【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==) return ;
         int n=matrix[].size();

         vector<int> dpHeight(n,);

         int result=;
         for(int i=;i<m;i++)
         {
             for(int j=;j<n;j++)
             {
                 if(matrix[i][j]=='') dpHeight[j]++;
                 else dpHeight[j]=;
             }

             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==) return ;

         stack<Node> stk;
         Node n(,dpHeight[]);
         stk.push(n);

         int result=;
         for(int i=;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;

     }
 };