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大家帮我想想这个算法问题怎么解决

Posted by ITT at 2009-10-19 14:21:58 and last updated at 2009-10-19 14:23:48
有一个长度为N的向量或数组,每个元素的取值是介于0到N-1之间的整数,即[0,N)
给定一个常数K,要求增加若干元素的值,使得该向量中相同值的元素个数不小于K个。同时要求各元素增加之和最小。示例:

输入:
N K
[A1,A2,A3,..,An]
输出:
[B1,B2,B3,..,Bn]

要求:向量B中每个同值元素出现至少K次,同时SUM(B1-A1,B2-A2,...,Bn-An)最小
注意:将所有元素增加成最大值能够保证K的要求,但是增量不是最小。感觉这是个最优化问题,应该有办法解决,又一时想不出算法来。

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