月度归档:2016年03月

Codeforces 659E. New Reform(图论+dfs)

Berland has n cities connected by m bidirectional roads. No road connects a city to itself, and each pair of cities is connected by no more than one road. It is not guaranteed that you can get from any city to any other one, using only the existing roads.

The President of Berland decided to make changes to the road system and instructed the Ministry of Transport to make this reform. Now, each road should be unidirectional (only lead from one city to another).

In order not to cause great resentment among residents, the reform needs to be conducted so that there can be as few separate cities as possible. A city is considered separate, if no road leads into it, while it is allowed to have roads leading from this city.

Help the Ministry of Transport to find the minimum possible number of separate cities after the reform.

Input

The first line of the input contains two positive integers, n and m — the number of the cities and the number of roads in Berland (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000).

Next m lines contain the descriptions of the roads: the i-th road is determined by two distinct integers xi, yi (1 ≤ xi, yi ≤ n, xi ≠ yi), wherexi and yi are the numbers of the cities connected by the i-th road.

It is guaranteed that there is no more than one road between each pair of cities, but it is not guaranteed that from any city you can get to any other one, using only roads.

Output

Print a single integer — the minimum number of separated cities after the reform.

Examples
input

output

input

output

input

output

Note

In the first sample the following road orientation is allowed: , , .

The second sample: , , , , .

The third sample: , , , , .

说实话这道题目比赛的时候没读懂,以为是一开始就是单向边,今天才发现居然是一开始是双向边变成单向边,求出最少的被孤立的点。

注意读入的时候可能并不是只有一个图。我们可以把就一个图分析,可以发现一个结论:如果在一个图中所有的边数等于或者大于节点数的话,那么一定就没有孤立的点。证明的话,我们可以通过树来想,一个树是只有n-1条边却拥有n个点的,那么当我们从根节点dfs的时候,那么除了根节点以外的节点都可以看成有别的节点指向它们。所以当我们多了一条边的时候,就可以形成一个环,从而有节点指向了原先的根节点(这时候再被叫为根节点有点不合适)》。。

所以我们可以遍历所有的根节点(其实是任意选的),判断该根节点是不是可以形成一棵树还是会出现回路,一旦出现树,就说明该根节点就会被孤立。

 

Codeforces 659D. Bicycle Race(计算几何水题)

Maria participates in a bicycle race.

The speedway takes place on the shores of Lake Lucerne, just repeating its contour. As you know, the lake shore consists only of straight sections, directed to the north, south, east or west.

Let’s introduce a system of coordinates, directing the Ox axis from west to east, and the Oy axis from south to north. As a starting position of the race the southernmost point of the track is selected (and if there are several such points, the most western among them). The participants start the race, moving to the north. At all straight sections of the track, the participants travel in one of the four directions (north, south, east or west) and change the direction of movement only in bends between the straight sections. The participants, of course, never turn back, that is, they do not change the direction of movement from north to south or from east to west (or vice versa).

Maria is still young, so she does not feel confident at some turns. Namely, Maria feels insecure if at a failed or untimely turn, she gets into the water. In other words, Maria considers the turn dangerous if she immediately gets into the water if it is ignored.

Help Maria get ready for the competition — determine the number of dangerous turns on the track.

Input

The first line of the input contains an integer n (4 ≤ n ≤ 1000) — the number of straight sections of the track.

The following (n + 1)-th line contains pairs of integers (xi, yi) ( - 10 000 ≤ xi, yi ≤ 10 000). The first of these points is the starting position. The i-th straight section of the track begins at the point (xi, yi) and ends at the point (xi + 1, yi + 1).

It is guaranteed that:

  • the first straight section is directed to the north;
  • the southernmost (and if there are several, then the most western of among them) point of the track is the first point;
  • the last point coincides with the first one (i.e., the start position);
  • any pair of straight sections of the track has no shared points (except for the neighboring ones, they share exactly one point);
  • no pair of points (except for the first and last one) is the same;
  • no two adjacent straight sections are directed in the same direction or in opposite directions.
Output

Print a single integer — the number of dangerous turns on the track.

Examples
input

output

input

output

Note

The first sample corresponds to the picture:

The picture shows that you can get in the water under unfortunate circumstances only at turn at the point (1, 1). Thus, the answer is 1.

 

比赛的时候没有想出来,以为要模拟着写,然后因为太瞌睡就放弃滚去睡觉了=-=早上爬起来再一看,发现大神们一种很漂亮的解法:

其实题目是给我们绘制了一个n边形,那么被这个多边形包围起来的地方里面就全是水。根据画图,我们可以发现所有的danger turn全部发生在内角为270度的地方。那么我们就可以得到一个公式了:ans*270+(n-x)*90=180*(n-2),180*(n-2)是多边形求内角和的公式=-=那么就可以O(1)复杂度解决啦~

 

 

hdu 1702 ACboy needs your help again!(模拟栈和队列)

传送门

纯粹模拟栈和队列。开始用了STL后来自己也写了一个栈和队列进行模拟。

STL版本:

 

自己手写的辣鸡版本: