洛谷P3048 [USACO12FEB]牛的IDCow IDs
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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
7 3
10110
/* 将串倒着存储 枚举每个编号对应的二进制串 如果还存在10子串,就swap 如果不再存在,就加一位 */ #include<iostream> #include<cstdio> using namespace std; int n,m,l; bool bin[100000000]; int main(){ scanf("%d%d",&n,&m); l=m; for(int i=1;i<=m;i++)bin[i]=1; for(int i=2;i<=n;i++){//从头枚举 bool flag=0; for(int j=1;j<l;j++){ if(bin[j]==1&&bin[j+1]==0){ flag=1; bin[j]=0;bin[j+1]=1; break; } } if(!flag){ for(int j=1;j<m;j++)bin[j]=1; for(int j=m;j<=l;j++)bin[j]=0; l++;bin[l]=1; } } for(int i=l;i>=1;i--)printf("%d",bin[i]); }
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