UVa11089 - Fi-binary Number

I IU P C2 0 06

Problem F: Fi-binary Number

Input: standard input

Output: standard output

 

A Fi-binary number is a number that contains only 0 and 1. It does not contain any leading 0. And also it does not contain 2 consecutive 1. The first few such number are 1, 10, 100, 101, 1000, 1001, 1010, 10000, 10001, 10010, 10100, 10101 and so on. You are given n. You have to calculate the n’th Fi-Binary number.

 

Input

The first line of the input contains one integer T the number of test cases. Each test case contains one integern.

 

Output

For each test case output one line containing the n’th Fi-Binary number.

 

Constraints

-           1 ≤ N ≤ 10⁹

 

Sample Input

Output for Sample Input

4
10
20
30
40

10010
101010
1010001
10001001

#include <cstdio>using namespace std;const int N = 50;long long f[N];void solve(long long x);void init();int main(){#ifndef ONLINE_JUDGEfreopen("d:\\OJ\\uva_in.txt", "r", stdin);#endifinit();int t;scanf("%d", &t);while (t--) {long long n;scanf("%lld", &n);solve(n);}return 0;}void init(){f[0] = f[1] = 1;for (int i = 2; i < N; i++) {f[i] = f[i - 2] + f[i - 1];}}void solve(long long x){x--;int n;for (n = 0; f[n] <= x; n++) x -= f[n];printf("1");while (n > 1) {if (x < f[n - 1]) {printf("0");n--;} else {printf("01");x -= f[n - 1];n -= 2;}}printf("%s\n", n ? "0" : "");}