# Codeforces1063d candies for Children [Classification discussion] [violence]

Source: Internet
Author: User

Question Analysis:

First, consider two brute force attacks. The time complexity of one is \$ O (N ^ 2) \$, and the other is \$ O ([\ frac {n} {k}] \$.

\$ N ^ 2 \$ violence can be enumerated in two sections, one for \$ I \$ and the other for \$ J \$.

You can calculate the cost of selecting them in each round, for example, \$ Alpha \$ and \$ beta \$. All you have to do is solve \$ (x + 1) * Alpha + x * Beta = K \$, which is not hard to solve.

Then there is \$ O ([\ frac {n} {k}]) \$ violence, enumerating the number of rounds of the election, that is, the above \$ x \$. Assume that each child chooses a candy, and the problem becomes that the child chooses or does not select a candy.

The new parameter \$ gamma \$ is introduced to indicate the number of sweets you need to select.

It is not difficult to find a group of solutions \$ (gamma,-gamma) \$. Then the Selection Range of the two solutions is \$[0 or 1, len1] \$ and \$ [0, len2] \$. Just tune it.

Code:

` 1 #include<bits/stdc++.h> 2 using namespace std; 3  4 long long n,l,r,k; 5  6 long long func(long long x,long long y,long long ki,int dr,long long ll,long long rr){ 7     if(y == 0){ 8     if(ki == 0 && dr == -1) return -1; 9     if(ki <= ll) return ki+rr;10     else return -1;11     }12     long long a = ki,b = -ki;13     long long hh = a/y;a %= y; b += hh*x;14     if(a > ll) return -1;15     if(dr == 1){16     if(b < 0) return -1;17     if(b <= rr)return b+a;18     else {19         hh = (b-rr)/x+((b-rr)%x!=0);20         b -= hh*x;21         a += hh*y;22         if(a <= ll) return b+a;23         else return -1;24     }25     }else{26     if(a == 0) a += y,b -= x;27     if(b < 0) return -1;28     if(b <= rr) return b+a;29     else {30         hh = (b-rr)/x+((b-rr)%x!=0);31         b -= hh*x;32         a += hh*y;33         if(a <= ll) return b+a;34         else return -1;35     }36     }37 }38 39 int main(){40     scanf("%I64d%I64d%I64d%I64d",&n,&l,&r,&k);41     long long um = (r-l+n)%n;42     l = 1; r = 1+um;43     if(k/n <= 5e6){44     long long len1 = r-l+1,len2 = n-len1;45     long long ans = -1;46     for(int i=0;i<=k/n;i++){47         long long zeta = k-i*n-len1;48         if(zeta>=0)ans = max(ans,func(i+1,i,zeta,1,len1,len2));49         zeta = k+1-i*n-len1;50         if(zeta>=0)ans = max(ans,func(i+1,i,zeta,-1,len1,len2));51     }52     printf("%I64d",ans);53     }else{54     int len1 = r-l+1,len2 = n-len1;55     int ans = -1;56     for(int i=0;i<=len1;i++){57         for(int j=0;j<=len2;j++){58         int alpha = len1+i,beta = len2+j;59         long long zeta = k-alpha;60         if(zeta % (alpha+beta) == 0) ans = max(ans,i+j);61         }62     }63     k++;64     for(int i=1;i<=len1;i++){65         for(int j=0;j<=len2;j++){66         int alpha = len1+i,beta = len2+j;67         long long zeta = k-alpha;68         if(zeta % (alpha+beta) == 0) ans = max(ans,i+j);69         }70     }71     printf("%d",ans);72     }73     return 0;74 }`

Codeforces1063d candies for Children [Classification discussion] [violence]

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