LeetCode:Maximal Square浅析

 

Maximal Square

 

Total Accepted:25468Total Submissions:110270Difficulty:Medium

 

 

Given a 2D binary matrix filled with 0's and 1's, find the largest square containing all 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 4.

 

Credits:
Special thanks to@Freezenfor adding this problem and creating all test cases.

 

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Dynamic Programming

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思路：

1.动态规划的题，可以维护一个ret[m*n]的整数数组去表示matrix各元素的状态；

2.首先边界i=0,j=0：第一行和第一列与matrix相同（即ret[i][0] = matrix[i][0],ret[0][i] = matrix[0][i]）；

3.当i>0,j>0时，

如果matrix[i][j]=='0',ret[i][j]=0;

如果matrix[i][j]=='1',ret[i][j]由左上角的3个值推出；

推导公式，即状态转移方程为：ret[i][j]=min(ret[i-1][j],ret[i][j-1],ret[i-1][j-1]) + 1;

 

 

code:

 

class Solution {
public:
    int maximalSquare(vector>& matrix) {
        
        int m = matrix.size();
        if(m==0) return 0;
        int n = matrix[0].size();
        vector> ret(m, vector(n,0));
        int maxSize = 0;
        
        for(int i=0;i
 
 
当然还可以有一些空间上的优化：Easy DP solution in C++ with detailed explanations (8ms, O(n^2) time and
 O(n) space)