填充对角线以使每一行，每一列和对角线的总和等于3×3矩阵

在3 x 3矩阵中给定9个元素，其中对角线的值为0 。我们需要找到对角线中的值，以使每一行，每一列和对角线的总和相等。
例子：

Input: 
0 3 6 
5 0 5
4 7 0
Output: 
6 3 6
5 5 5
4 7 4
Explanation: 
    Now the value of the sum of 
    any row or column is 15

Input: 
0 4 4
4 0 4
4 4 0
Output: 
4 4 4
4 4 4
4 4 4

方法：

• 假设对角线是x，y和z。
• x的值将是(x _2，3 + x _3，2 )/ 2。
• z的值将是(x _1，2 + x _2，1 )/ 2。
• y的值将为(x + z)/ 2。

下面是上述方法的实现：
程序：

C++

// C++ program to implement
// the above problem
 
#include 
using namespace std;
 
// Function to print the matrix
void print(int arr[3][3])
{
    int i = 0, j = 0;
 
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++)
            cout << arr[i][j] << " ";
        cout << endl;
    }
}
 
// Function to find the diagonal values
void find(int arr[3][3])
{
    arr[0][0] = (arr[1][2] + arr[2][1]) / 2;
    arr[2][2] = (arr[0][1] + arr[1][0]) / 2;
    arr[1][1] = (arr[0][0] + arr[1][1]) / 2;
 
    // Print the new matrix with diagonals
    cout << "Matrix with diagonals:\n";
    print(arr);
}
 
// Driver code
int main()
{
    // Initialize all the elements of a matrix
    int arr[3][3] = { { 0, 54, 48 },
                      { 36, 0, 78 },
                      { 66, 60, 0 } };
 
    cout << "Matrix initially:\n";
    print(arr);
 
    find(arr);
 
    return 0;
}

Java

// Java program to implement
// the above problem
class GFG
{
 
// Function to print the matrix
static void print(int arr[][])
{
    int i = 0, j = 0;
 
    for (i = 0; i < 3; i++)
    {
        for (j = 0; j < 3; j++)
            System.out.print( arr[i][j] + " ");
        System.out.println();
    }
}
 
// Function to find the diagonal values
static void find(int arr[][])
{
    arr[0][0] = (arr[1][2] + arr[2][1]) / 2;
    arr[2][2] = (arr[0][1] + arr[1][0]) / 2;
    arr[1][1] = (arr[0][0] + arr[1][1]) / 2;
 
    // Print the new matrix with diagonals
    System.out.print( "Matrix with diagonals:\n");
    print(arr);
}
 
// Driver code
public static void main(String args[])
{
    // Initialize all the elements of a matrix
    int arr[][] = { { 0, 54, 48 },
                    { 36, 0, 78 },
                    { 66, 60, 0 } };
 
    System.out.print( "Matrix initially:\n");
    print(arr);
 
    find(arr);
}
}
 
// This code is contributed by Arnab Kundu

Python3

# Python3 program to implement
# the above problem
 
# Function to print the matrix
def print_(arr, n):
    for i in range(n):
        for j in range(n):
            print(arr[i][j], end = " ")
        print("\n", end= "")
 
# Function to find the diagonal values
def find(arr, n):
    arr[0][0] = (arr[1][2] + arr[2][1]) // 2
    arr[2][2] = (arr[0][1] + arr[1][0]) // 2
    arr[1][1] = (arr[0][0] + arr[1][1]) // 2
    print("\nMatrix with diagonals:")
    print_(arr, n)
 
# Driver code
arr = [[0, 54, 48],
       [36, 0, 78],
       [66, 60, 0]]
 
n = 3
print("Matrix initally:")
print_(arr, n)
find(arr, n)
 
# This code is contributed by Shrikant13

C#

// C# program to implement
// the above problem
using System;
 
class GFG
{
 
    // Function to print the matrix
    static void print(int [,]arr)
    {
        int i = 0, j = 0;
     
        for (i = 0; i < 3; i++)
        {
            for (j = 0; j < 3; j++)
                Console.Write( arr[i, j] + " ");
                 
            Console.WriteLine();
        }
    }
     
    // Function to find the diagonal values
    static void find(int [,]arr)
    {
        arr[0, 0] = (arr[1, 2] + arr[2, 1]) / 2;
        arr[2, 2] = (arr[0, 1] + arr[1, 0]) / 2;
        arr[1, 1] = (arr[0, 0] + arr[1, 1]) / 2;
     
        // Print the new matrix with diagonals
        Console.Write( "Matrix with diagonals:\n");
        print(arr);
    }
     
    // Driver code
    public static void Main()
    {
        // Initialize all the elements of a matrix
        int [,]arr = { { 0, 54, 48 },
                        { 36, 0, 78 },
                        { 66, 60, 0 } };
     
        Console.Write( "Matrix initially:\n");
        print(arr);
     
        find(arr);
    }
}
 
// This code is contributed by Ryuga

Javascript

// Java script program to implement
// the above problem
 
// Function to print the matrix
function print(arr)
{
    let i = 0, j = 0;
 
    for (i = 0; i < 3; i++)
    {
        for (j = 0; j < 3; j++)
            document.write( parseInt(arr[i][j]) + " ");
        document.write("<br>");
    }
}
 
// Function to find the diagonal values
function find(arr)
{
    arr[0][0] = (arr[1][2] + arr[2][1]) / 2;
    arr[2][2] = (arr[0][1] + arr[1][0]) / 2;
    arr[1][1] = (arr[0][0] + arr[1][1]) / 2;
 
    // Print the new matrix with diagonals
    document.write( "Matrix with diagonals:<br>");
    print(arr);
}
 
// Driver code
 
    // Initialize all the elements of a matrix
    let arr = [[ 0, 54, 48 ],
                    [36, 0, 78 ],
                    [ 66, 60, 0 ]];
 
    document.write( "Matrix initially:<br>");
    print(arr);
 
    find(arr);
 
// This code is contributed by sravan kumar Gottumukkala

输出：

Matrix initially:
0 54 48 
36 0 78 
66 60 0 

Matrix with diagonals:
69 54 48 
36 34 78 
66 60 45

想要从精选的最佳视频中学习并解决问题，请查看有关从基础到高级C++的C++基础课程以及有关语言和STL的C++ STL课程。要完成从学习语言到DS Algo等的更多准备工作，请参阅“完整面试准备课程” 。