P3048 [USACO12FEB]牛的IDCow IDs

    • 65通过
    • 210提交
  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 位运算,按位 组合数学 USACO 2012
  • 难度 提高+/省选-
  • 时空限制 1000ms / 128MB

题解

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    题目描述

    Being a secret computer geek, Farmer John labels all of his cows with binary numbers. However, he is a bit superstitious, and only labels cows with binary numbers that have exactly K "1" bits (1 <= K <= 10). The leading bit of each label is always a "1" bit, of course. FJ assigns labels in increasing numeric order, starting from the smallest possible valid label -- a K-bit number consisting of all "1" bits. Unfortunately, he loses track of his labeling and needs your help: please determine the Nth label he should assign (1 <= N <= 10^7).

    FJ给他的奶牛用二进制进行编号,每个编号恰好包含K 个"1" (1 <= K <= 10),且必须是1开头。FJ按升序编号,第一个编号是由K个"1"组成。

    请问第N(1 <= N <= 10^7)个编号是什么。

    输入输出格式

    输入格式:

    * Line 1: Two space-separated integers, N and K.

    输出格式:

    输入输出样例

    输入样例#1: 复制
    7 3 
    
    输出样例#1: 复制
    10110 
    
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