codeforces Round #440 C Maximum splitting【数学/素数与合数/思维/贪心】
2 seconds
256 megabytes
standard input
standard output
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.
An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself.
The first line contains single integer q (1 ≤ q ≤ 105) — the number of queries.
q lines follow. The (i + 1)-th line contains single integer ni (1 ≤ ni ≤ 109) — the i-th query.
For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings.
1
12
3
2
6
8
1
2
3
1
2
3
-1
-1
-1
12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.
8 = 4 + 4, 6 can't be split into several composite summands.
1, 2, 3 are less than any composite number, so they do not have valid splittings.
【题意】:一个数拆分成几个合数之和,求最多能拆分成几个数之和。
【分析】:其实就是除4看余数,显然4要尽量多取,枚举%4余数讨论一下。这篇博客讲的很不错:http://blog.csdn.net/i1020/article/details/78244053
【代码】:
#include <bits/stdc++.h>
using namespace std;
int main(){
int n,t;
cin>>t;
while(t--){
cin>>n;
if(n<) puts("-1");
else if(n==) puts("-1");
else if(n%==) cout<<n/-<<"\n";
else if(n%==) cout<<n/<<"\n";
else if(n%==) cout<<n/<<"\n";
else if(n==||n==) puts("-1");
else cout<<n/-<<"\n";
}
return ;
}
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