ORIGIN

HDU-2018 Story of Cow

2019-12-20

ACM Force HDU Regular Pattern 1 mins237 words

Story of Cow

There is a cow that gives birth to a heifer at the beginning of each year. Each heifer starts in the fourth year and a heifer is born at the beginning of each year. Please program how many cows will there be in year n?

Input

The input data consists of multiple test cases, each test case occupies one line, including an integer n (0 <n <55), the meaning of n is as described in the title.
n = 0 means the end of the input data, no processing.

Output

For each test case, the number of cows at year n is output.
One line per output.

Sample Input

Sample Output

1
2
3

2
4
6

Analysis

Let’s stimulate the situation by ourselves first.

Year	1	2	3	4	5	6	7	8	9	10
Number	1	2	3	4	6	9	13	19	28	41

We can draw a conclusion that:
$$
cow[i] = cow[i - 3] + cow[i - 1] \space \space\space \space\space \space (i>3)
$$

Code

#include<bits/stdc++.h>

using namespace std;

long long arr[1000];
int main() {
	arr[1] = 1; arr[2] = 2; arr[3] = 3;
	for(int i = 4; i <= 55; i ++) {
		arr[i] = arr[i - 1] + arr[i - 3];
	}
	int n;
	while(cin >> n, n) {
		cout << arr[n] << endl;
	}
	return 0;
}