SGU135 Drawing Lines

SGU135 Drawing Lines

题目大意

问N条直线最多能把平面划分为多少个区域

算法思路

当平面上有N条直线时，再画一条直线会多出N+1个区域

因此，fN+1=fN+N+1f_{N+1} = f_{N} + N + 1

不难得出通项公式，fN=N(N+1)2+1f_{N} = \frac{N(N + 1)}{2} + 1

时间复杂度: O(1)O(1)

代码

/**
* Copyright © 2015 Authors. All rights reserved.
*
* FileName: 135.cpp
* Author: Beiyu Li <sysulby@gmail.com>
* Date: 2015-06-14
*/
#include <bits/stdc++.h>

using namespace std;

#define rep(i,n) for (int i = 0; i < (n); ++i)
#define For(i,s,t) for (int i = (s); i <= (t); ++i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)

typedef long long LL;
typedef pair<int, int> Pii;

const int inf = 0x3f3f3f3f;
const LL infLL = 0x3f3f3f3f3f3f3f3fLL;

int main()
{
int n;
scanf("%d", &n);
printf("%d\n", (n & 1? (n + 1) / 2 * n: n / 2 * (n + 1)) + 1);

return 0;
}