URAL1081——DP—— Binary Lexicographic Sequence

Description

Consider all the sequences with length (0 <  N < 44), containing only the elements 0 and 1, and no two ones are adjacent (110 is not a valid sequence of length 3, 0101 is a valid sequence of length 4). Write a program which finds the sequence, which is on K-th place (0 < K < 10 ⁹) in the lexicographically sorted in ascending order collection of the described sequences.

Input

The first line of input contains two positive integers N and K.

Output

Write the found sequence or −1 if the number K is larger then the number of valid sequences.

Sample Input

3 1

000

大意：两个1不能相邻，很像那道完美串，用dp来计算长度为多少时当前为什么数的时候的个数

状态转移方程  dp[i][1] = dp[i-1][0]

　　　　　　dp[i][0] = dp[i-1][0] + dp[i-1][1]

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int dp[45][2];
int main()
{
    int n,k;
    dp[1][0] = dp[1][1]= 1;
    for(int i = 2; i <= 44; i++){
        dp[i][1] = dp[i-1][0];
        dp[i][0] = dp[i-1][0]+dp[i-1][1];
    }
    while(~scanf("%d%d",&n,&k)){
        if(k > dp[n][1] + dp[n][0]){
            printf("-1\n");
            continue;
        }
        while(n){
            if(dp[n][0] >= k)
                printf("0");
            else {
                k -= dp[n][0];
                printf("1");
            }
            n--;
            }
        printf("\n");
    }
    return 0;
}