codeforces 659E New Reform

解决Berland国家的道路改革挑战,通过调整双向道路为单向,确保最少数量的城市变为孤立无援的状态。本篇介绍了一种有效算法,通过深度优先搜索(DFS)来确定最优方案。

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E. New Reform
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 0001 ≤ 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 ≤ nxi ≠ yi), where xi 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
4 3
2 1
1 3
4 3
output
1
input
5 5
2 1
1 3
2 3
2 5
4 3
output
0
input
6 5
1 2
2 3
4 5
4 6
5 6
output
1
Note

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

The second sample: .

The third sample: .



只要有一个环的连通分支,那么肯定可以做到环内的点都有入度,对于环外的点可以看成DFS遍历的生成树的节点,肯定可以有一条有向的通路,

通路上的点都有入度,这个连通分支可以做到最少为0个没有入度的点

如果没有环的连通分支,那么只需要找一个点作为生成树的根节点,那么就可以做到最少只有1个点没有入度



#include <cstdio>
#include <cstring>
#include <iostream>
#include <vector>

using namespace std;

const int maxn = 100000 + 10;
vector<int> G[maxn];
bool vis[maxn], flag;
int n, m, ans;

void dfs(int s, int pre) {
	vis[s] = true;
	for (int i = 0; i < G[s].size(); i++) {
		if (vis[G[s][i]] && G[s][i] != pre) {
			flag = true;
		}
		else if (!vis[G[s][i]]) {
			dfs(G[s][i], s);
		}
	}
}

int main()
{
	scanf("%d%d", &n, &m);
	for (int i = 0; i < m; i++) {
		int u, v;
		scanf("%d%d", &u, &v);
		G[u].push_back(v);
		G[v].push_back(u);
	}
	memset(vis, false, sizeof(vis));
	ans = 0;
	for (int i = 1; i <= n; i++) {
		if (!vis[i]) {
			flag = false;
			dfs(i, i);
			if (!flag) ans++;
		}
	}
	printf("%d\n", ans);
	return 0;
}





### Codeforces 887E Problem Solution and Discussion The problem **887E - The Great Game** on Codeforces involves a strategic game between two players who take turns to perform operations under specific rules. To tackle this challenge effectively, understanding both dynamic programming (DP) techniques and bitwise manipulation is crucial. #### Dynamic Programming Approach One effective method to approach this problem utilizes DP with memoization. By defining `dp[i][j]` as the optimal result when starting from state `(i,j)` where `i` represents current position and `j` indicates some status flag related to previous moves: ```cpp #include <bits/stdc++.h> using namespace std; const int MAXN = ...; // Define based on constraints int dp[MAXN][2]; // Function to calculate minimum steps using top-down DP int minSteps(int pos, bool prevMoveType) { if (pos >= N) return 0; if (dp[pos][prevMoveType] != -1) return dp[pos][prevMoveType]; int res = INT_MAX; // Try all possible next positions and update 'res' for (...) { /* Logic here */ } dp[pos][prevMoveType] = res; return res; } ``` This code snippet outlines how one might structure a solution involving recursive calls combined with caching results through an array named `dp`. #### Bitwise Operations Insight Another critical aspect lies within efficiently handling large integers via bitwise operators instead of arithmetic ones whenever applicable. This optimization can significantly reduce computation time especially given tight limits often found in competitive coding challenges like those hosted by platforms such as Codeforces[^1]. For detailed discussions about similar problems or more insights into solving strategies specifically tailored towards contest preparation, visiting forums dedicated to algorithmic contests would be beneficial. Websites associated directly with Codeforces offer rich resources including editorials written after each round which provide comprehensive explanations alongside alternative approaches taken by successful contestants during live events. --related questions-- 1. What are common pitfalls encountered while implementing dynamic programming solutions? 2. How does bit manipulation improve performance in algorithms dealing with integer values? 3. Can you recommend any online communities focused on discussing competitive programming tactics? 4. Are there particular patterns that frequently appear across different levels of difficulty within Codeforces contests?
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