确定给定矩阵是否为稀疏矩阵的程序

17 Mar 2025 | 4 分钟阅读

说明

在这个程序中，我们需要检查给定的矩阵是否为稀疏矩阵。

稀疏矩阵

如果矩阵中的大多数元素都是0，则称该矩阵为稀疏矩阵。这意味着它包含非常少的非零元素。

要检查给定矩阵是否为稀疏矩阵，我们首先计算矩阵中零元素的数量。然后计算矩阵的大小。为了使矩阵成为稀疏矩阵，零元素的计数必须大于大小/2。

Program to determine whether a given matrix is a sparse matrix

上述矩阵中零的个数为6，矩阵的大小为3 * 3 = 9。由于6 > 4.5，这意味着给定数组的大多数元素都是零。因此，上述矩阵是一个稀疏矩阵。

算法

声明并初始化一个二维数组 a。
计算给定数组中的行数和列数，并将它们分别存储在变量rows和cols中。
遍历数组并计算给定数组中零的个数，并将其存储在变量count中。
通过将行数乘以列数来计算数组的大小。
如果count大于size/2，则给定的矩阵是稀疏矩阵。这意味着数组的大多数元素都是零。
否则，该矩阵不是稀疏矩阵。

解决方案

Python

#Initialize matrix a
a = [  
        [4, 0, 0],
        [0, 5, 0],
        [0, 0, 6]
    ];
 
count = 0;
 
#Calculates number of rows and columns present in given matrix
rows = len(a);
cols = len(a[0]);
 
#Calculates the size of the array

size = rows * cols;
 
#Count all zero element present in matrix
for i in range(0, rows):
    for j in range(0, cols):
        if(a[i][j] == 0):
            count = count + 1;
 
if(count > (size/2)):
    print("Given matrix is a sparse matrix");
else:
    print("Given matrix is not a sparse matrix");

输出

Given matrix is a sparse matrix

C

#include <stdio.h>
 
int main()
{
    int rows, cols, size, count = 0;
        
    //Initialize matrix a
    int a[][3] = {   
                    {4, 0, 0},
                    {0, 5, 0},
                    {0, 0, 6}
                };
    
    //Calculates number of rows and columns present in given matrix
    rows = (sizeof(a)/sizeof(a[0]));
    cols = (sizeof(a)/sizeof(a[0][0]))/rows;
    
    //Calculates the size of array
    size = rows * cols;
 
    //Count all zero element present in matrix
    for(int i = 0; i < rows; i++){
        for(int j = 0; j < cols; j++){
          if(a[i][j] == 0)
            count++;
        }
    }
    
    if(count > (size/2))
        printf("Given matrix is a sparse matrix");
    else
        printf("Given matrix is not a sparse matrix");
        
    return 0;
}

输出

Given matrix is a sparse matrix

JAVA

public class SparseMatrix
{
    public static void main(String[] args) {
        int rows, cols, size, count = 0;
        
        //Initialize matrix a
        int a[][] = {   
                        {4, 0, 0},
                        {0, 5, 0},
                        {0, 0, 6}
                    };
          
          //Calculates number of rows and columns present in given matrix
          rows = a.length;
        cols = a[0].length;
        
        //Calculates the size of array
        size = rows * cols;
        
        //Count all zero element present in matrix
        for(int i = 0; i < rows; i++){
            for(int j = 0; j < cols; j++){
                if(a[i][j] == 0)
                    count++;
                }
            }
            
        if(count > (size/2))
            System.out.println("Given matrix is a sparse matrix");
        else
            System.out.println("Given matrix is not a sparse matrix");
    }
}

输出

Given matrix is a sparse matrix

C#

using System;
                    
public class SparseMatrix
{
    public static void Main()
    {
        int rows, cols, size, count = 0;
        
        //Initialize matrix a
        int[,] a = {   
                        {4, 0, 0},
                        {0, 5, 0},
                        {0, 0, 6}
                   };
          
          //Calculates number of rows and columns present in given matrix
          rows = a.GetLength(0);
        cols = a.GetLength(1);
        
        //Calculates the size of array
        size = rows * cols;
        
        //Count all zero element present in matrix
        for(int i = 0; i < rows; i++){
            for(int j = 0; j < cols; j++){
                if(a[i,j] == 0)
                    count++;
                }
            }
            
        if(count > (size/2))
            Console.WriteLine("Given matrix is a sparse matrix");
        else
            Console.WriteLine("Given matrix is not a sparse matrix");
    }
}

输出

Given matrix is a sparse matrix

PHP

<!DOCTYPE html>
<html>
<body>
<?php
//Initialize matrix a
$a = array(   
            array(4, 0, 0),
            array(0, 5, 0),
            array(0, 0, 6)
           );
 
$count = 0;
    
//Calculates number of rows and columns present in given matrix
$rows = count($a);
$cols = count($a[0]);
 
//Calculates the size of array
$size = $rows * $cols;
 
//Count all zero element present in matrix
for($i = 0; $i < $rows; $i++){
    for($j = 0; $j < $cols; $j++){
      if($a[$i][$j] == 0)
        $count++;
    }
}
 
if($count > ($size/2))
    print("Given matrix is a sparse matrix");
else
    print("Given matrix is not a sparse matrix");
?>
</body>
</html>

输出

Given matrix is a sparse matrix

下一主题#

确定给定矩阵是否为稀疏矩阵的程序

说明

稀疏矩阵

算法

解决方案

Python

C

JAVA

C#

PHP

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程序

确定给定矩阵是否为稀疏矩阵的程序

说明

稀疏矩阵

算法

解决方案

Python

C

JAVA

C#

PHP

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