BestCoder Round #6（1002）hdu4982（贪心）

Goffi and Squary Partition

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 18    Accepted Submission(s): 12

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:
     
     
     
     

     
     
     
     
 
      
 
      
the sum of  k  positive integers is equal to  n 
 
      
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 2
4 2
22 4
    
    
    
    

 

Sample Output

    
    
    
    

     
     
     
     NO
YES
YES
    
    
    
    

题意：构造k个数，使得总和为n，且存在k-1个数的总和为一个完全平方数，能构造输出YES，否则输出NO

思路：贪心，先找到小于n且最接近n的完全平方数x，然后构造前k-1个数使得总和为x，那么第k个数固定为y=n-x

          做到这里就可以分情况讨论了

         1.  y不等于1~k-1里的数，如果 y 不等于 k 则有解，如果 y=k ，如果x-k*(k-1)/2=1，则无解，否则有解

         2.  y等于1~k-1里的数，显然y不可能等于k了，则将1~k-1里等于y的数替换为k即可，只要前k-1个数的总和<=x则有解，否则无解