Triangle

题目连接：

http://acm.hdu.edu.cn/showproblem.php?pid=5914

Description

Mr. Frog has n sticks, whose lengths are 1,2, 3⋯n respectively. Wallice is a bad man, so he does not want Mr. Frog to form a triangle with three of the sticks here. He decides to steal some sticks! Output the minimal number of sticks he should steal so that Mr. Frog cannot form a triangle with

any three of the remaining sticks.

Input

The first line contains only one integer T (T≤20), which indicates the number of test cases.

For each test case, there is only one line describing the given integer n (1≤n≤20).

Output

For each test case, output one line “Case #x: y”, where x is the case number (starting from 1), y is the minimal number of sticks Wallice should steal.

Sample Input

3

4

5

6

Sample Output

Case #1: 1

Case #2: 1

Case #3: 2

Hint

题意

你有1-n的n条边，让你拿走尽量少的边，使得剩下的边，任意取三个都不能组成三角形。

题解：

最后剩下的边是Fib数列就可以了，这样就保证了任意三个都不能组成三角形。

证明也很简单。

代码

#include<bits/stdc++.h>

using namespace std;

const int maxn = 25;

int dp[maxn];

int main()

{

	dp[1]=1,dp[2]=1,dp[3]=1,dp[5]=1,dp[8]=1,dp[13]=1,dp[21]=1;

	for(int i=1;i<=20;i++)

		dp[i]+=dp[i-1];

	for(int i=1;i<=20;i++)

		dp[i]=i-dp[i];

	int t;

	scanf("%d",&t);

	for(int cas=1;cas<=t;cas++){

		int x;scanf("%d",&x);

		printf("Case #%d: %d\n",cas,dp[x]);

	}

}