largest square

Find the largest square with all 1s in a 2D 01 matrix

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Yes

Sample

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

return 4

topic address

The dynamic programming method, we can first find the maximum side length of the square, the formula we deduce is, the original array is arr[][];
f[][] is the table to store the result, when the largest square includes arr[] When i][j], f[i][j] = min(f[i-1][j-1],f[i][j-1],f[i-1][j]) +1; When f[i][j] is not included, f[i][j] = 0; the maximum side length at this time is num = max(f[i][j],num )

The complete code is as follows:

package lintcode;

import java.util.Scanner;

/**
 * Created by Taoyongpan on 2017/11/15.
 * 436, find the largest square with all 1s in a two-dimensional 01 matrix
 * The idea of ​​dynamic programming
 * Find the longest side of the square
 */
public class MaxSquare {

    public static int SquareMax(int[][] arr){
        int n = arr.length;
        int m = arr[0].length;
        int num = 0;
        int[][] f = new int[n+1][m+1];
        if (n<=0||m<=0){
            return num;
        }
        //initialize the f array
        for (int i = 0;i<n;i++){
            f[i][0] = arr[i][0];
            num = Math.max(f[i][0],num);
        }
        for (int j = 0; j<m;j++){
            f[0][j] = arr[0][j];
            num = Math.max(f[0][j],num);
        }

        for (int i = 1;i<n;i++){
            for (int j = 1;j<m;j++){
                if (arr[i][j]==1)
                    f[i][j] = Math.min(Math.min(f[i-1][j-1],f[i][j-1]),f[i-1][j])+1;
                else
                    f[i][j] = 0;
                num = Math.max(f[i][j],num);
            }
        }
        return num;
    }
    // main function
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        while (sc.hasNext()){
            int n = sc.nextInt();
            int m = sc.nextInt();
            int[][] arr = new int[n+1][m+1];
            for (int i = 0 ;i<n;i++){
                for (int j = 0;j<m;j++){
                    arr[i][j] = sc.nextInt();
                }
            }
            System.out.println(SquareMax(arr));
        }
    }
}