Staggered and permutation combination formula

Dislocation

> Concept

First introduce a concept , What is wrong arrangement ;
Staggering is talking about an array with order , Each of these numbers , It is not in its original position after arrangement .
for example 1 2 3 4 5
among 1 You can't put it in the first place ,2 You can't put it in the second place , And so on .
Here is a diagram for you to understand the following formula
If you want to understand better, here is a link
Heigu Xiaojian Mogok yyds

The formula

		int dp[25];
            dp[1]=0;
            dp[2]=1;
		for(i=3;i<=n;i++)// Since the first two need to be pre stored, start from three 
          dp[i]=(i-1)*(dp[i-1]+dp[i-2]);

For staggered arrangement, we can use the formula

Combined calculation

So we can calculate n,m,n-m To find the factorial of

int mo=1,zi=1,z2=1,z3=1;
            for(i=1;i<=n;i++)// This is a n The factorial 
                   mo*=i;
            for(i=1;i<=(n-m);i++)//n-m The factorial 
                   z2*=i;
            for(i=1;i<=m;i++)//m The factorial 
                    z3*=i;

This is a wrong question （ Statistics of students' grades ）

The main idea of the topic , Given a number of students , Yes n Famous student ,1≤n≤15, Mr. Ke said that the ranking statistics of all students were wrong

We can assume that the correct order is 1 2 3 ……, Or in any order .
The code is as follows

#include<bits/stdc++.h>
using namespace std;

#define MAX 0x3f3f3f3f
typedef long long ll;
#define bug(a) cout<<endl<<"*"<<a<<endl;


int main()
{
    
	ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    ll n;
    cin>>n;
    ll dis[30];
    dis[1]=0;
    dis[2]=1;
    for(int i=3;i<=n;i++){
    
    	dis[i]=(i-1)*(dis[i-2]+dis[i-1]);
    }
    cout<<dis[n]<<endl;
}

Input
3
Output
2

n=3 when , There are two situations ：
3 1 2
2 3 1
Finally, let's say , Mogok yyds.