两组笛卡尔乘积
原文:https://www.geeksforgeeks.org/cartesian-product-two-sets/
设 A 和 B 是两个集合，笛卡儿积 A × B 是 A 和 B 中所有有序元素对的集合 A × B = {{x，y} : x ∈ A，y∈B }T5】
设 A = {a，B，c}和 B = {d，e，f} 两个集合的笛卡儿积为 A x B = {a，d}，{a，e}，{a，f}，{b，d}，{b，f}，{c，d}，{c，e}，{c，e}，{ c，f}} A 有 3 个元素，B 也有 3 个元素。笛卡尔乘积有 3×3 = 9 个元素。 一般来说，如果集合 A 中有 m 个元素，集合 B 中有 n 个元素，那么笛卡儿积中的元素个数就是 m x n
给定两个有限非空集合，编写程序打印笛卡儿积。 例:
Input : A = {1, 2}, B = {3, 4}
Output : A × B = {{1, 3}, {1, 4}, {2, 3}, {2, 4}}
Input : A = {1, 2, 3} B = {4, 5, 6}
Output : A × B = {{1, 4}, {1, 5}, {1, 6}, {2, 4},
{2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}}
卡片打印处理机（Card Print Processor 的缩写）
// C++ Program to find the Cartesian Product of Two Sets
#include <stdio.h>
void findCart(int arr1[], int arr2[], int n, int n1)
{
for (int i = 0; i < n; i++)
for (int j = 0; j < n1; j++)
printf("{%d, %d}, ", arr1[i], arr2[j]);
}
int main()
{
int arr1[] = { 1, 2, 3 }; // first set
int arr2[] = { 4, 5, 6 }; // second set
int n1 = sizeof(arr1) / sizeof(arr1[0]);
int n2 = sizeof(arr2) / sizeof(arr2[0]);
findCart(arr1, arr2, n1, n2);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to find the
// Cartesian Product of Two Sets
import java.io.*;
import java.util.*;
class GFG {
static void findCart(int arr1[], int arr2[],
int n, int n1)
{
for (int i = 0; i < n; i++)
for (int j = 0; j < n1; j++)
System.out.print("{"+ arr1[i]+", "
+ arr2[j]+"}, ");
}
// Driver code
public static void main (String[] args) {
// first set
int arr1[] = { 1, 2, 3 };
// second set
int arr2[] = { 4, 5, 6 };
int n1 = arr1.length;
int n2 = arr2.length;
findCart(arr1, arr2, n1, n2);
}
}
// This code is contributed by Nikita Tiwari.
Python 3
# Python3 Program to find the
# Cartesian Product of Two Sets
def findCart(arr1, arr2, n, n1):
for i in range(0,n):
for j in range(0,n1):
print("{",arr1[i],", ",arr2[j],"}, ",sep="",end="")
# Driver code
arr1 = [ 1, 2, 3 ] # first set
arr2 = [ 4, 5, 6 ] # second set
n1 = len(arr1) # sizeof(arr1[0])
n2 = len(arr2) # sizeof(arr2[0]);
findCart(arr1, arr2, n1, n2);
# This code is contributed
# by Smitha Dinesh Semwal
C
// C# Program to find the
// Cartesian Product of Two Sets
using System;
class GFG {
static void findCart(int []arr1, int []arr2,
int n, int n1)
{
for (int i = 0; i < n; i++)
for (int j = 0; j < n1; j++)
Console.Write("{" + arr1[i] + ", "
+ arr2[j] + "}, ");
}
// Driver code
public static void Main () {
// first set
int []arr1 = { 1, 2, 3 };
// second set
int []arr2 = { 4, 5, 6 };
int n1 = arr1.Length;
int n2 = arr2.Length;
findCart(arr1, arr2, n1, n2);
}
}
// This code is contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the
// Cartesian Product of Two Sets
function findCart($arr1, $arr2, $n, $n1)
{
for ($i = 0; $i < $n; $i++)
for ( $j = 0; $j < $n1; $j++)
echo "{", $arr1[$i] ," , ",
$arr2[$j], "}",",";
}
// Driver Code
// first set
$arr1 = array ( 1, 2, 3 );
// second set
$arr2 = array ( 4, 5, 6 );
$n1 = sizeof($arr1) ;
$n2 = sizeof($arr2);
findCart($arr1, $arr2, $n1, $n2);
// This code is contributed by m_kit.
?>
java 描述语言
<script>
// JavaScript Program to find the
// Cartesian Product of Two Set
function findCart(arr1, arr2, n, n1)
{
for (let i = 0; i < n; i++)
for (let j = 0; j < n1; j++)
document.write("{"+ arr1[i]+", "
+ arr2[j]+"}, ");
}
// Driver Code
// first set
let arr1 = [ 1, 2, 3 ];
// second set
let arr2 = [4, 5, 6 ];
let n1 = arr1.length;
let n2 = arr2.length;
findCart(arr1, arr2, n1, n2);
// This code is contributed by chinmoy1997pal.
</script>
输出:
{{1, 4}, {1, 5}, {1, 6}, {2, 4}, {2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}}
实例: 1)一套扑克牌是一个四元集与一套十三元集的笛卡尔乘积。 2)二维坐标系是两组实数的笛卡尔乘积。 参考: https://en.wikipedia.org/wiki/Cartesian_product
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