用行或列的最大 GCD 替换每个矩阵元素

给定一个n行m列的矩阵。任务是用其行或列的最大公约数替换每个矩阵元素，以最大值为准。也就是说，对于每个元素 (i, j)，从第 i 行的 GCD 或第 j 行的 GCD 替换它，以较大者为准。
例子：

Input : mat[3][4] = {1, 2, 3, 3,
                     4, 5, 6, 6
                     7, 8, 9, 9}  
Output :  1 1 3 3
          1 1 3 3
          1 1 3 3
For index (0,2), GCD of row 0 is 1, GCD of row 2 is 3.
So replace index (0,2) with 3 (3>1).

这个想法是对我们这里讨论的一个数组的 LCM 概念，用于查找行和列的 GCD。
使用蛮力，我们可以遍历矩阵的元素，找到该元素对应的行和列的GCD，并将其替换为两者中的最大值。
一种有效的方法是分别为行和列制作两个大小为 n 和 m 的数组。并存储每一行每一列的GCD。大小为 n 的数组将包含每一行的 GCD，大小为 m 的数组将包含每一列的 GCD。并将每个元素替换为其对应的行 GCD 或列 GCD 的最大值。
下面是这种方法的实现：

C++

// C++ program to replace each element with
// maximum of GCD of row or column.
#include
using namespace std;
#define R 3
#define C 4
 
// returning the greatest common divisor of two number
int gcd(int a, int b)
{
    if (b == 0)
        return a;
    return gcd(b, a%b);
}
 
// Finding GCD of each row and column and replacing
// with each element with maximum of GCD of row or
// column.
void replacematrix(int mat[R][C], int n, int m)
{
    int rgcd[R] = { 0 }, cgcd[C] = { 0 };
 
    // Calculating GCD of each row and each column in
    // O(mn) and store in arrays.
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < m; j++)
        {
            rgcd[i] = gcd(rgcd[i], mat[i][j]);
            cgcd[j] = gcd(cgcd[j], mat[i][j]);
        }
    }
 
    // Replacing matrix element
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            mat[i][j] = max(rgcd[i], cgcd[j]);
}
 
// Driven Program
int main()
{
    int m[R][C] =
    {
        1, 2, 3, 3,
        4, 5, 6, 6,
        7, 8, 9, 9,
    };
 
    replacematrix(m, R, C);
 
    for (int i = 0; i < R; i++)
    {
        for (int j = 0; j < C; j++)
            cout << m[i][j] << " ";
        cout<


Java
// Java program to replace each element with
// maximum of GCD of row or column.
import java .io.*;
 
class GFG
{
      static int R = 3;
      static int C = 4;
 
      // returning the greatest common
      // divisor of two number
      static int gcd(int a, int b)
      {
         if (b == 0)
         return a;
         return gcd(b, a%b);
      }
 
// Finding GCD of each row and column and
// replacing with each element with maximum
// of GCD of row or column.
static void replacematrix(int [][]mat, int n, int m)
{
    int []rgcd = new int[R] ;
    int []cgcd = new int[C];
 
    // Calculating GCD of each row and each column in
    // O(mn) and store in arrays.
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < m; j++)
        {
            rgcd[i] = gcd(rgcd[i], mat[i][j]);
            cgcd[j] = gcd(cgcd[j], mat[i][j]);
        }
    }
 
    // Replacing matrix element
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            mat[i][j] = Math.max(rgcd[i], cgcd[j]);
}
 
// Driver program
    static public void main (String[] args){
    int [][]m =
    {
        {1, 2, 3, 3},
        {4, 5, 6, 6},
        {7, 8, 9, 9},
    };
 
    replacematrix(m, R, C);
 
    for (int i = 0; i < R; i++)
    {
        for (int j = 0; j < C; j++)
        System.out.print(m[i][j] + " ");
        System.out.println();
    }
    }
}
 
//This code is contributed by vt_m.

Python3
# Python3 program to replace each element
# with maximum of GCD of row or column.
 
R = 3
C = 4
 
# returning the greatest common
# divisor of two number
def gcd(a, b):
    if (b == 0):
        return a
    return gcd(b, a % b)
 
# Finding GCD of each row and column
# and replacing with each element with
# maximum of GCD of row or column.
def replacematrix(mat, n, m):
 
    rgcd = [0] * R
    cgcd = [0] * C
 
    # Calculating GCD of each row and each
    # column in O(mn) and store in arrays.
    for i in range (n):
        for j in range (m):
         
            rgcd[i] = gcd(rgcd[i], mat[i][j])
            cgcd[j] = gcd(cgcd[j], mat[i][j])
 
    # Replacing matrix element
    for i in range (n):
        for j in range (m):
            mat[i][j] = max(rgcd[i], cgcd[j])
 
# Driver Code
if __name__ == "__main__":
 
    m = [[1, 2, 3, 3],
         [4, 5, 6, 6],
         [7, 8, 9, 9]]
 
    replacematrix(m, R, C)
 
    for i in range(R):
        for j in range (C):
            print ( m[i][j], end = " ")
        print ()
     
# This code is contributed by ita_c

C#
// C# program to replace each element with
// maximum of GCD of row or column.
using System;
 
class GFG
{
      static int R = 3;
      static int C = 4;
   
      // returning the greatest common
      // divisor of two number
      static int gcd(int a, int b)
      {
        if (b == 0)
        return a;
        return gcd(b, a%b);
      }
 
// Finding GCD of each row and column and
// replacing with each element with maximum
// of GCD of row or column.
static void replacematrix(int [,]mat, int n, int m)
{
    int []rgcd = new int[R] ;
    int []cgcd = new int[C];
 
    // Calculating GCD of each row and each column in
    // O(mn) and store in arrays.
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < m; j++)
        {
            rgcd[i] = gcd(rgcd[i], mat[i,j]);
            cgcd[j] = gcd(cgcd[j], mat[i,j]);
        }
    }
 
    // Replacing matrix element
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            mat[i,j] = Math.Max(rgcd[i], cgcd[j]);
}
 
// Driver program
    static public void Main (){
    int [,]m =
    {
        {1, 2, 3, 3},
        {4, 5, 6, 6},
        {7, 8, 9, 9},
    };
 
    replacematrix(m, R, C);
 
    for (int i = 0; i < R; i++)
    {
        for (int j = 0; j < C; j++)
        Console.Write(m[i,j] + " ");
        Console.WriteLine();
    }
    }
}
 
//This code is contributed by vt_m.

Javascript

输出：

1 1 3 3 
1 1 3 3 
1 1 3 3