CF1063D Candies for Children

CF1063D Candies for Children 

分类讨论题

n<=1e11，

整体上先分n<=2e6与否讨论

len长度，ans贪心的人，p就是len这一段贪心的人

n<=2e6

枚举答案ans

要满足：

p>=0,

p>=ans-(n-len)

p<=ans,

p<=len

p+len=k mod (ans+n)=r

p=r-len

判断p是否合法即可

 

n>=2e6

枚举i

i*ans+p=k-i*n-len=M

观察，ans++，p-=i

p最小时候，ans最大

p最小是:M%i

考虑要满足的条件：

p>=0,p<=len,p<=ans

ans>=0,ans<=p+(n-len),ans<=n

先把ans调整到n以内，再调整到p+(n-len)以内

判断p是否合法即可

因为最大合法的ans一定是最优的，ans更小，p更大，本身答案更劣，而且也更可能不合法

 

至于最后一个取1个，但是是贪心的，

只需要k=k+1再做一遍，并且要求p>=1

#include<bits/stdc++.h>
#define reg register int
#define il inline
#define fi first
#define se second
#define mk(a,b) make_pair(a,b)
#define numb (ch^'0')
#define pb push_back
#define solid const auto &
#define enter cout<<endl
#define pii pair<int,int>
using namespace std;
#define int long long 
typedef long long ll;
template<class T>il void rd(T &x){
    char ch;x=0;bool fl=false;
    while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*10+numb);
    (fl==true)&&(x=-x);
}
template<class T>il void output(T x){if(x/10)output(x/10);putchar(x%10+'0');}
template<class T>il void ot(T x){if(x<0) putchar('-'),x=-x;output(x);putchar(' ');}
template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar('\n');}

namespace Miracle{
ll n,l,r,k;
ll len;
ll che(ll i,ll M){
    // cout<<" che "<<i<<" "<<M<<endl;
    ll ret=-1;
    if(i==0){
        ll p=M;
        if(p<=len) ret=max(ret,p+n-len);
        p=M+1;
        if(p>=1&&p<=len) ret=max(ret,p+n-len);
    }
    else{
        ll p=M%i;
        ll ans=(M-p)/i;
        if(ans>n) {
            p+=(ans-n)*i;
            ans=n;
        }
        if(ans>n-len+p){
            ll tmp=(ans-(n-len+p)+i)/(i+1);
            ans-=tmp;
            p+=tmp*i;
        }
        if(p>=0&&p<=min(ans,len)) ret=max(ret,ans);

        p=(M+1)%i;
        ans=(M+1-p)/i;
        if(ans>n){
            p+=(ans-n)*i;
            ans=n;
        }
        if(ans>n-len+p){
            ll tmp=(ans-(n-len+p)+i)/(i+1);
            ans-=tmp;
            p+=tmp*i;
        }
        if(p>=1&&p<=min(ans,len)) ret=max(ret,ans);
    }
    // cout<<" ret "<<ret<<endl;
    return ret;
}
int main(){
    rd(n);rd(l);rd(r);rd(k);
    if(l<=r) len=r-l+1;
    else len=n-l+1+r;
    // cout<<" len "<<len<<endl;
    if(n<=2e6){
        ll ans=0;
        for(ans=n;ans>=0;--ans){
            ll r=k%(ans+n);
            if(r==0) r+=ans+n;
            int p=r-len;
            if(p>=max((ll)0,ans-(n-len))&&p<=min(ans,len)) break;
            r=(k+1)%(ans+n);
            p=r-len;
            if(p>=max((ll)1,ans-(n-len))&&p<=min(ans,len)) break;
        }
        if(ans>=0) printf("%lld",ans);
        else printf("-1");
    }else{
        ll M=k-len;
        ll ans=-1;
        for(ll i=0;M>=0;++i,M-=n){
            ll ret=che(i,M);
            ans=max(ans,ret);
        }
        printf("%lld",ans);
    }
    return 0;
}   

}
signed main(){
    Miracle::main();
    return 0;
}

/*
   Author: *Miracle*
*/