蒟蒻成长记录

排列数

算是记录一个求全排列的方法吧,()

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <math.h>
#include <cstdio>
#include <utility>
#define inf 0x3f3f3f3f
#define endl '\n'
#define int long long

using namespace std;

const int N = 1e5+10;

//typedef long long ll;

int n,m,t,a[N];
bool vis[N];
void dfs(int x){
    //if(x > n) return;
    if(x > n){
        for(int i = 1; i <= n; i++)
         {
             cout << a[i] << ' ';
         }
         cout << endl;
         return ;
    }
    for(int i = 1; i <= n; i ++)
    {
        if(!vis[i]){
            vis[i] = 1;
            a[x] = i;
            dfs(x + 1);
            vis[i] = 0;
            a[x] = 0;
        }
    }
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    cin >> n;
    dfs(1);
    return 0;
}

以后可以不用一直想着那个next_permutation那个了(又难记又不好控制)

该方法应用P1088 [NOIP2004 普及组] 火星人 - 洛谷 | 计算机科学教育新生态 (luogu.com.cn)

还可以从任意给定的顺序进行全排列

如何控制可以看看该题题解:

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <math.h>
#include <cstdio>
#include <utility>
#define inf 0x3f3f3f3f
#define endl '\n'
#define int long long

using namespace std;

const int N = 1e5+10, M = 20;

//typedef long long ll;
int n,m,mars[N],ans;
bool return0, vis[N] ;
int a[N];
void dfs(int x)
{
    if(return0) return ;
    if(x > n)
    {
        ans++;
        if(ans == m + 1){
            return0 = 1;
            for(int i = 1; i <= n; i++)
             cout << a[i] << ' ';
        }
        return ;
    }
    for(int i = 1; i <= n ; i++ )
    {
        if(!ans){
            i = mars[x];//从给定的顺序进行排列
        }
        if(!vis[i]){
            vis[i] = 1;
            a[x] = i;
            dfs(x + 1);
            a[x] = 0;
            vis[i] = 0;
        }
    }
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    cin >> n >> m;
    for(int i = 1; i <= n ;i ++)
    {
        cin >> mars[i];
    }
    dfs(1);
    return 0;
}

组合数

C(5,3)

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <math.h>
#include <cstdio>
#include <utility>
#define inf 0x3f3f3f3f
#define endl '\n'
#define int long long

using namespace std;

const int N = 1e5+10, M = 20;

//typedef long long ll;
int n,m,arr[N],ans = 1e9 ,A,B; 
bool return0, vis[N] ;
void dfs(int x, int y)
{
    if(x > m)
    {
        for(int i = 1; i <= m; i++) 
         cout << arr[i] << ' ';
        cout << endl;
        return ;
    }
    for(int i = y;i <= n; i++)
    {
        if(!vis[i])
        {
        vis[i] = 1;
        arr[x] = i;
        dfs(x + 1, i + 1);
        vis[i] = 0;
        arr[x] = 0;
        }
        }    
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    cin >> n >> m;
    dfs(1,1);
    return 0;
}