2019牛客暑期多校训练营（第九场）

The power of Fibonacci

 Quadratic equation

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const ll mod=1000000007;
ll pow_mod(ll a,ll b)
{
    ll ret=1;
    while (b)
    {
        if (b&1)
        {
            ret=ret*a%mod;
        }
        a=a*a%mod;
        b>>=1;
    }
    return ret;
}

ll modsqr(ll a)
{
    ll x=pow_mod(a,(mod+1)/4);
    if (x*x%mod!=a) return -1;
    return x;
}
int main()
{
    int _;
    ll b,c;
    scanf("%d",&_);
    ll inv2=pow_mod(2,mod-2);
    while (_--)
    {
        scanf("%lld%lld",&b,&c);
        ll x=modsqr((b*inv2%mod*b%mod*inv2%mod-c+mod)%mod);
        if (x==-1)
        {
            printf("-1 -1
");
            continue;
        }
        x=(x+b*inv2%mod)%mod;
        ll y=(b-x+mod)%mod;
        if (x>y)
        {
            swap(x,y);
        }
        printf("%lld %lld
",x,y);
    }
    return 0;
}

Knapsack Cryptosystem

#pragma GCC optimize(2)

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
ll a[100],S,n,c[100],sum,b[800000],ans1,ans2;
map<ll,ll>mp;
int main()
{
    scanf("%d%lld",&n,&S);
    for(register int i=1; i<=n; ++i)
    {
        scanf("%lld",&a[i]);
    }
    int mid=n>>1;
    for (int i=0; i<(1<<mid); i++)
    {
        sum=0;
        for (int j=0; j<mid; j++)
        {
            if ((i>>j)&1)
            {
                sum+=a[mid-j];
            }
        }
        if (S>=sum)
        {
            mp[S-sum]=i+1;
        }
    }
    int nn=n-mid;
    for (int i=0; i<(1<<nn); i++)
    {
        sum=0;
        for (int j=0; j<n-mid; j++)
        {
            if ((i>>j)&1)
            {
                sum+=a[n-j];
            }
        }
        if (mp[sum]>0)
        {
            ans1=mp[sum]-1;
            ans2=i;
            break;
        }
    }
    for (int i=0; i<mid; i++)
    {
        if ((ans1>>i)&1)
        {
            c[mid-i]=1;
        }
    }
    for (int i=0; i<n-mid; i++)
    {
        if ((ans2>>i)&1)
        {
            c[n-i]=1;
        }
    }
    for (int i=1; i<=n; i++)
    {
        printf("%d",c[i]);
    }
    printf("
");
}

 All men are brothers

#include<bits/stdc++.h>
 
using namespace std;
typedef unsigned long long ull;
const int maxn=100100;
ull c2,c4,tmp,a,b;
int f[maxn],siz[maxn],n,m,kk;
int get_f(int x)
{
    return x==f[x]?x:f[x]=get_f(f[x]);
}
 
void merge1(int x,int y)
{
    if (siz[x]>siz[y])
    {
        f[y]=x;
        siz[x]+=siz[y];
    }
    else
    {
        f[x]=y;
        siz[y]+=siz[x];
    }
}
int main()
{
    scanf("%d%d",&n,&m);
    for (int i=1; i<=n; i++)
    {
        siz[i]=1;
        f[i]=i;
    }
    c2=1ull*n*(n-1)/2;
    c4=1ull*n*(n-1)/2*(n-2)/3*(n-3)/4;
    printf("%llu
",c4);
    for (int i=1; i<=m; i++)
    {
        int x,y;
        scanf("%d%d",&x,&y);
        x=get_f(x);
        y=get_f(y);
        if (n-kk<4)
        {
            printf("0
");
            continue;
        }
        if (x==y)
        {
            printf("%llu
",c4);
            continue;
        }
        kk++;
        a=siz[y];
        b=siz[x];
        c2-=a*b;
        tmp=a*b*(c2-(a+b)*(n-a-b));
        c4-=tmp;
        printf("%llu
",max(0ull,c4));
        merge1(x,y);
    }
}

 Symmetrical Painting

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef pair<ll,ll>PII;
vector<PII>a;
int main()
{
    int n;
    scanf("%d",&n);
    for (int i=1; i<=n; i++)
    {
        ll l,r;
        scanf("%lld%lld",&l,&r);
        a.push_back(make_pair(l+l,1ll));
        a.push_back(make_pair(l+r,-2ll));
        a.push_back(make_pair(r+r,1ll));
    }
    sort(a.begin(),a.end());
    ll last=0,sum=0,ans=0,se=0;
    for (vector<PII>::iterator it=a.begin(); it!=a.end(); it++)
    {
        sum+=se*(it->first-last);
        ans=max(ans,sum);
        se+=it->second;
        last=it->first;
    }
    printf("%lld
",ans);
}