AtCoder Grand Contest 010

%%%leoly
%%%Visjiao
%%%Elijahqi
题解可以去看VisJiao大佬的：传送门
AtCoder Grand Contest 010
A.Addition（数学，奇偶性）
B.Boxes (数学)
C.Cleaning（树+结论）
D.Decrementing(数论+gcd+奇偶性)
都是思维题，这我哪会啊。。。Visjiao大佬的题解写的很详细orz

A.Addition

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define N 100010
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*f;
}
int n,tot=0;
int main(){
//  freopen("a.in","r",stdin);
    n=read();
    for(int i=1;i<=n;++i){
        int x=read();if(x&1) tot++;
    }puts(tot&1?"NO":"YES");
    return 0;
}

B.Boxes

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define N 100010
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*f;
}
int n,aa[N],a[N],k;
ll sum=0;
int main(){
//  freopen("a.in","r",stdin);
    n=read();
    for(int i=1;i<=n;++i) aa[i]=read(),sum+=aa[i];
    ll t=(ll)n*(n+1)/2;
    if(sum%t){puts("NO");return 0;}k=sum/t;
    for(int i=2;i<=n;++i) a[i]=aa[i]-aa[i-1];a[1]=aa[1]-aa[n];
    for(int i=1;i<=n;++i)
        if((k-a[i])%n){puts("NO");return 0;}//x<0也不行啊。 
        else if((k-a[i])/n<0){puts("NO");return 0;}
    puts("YES");return 0;
}

C.Cleaning

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define N 100010
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*f;
}
int n,a[N],h[N],num=0,du[N],fa[N];
struct edge{
    int to,next;
}data[N<<1];
bool dfs(int x){
    if(du[x]==1) return 1;
    ll sum=0;int mx=0;
    for(int i=h[x];i;i=data[i].next){
        int y=data[i].to;if(fa[x]==y) continue;
        fa[y]=x;if(!dfs(y)) return 0;mx=max(mx,a[y]);sum+=a[y];
    }if(a[x]>sum) return 0;if(a[x]==sum) return 1;
    ll res= mx>sum-mx?sum-mx:sum/2;//内部交流最多res对
    if(sum-a[x]>res||a[x]-(sum-a[x])<0) return 0;
    a[x]-=sum-a[x];return 1; 
}
int main(){
//  freopen("a.in","r",stdin);
    n=read();for(int i=1;i<=n;++i) a[i]=read();
    for(int i=1;i<n;++i){
        int x=read(),y=read();du[x]++;du[y]++;
        data[++num].to=y;data[num].next=h[x];h[x]=num;
        data[++num].to=x;data[num].next=h[y];h[y]=num;
    }if(n==2){puts(a[1]==a[2]?"YES":"NO");return 0;}
    for(int i=1;i<=n;++i)
        if(du[i]!=1){
            if(!dfs(i)) puts("NO");
            else puts(a[i]?"NO":"YES");return 0;
        }
}

D.Decrementing

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define N 100010
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*f;
}
int n,a[N];
ll sum=0;
inline int gcd(int x,int y){
    return y==0?x:gcd(y,x%y);
}
int main(){
//  freopen("a.in","r",stdin);
    n=read();
    for(int i=1;i<=n;++i) a[i]=read(),sum+=a[i];
    if(n%2==0){
        puts(sum&1?"First":"Second");return 0;
    }if(sum%2==0){puts("First");return 0;}
    while(1){
        bool flag=0;int g=0;
        for(int i=1;i<=n;++i){
            if(a[i]==1||(a[i]&1&&flag)){puts("Second");return 0;}
            if(a[i]&1){a[i]--;flag=1;}
            g=gcd(g,a[i]);
        }if((sum/=g)%2==0){puts("Second");return 0;}
        for(int i=1;i<=n;++i) a[i]/=g;
        flag=0;g=0;
        for(int i=1;i<=n;++i){
            if(a[i]==1||(a[i]&1&&flag)){puts("First");return 0;}
            if(a[i]&1){a[i]--;flag=1;}
            g=gcd(g,a[i]);
        }if((sum/=g)%2==0){puts("First");return 0;}
        for(int i=1;i<=n;++i) a[i]/=g;
    }
}