[CareerCup][Google Interview] 打印所有的Binary Number
If the Fibonacci series is 1,2,3,5,8,13,….. then 10 can be written as 8 + 2 ==> 10010 and 17 can be written as 13 + 3 + 1 ==> 100101. Got it?? The Question was, given n, I need to get all possible representations of n in Fibonacci Binary Number System. as 10 = 8 + 2 ==> 10010 also 10 = 5 + 3 + 2 ==> 1110
这里8+2= 10,
1 2 3 5 8 13
0 1 0 0 1 -->二进制数为10010
DP来解决,复杂度O(n * n * m), m是给的数,n是小于m的fib数的个数。
sum[i][k]表示用前i个数(第i个数一定会用到),和为k的情况总数。
最后sum[i][m], 0 < i < n,的和就是总的组合数
1 #include <iostream> 2 using namespace std; 3 4 int main() 5 { 6 int f[10]; 7 8 f[0] = 1; 9 f[1] = 2; 10 11 for(int i = 2; i < 10; i++) 12 f[i] = f[i-1] + f[i-2]; 13 14 int sum[10][100]; 15 16 int size = 0; 17 18 int N = 13; 19 20 while(size < 10) 21 { 22 if (f[size] <= N) 23 size++; 24 else 25 break; 26 } 27 28 memset(sum, 0, sizeof(sum)); 29 30 for(int i = 0; i < size; i++) 31 { 32 sum[i][f[i]] = 1; 33 for(int j = 0; j < i; j++) 34 for(int k = 1; k <= N - f[i]; k++) 35 sum[i][k + f[i]] += sum[j][k]; 36 } 37 38 int ret = 0; 39 for(int i = 0; i < size; i++) 40 ret += sum[i][N]; 41 42 cout << ret << endl; 43 }