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HDU 4982 Goffi and Squary Partition

2024-11-01 17:28:02   205人阅读

Goffi and Squary Partition


Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 856    Accepted Submission(s): 50


Problem Description
Recently, Goffi is interested in squary partition of integers.

A set X of k distinct positive integers is called squary partition of n if and only if it satisfies the following conditions:

    1. the sum of k positive integers is equal to n

  1. one of the subsets of X containing k−1 numbers sums up to a square of integer.

For example, a set {1, 5, 6, 10} is a squary partition of 22 because 1 + 5 + 6 + 10 = 22 and 1 + 5 + 10 = 16 = 4 × 4.

Goffi wants to know, for some integers n and k, whether there exists a squary partition of n to k distinct positive integers.
 
Input
Input contains multiple test cases (less than 10000). For each test case, there‘s one line containing two integers n and k (2≤n≤200000,2≤k≤30).
 
Output
For each case, if there exists a squary partition of n to k distinct positive integers, output "YES" in a line. Otherwise, output "NO".
 
Sample Input
2 24 222 4
 
Sample Output
NOYESYES
 
#include <vector> #include <list> #include <map> #include <set> #include <deque> #include <queue> #include <stack> #include <bitset> #include <algorithm> #include <functional> #include <numeric> #include <utility> #include <sstream> #include <iostream> #include <iomanip> #include <cstdio> #include <cmath> #include <cstdlib> #include <cctype> #include <string> #include <cstring> #include <ctime> using namespace std;#define _int64 long longint main(){  int n,k,tmp,sum,rem,b1,i;  while (scanf("%d%d",&n,&k)!=EOF)  {    sum=(k*(k-1)/2);
　　//假设这个序列是从1到k-1的
　　//此处记录1到k-1的和    b1=0;
　　//flag    for (i=1;i*i<n;i++)    {      rem=n-i*i;      tmp=i*i;      if (tmp<sum) continue;      if ((rem<=k-1)&&(tmp-sum<k-rem)) continue;      //if ((tmp==sum)&&(rem<=k-1)) continue;      if ((tmp==sum+1)&&(rem==k)) continue;      b1=1;      //cout<<i<<endl;      break;    }    if (b1==1) printf("YES\n");    else printf("NO\n");  }  return 0;}

 

HDU 4982 Goffi and Squary Partition


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