【leetcode】Maximal Rectangle

Maximal Rectangle

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

 

 

使用dpHeight[]数组来记录到第i行为止，第j个位置垂直连续包含多少个1（包括matrxi[i][j]）。如：

1 0 1 1 0

1 1 0 1 0

0 1 1 1 1

有如下结果：

第1行： dpHeight[] = {1, 0, 1, 1, 0}

第2行： dpHeight[] = {2, 1, 0, 2, 0}

第3行： dpHeight[] = {0, 2, 1, 3, 0}

 

对每个dpHeight求最大矩形面积，利用Largest Rectangle in Histogram里面的求解方法即可

 

  

 

class Solution {
public:
    int maximalRectangle(vector<vector<char> > &matrix) {
       
       
        int m=matrix.size();
        if(m==0) return 0;
        int n=matrix[0].size();
       
        vector<int> dpHeight(n,0);
       
        int result=0;
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(matrix[i][j]=='1') dpHeight[j]++;
                else dpHeight[j]=0;
            }
           
            int tmp=lineMaximalRectangle(dpHeight);
            if(tmp>result) result=tmp;
        }
       
        return result;
    }
   
    struct Node
    {
        int index;
        int height;
        Node(int i,int h):index(i),height(h){};
    };
   
    int lineMaximalRectangle(vector<int> &dpHeight)
    {
       
       
        int len=dpHeight.size();
        if(len==0) return 0;
       
        stack<Node> stk;
        Node n(0,dpHeight[0]);
        stk.push(n);
       
        int result=0;
        for(int i=1;i<len;i++)
        {
            int height=dpHeight[i];
           
            if(height>=stk.top().height)
            {
                stk.push(Node(i,height));
            }
            else
            {
                int nodeIndex=i;
                while(!stk.empty()&&height<stk.top().height)
                {
                    int tmp=(i-stk.top().index)*stk.top().height;
                    if(tmp>result) result=tmp;
                    nodeIndex=stk.top().index;
                    stk.pop();
                }
                stk.push(Node(nodeIndex,height));
            }
        }
        while(!stk.empty())
        {
            int index=stk.top().index;
            int height=stk.top().height;
            int tmp=(len-index)*height;
            if(tmp>result) result=tmp;
            stk.pop();
        }
       
        return result;
       
    }
};