fjnu 1189 Recurrence Relations

Description

Recurrence relations are where a function is defined in terms of itself and maybe other functions as well. in this problem, we have two functions of interest:

F (N) = F (N - 1) + G (N - 1) ; F (1) = 1

G (N) = G (N - 1) + G (N - 3) ; G (1) = 1, G (2) = 0, G (3) = 1

For a given value of N, compute F (N).

Input

Each line of input will have exactly one integer, 57 > = N > 0.

Output

For each line of input, output F(N).

Sample Input

1457

 

Sample Output

132035586497

 

 

 

Source:

#include<iostream>
using namespace std;

unsigned F[60]=...{0,1};
unsigned G[60]=...{0,1,0,1};

void list()
...{
    int i;
    for(i=4;i<=57;i++)
        G[i]=G[i-1]+G[i-3];
    for(i=2;i<=57;i++)
        F[i]=F[i-1]+G[i-1];
}

int main()
...{
    list();
    int n;
    while(cin>>n)
    ...{
        cout<<F[n]<<endl;
    }
    return 0;
}

KEY: 不能使用递归的方法，会TLE的，所以采用数组来算，后面的只要出数组拿值；