Solution to combination arrangement problem in Java

This article introduces the solution to the combination arrangement problem in Java

1.

Select 2 people from 4 people to participate in the event. There are 6 selection methods in total.

How many ways are there to select m people from n people to participate in the event?

C(m/n)=C((m-1)/(n-1))+C(m/(n-1)) Mathematical algorithm

public class Main {	
	public static void main(String[] args) {
		System.out.println("请输入总人数:");
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		System.out.println("请输入选择人数:");
		int m=sc.nextInt();
		System.out.println("一共有"+fun(n,m)+"种方法!");
	}	
	private static int fun(int n, int m) {		
		if(m>n)return 0;		
		if(m==0)return 1; 		
		return fun(n-1,m-1) + fun(n-1,m);
	}
}

2.

The problem of calculating how many arrangements of 3 A and 2 B can be formed (such as: AAABB, AABBA) is " The research field of Combinatorial Mathematics

. But in some cases, the fast computing speed of computers can also be used to solve problems through clever reasoning.

The following program calculates how many different arrangements m A's and n B's can be combined into. Please improve it.

A(n/m)=A(n/(m-1))+A((n-1)/m)

public class Main {
	public static void main(String[] args) {
		int m=3;
		int n=2;
		System.out.println(pailie(m, n));
	}
	public static int pailie(int m,int n){	
		if (m==0||n==0)return 1;	
		return pailie(m-1,n)+pailie(m, n-1); 
	}
}

Method 2

public class Main {
	public static void main(String[] args) {
		char[] date="ABC".toCharArray();
		f(date,0);
	}
	private static void f(char[] date, int k) {	
		if (k==date.length) {
			for (int i = 0; i < date.length; i++) {
				System.out.print(date[i]+" ");
			}
			System.out.println();
		}	
		for (int i = k; i < date.length; i++) {
			{char t=date[k];date[k]=date[i];date[i]=t;}//试探		
			f(date,k+1);		
			{char t=date[k];date[k]=date[i];date[i]=t;}//回溯
		}	
	}
}

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