HDU 5914 Triangle 数学找规律

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
",cas,dp[x]);
	}
}