Solution of Codeforces 1957B

Description

Given integers \(n\) and \(k\), find a non-negative sequence \(\{a_n\}\) satisfying the following conditions:

  1. The summation of \(\{a_n\}\) equals to \(k\), that is,

\[\sum_{i=1}^n a_i = k \]

  1. The binary representation of \(a_1\mid a_2\mid \dots\mid a_n\) has the maximum number of \(1\)s, where \(\mid\) represents the bitwise OR operation.

Multiple tests.

Data Range: \(1\leq n\leq 2\cdot 10^5\), \(1\le k\le 10^9\), \(1\le t\le 10^4\).

Solution

For \(n=1\), there is only one way to construct the sequence: to output \(k\) itself.

For \(n>1\), We can easily find out that the answer must be less or equal to \(\log_2 k\), therefore, we only need to find the number of bits in the binary representation of \(k\) (denoted by \(b\)), then a valid sequence is constructed by:

\(2^{b-1}, k - 2^{b-1}\) and \(n-2\) of \(0\)s.

posted @ 2024-04-28 11:59  feicheng  阅读(5)  评论(0)  编辑  收藏  举报