luoguP2822 组合数问题

Posted 2021-01-02 dream-runner

二维or一维前缀和都可以，我是二维。哈哈哈，刚好借助这道题练了一下对拍，顺便把对拍的程序也挂上。

 

数据制作器

#include<bits/stdc++.h>
#include<ctime>
using namespace std;
int main(){
    freopen("text.txt","w",stdout);
    srand(time(0));
    int t=rand()%10+1,k=rand()%20+1;
    printf("%d %d
",t,k);
    for(int i=1;i<=t;++i){
        int n,m=rand()%10;
        n=m+rand()%10;
        printf("%d %d
",n,m);
    }
    return 0;
}

 

对拍器

#include<bits/stdc++.h>
#include<windows.h>
#include<ctime>
using namespace std;
int main(){
    for(int i=1;i<=100;++i){
        system("maker.exe");
        system("brute.exe");
        system("std.exe");
        if(system("fc s.out b.out")){
            puts("GG");
            exit(0);
        }
        printf("
passed %d
",i);
        Sleep(1000);
    }
    return 0;
}

 

暴力

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll C(ll n,ll m){
    ll ret=1;
    for(ll i=n;i>=n-m+1;--i){
        ret*=i;
    }
    for(ll i=1;i<=m;++i){
        ret/=i;
    }
    return ret;
}
int main(){
    freopen("text.txt","r",stdin);
    freopen("b.out","w",stdout);
    ll T,k;
    scanf("%d%d",&T,&k);
    while(T--){
        ll n,m,ans=0;
        scanf("%d%d",&n,&m);
        for(ll i=0;i<=n;++i){
            for(ll j=0;j<=min(i,m);++j){
                if(C(i,j)%k==0)++ans;
            }
        }
        printf("%d
",ans);
    }
    return 0;
}

 

std

#include<bits/stdc++.h>
using namespace std;
const int maxn=2010;
int a[maxn][maxn],f[maxn][maxn];
int main(){
    freopen("text.txt","r",stdin);
    freopen("s.out","w",stdout);
    int T,k;
    scanf("%d%d",&T,&k);
    for(int i=0;i<=2000;++i){
        for(int j=0;j<=i;++j){
            if(j==0)a[i][j]=1;
            else a[i][j]=a[i-1][j]+a[i-1][j-1];
            if(a[i][j]%k==0)f[i][j]=1;
            a[i][j]%=k;
        }
    }
    for(int i=0;i<=2000;++i){
        for(int j=0;j<=2000;++j){
            if(j!=0)f[i][j]+=f[i][j-1];
            if(i!=0)f[i][j]+=f[i-1][j];
            if(i!=0&&j!=0)f[i][j]-=f[i-1][j-1];
        }
    }
    while(T--){
        int n,m;
        scanf("%d%d",&n,&m);
        printf("%d
",f[n][m]);
    }
    return 0;
}