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

input	output
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;

}