >= 0)                    {                        minWidth = min(minWidth, ones[idx][j]);                        int area = minWidth * (i-idx+1);                        max_area = max(max_area, area);                        idx--;                    }                }            }        }        return max_area;    }};

第二种，利用了Largest Rectangle in Histogram的答案。逐行求解。Time O(n^2)， Space O（n）。

http://www.cnblogs.com/lichen782/p/leetcode_maximal_rectangle.html

class Solution {public:    int maximalRectangle(vector<vector<char> > &matrix) {        int rows = matrix.size();        if(rows == 0) return 0;        int cols = matrix[0].size();                vector<int> heights(cols, 0);        int result = 0;                for(int i=0; i<rows; i++)        {            for(int j=0; j<cols; j++)            {                if(matrix[i][j] == '1')                    heights[j]++;                else                    heights[j] = 0;            }            int res = largestRectangleArea(heights);            result = max(result, res);        }        return result;    }            int largestRectangleArea(vector<int> &height) {        const int n = height.size();        if(n == 0) return 0;                int max_area = 0;        int area_top = 0;        int idx = 0;                stack<int> hists;        while(idx < n)        {            if(hists.empty() || height[idx] >= height[hists.top()])                hists.push(idx++);            else            {                int top = hists.top();                hists.pop();                                int area_top = height[top]*(hists.empty()?idx:(idx-hists.top()-1));                max_area = std::max(max_area, area_top);            }        }                while(!hists.empty())        {            int top = hists.top();            hists.pop();                            int area_top = height[top]*(hists.empty()?idx:(idx-hists.top()-1));            max_area = std::max(max_area, area_top);        }        return max_area;    }};

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