// poj 1737 Connected Graph // // 题目大意: // // 带标号的连通分量计数 // // 解题思路: // // 设f(n)为连通图的数量,g(n)为非连通图的数量,h(n)为所有的 // 图的数量,h(n) = 2 ^(n * (n - 1) / 2); // f(n) + g[n] = h(n). // // 考虑标号为1在哪个连通分量内,设连通分量内有k个点,则问题为 // 在n-1个点中选择k-1个点的方法数 C(n-1,k-1),此时1所在的连通图数…

Connected Graph Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 3156   Accepted: 1533 Description An undirected graph is a set V of vertices and a set of E∈{V*V} edges.An undirected graph is connected if and only if for every pair (u,v)…

Connected Graph Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 3156   Accepted: 1533 Description An undirected graph is a set V of vertices and a set of E∈{V*V} edges.An undirected graph is connected if and only if for every pair (u,v)…

Connected Graph 求n个点的无向联通图数量,\(n\leq 50\). 解 直接无向联通图做状态等于是以边点做考虑,难以去重,考虑联通对立面即不联通. 不难求出n个点的总方案数为\(2^{\frac{n\times (n-1)}{2}}\),所以设\(f_i\)表示n个点的无向联通图个数,因此我们有 \[f_i=2^{\frac{n(n-1)}{2}}-\sum_{j=1}^{i-1}f_jC_i^j2^{\frac{(i-j)(i-j-1)}{2}}\] 但是这样的转移存在重复,…

http://poj.org/problem?id=1737 (题目链接) 题意 求n个节点的无向连通图的方案数,不取模w(ﾟДﾟ)w Solution 刚开始想了个第二类斯特林数,然而并不知道怎么求具体方案,于是翻了题解.. 设${f_n}$表示n个节点的方案数. 那么n个节点所能够构成的无向图,无论连不连通,一共有${\frac{n*(n+1)}{2}}$条边,于是就有${2^{\frac{n*(n+1)}{2}}}$种图.考虑如何减去不连通的图的方案数. 我们选择枚举1号节点与i个节点连通…

http://blog.csdn.net/sdj222555/article/details/12453629 这个递推可以说是非常巧妙了. import java.util.*; import java.io.*; import java.math.*; public class Main{ static BigInteger[] g=new BigInteger[60]; static BigInteger[] f=new BigInteger[60]; static BigInteger[…

题意:输出题中带有$n$个标号的图中连通图的个数. 解题关键: 令$f(n)$为连通图的个数,$g(n)$为非联通图的个数,$h(n)$为总的个数. 则$f(n) + g(n) = h(n)$ 考虑标号1所在的联通分量中连通图的个数. 转移方程:$g(n) = \sum\limits_{k = 1}^{n - 1} {C_{n - 1}^{k - 1}f(k)h(n - k)} $ $h(n) = \frac{{n(n - 1)}}{2}$ import java.math.*; import…

题面 \(solution:\) 首先做个推销:带负数的压位高精度(加减乘+读写) 然后:由 \(N\) 个节点组成的无向图的总数为: \(2^{N*(N-1)/2}\) (也就是说这个图总共有 \(N*(N-1)/2\) 条边,每一条边选或不选就可以得出来) 然后我们直接开始分析题目,因为这道题需要求无向连通图的方案数,这道题似乎也不是一个结论题, \(wch\) 决定去找找规律,是不是 \(n\) 和 \(n-1\) 有什么关系,但是 $wch $ 发现他打不出表. 然后 $wch $ 想到…

题目链接: http://poj.org/problem?id=1737 题意: 求 \(n\) 个点的无向简单(无重边无自环)连通图的个数.\((n<=50)\) 题解: 这题你甚至能OEIS. http://oeis.org/A001187 但不支持这样做.TAT 间接做. 总方案数减去不合法方案. 因为\(n\)个点的完全图有 \(C(n,2)={n(n-1) \over 2}\) 条边,显然就有 \(2^{C(n,2)}\) 种子图,即枚举每条边是否选择. 设$ f[i]$ 表示每个点都…

AcWing Description 求$N$个节点的无向连通图有多少个,节点有标号,编号为$1~N$. $1<=N<=50$ Sol 在计数类$DP$中,通常要把一个问题划分成若干个子问题,以便于执行递推. 一个连通图不容易划分,而一个不连通的无向图则很容易划分成结点更少的两部分.所以我们把问题转化成用$N$个点的无向图总个数减去$N$个点的不连通无向图的个数. $N$个点的无向图总个数显然是$2^{N*(N-1)/2}$,还是简单说下叭,就是$N$个点连成完全图的边数显然是$N*(N-1)…

记$G[S]$表示图$G$在点集$S$上的导出子图,即$G[S]=(S,{(x,y)|x,y\in S且(x,y)\in E})$ 定义$g(S)$为所有$E'$(满足$E'\subseteq G[S].E$)的图$G'=(S,E')$的染色方式之和,考虑枚举其中一种颜色的点集,则有$g(S)=\sum_{T\subseteq S}2^{|\{(x,y)|(x,y)\in E且x\in T且y\in C_{S}T\}|}$(这些边可以选或不选) 考虑计算$|\{(x,y)|(x,y)\in G[…

Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree. For example: Given n = 5 and edges = [[0, 1], [0, 2], [0, 3], [1, 4]], return tru…

Strongly Connected Components A directed graph is strongly connected if there is a path between all pairs of vertices. A strongly connected component (SCC) of a directed graph is a maximal strongly connected subgraph. For example, there are 3 SCCs in…

Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree. For example: Given n = 5 and edges = [[0, 1], [0, 2], [0, 3], [1, 4]], return tru…

题面 Time limit : 2sec / Memory limit : 1024MB Score : 600 points Problem Statement-题目描述 Kenkoooo found a simple connected graph. The vertices are numbered 1" role="presentation">11 through n" role="presentation">nn. The…

Leha plays a computer game, where is on each level is given a connected graph with n vertices and m edges. Graph can contain multiple edges, but can not contain self loops. Each vertex has an integer di, which can be equal to 0, 1 or  - 1. To pass th…

背景 不同的数据结构有不同的用途,像:数组.链表.队列.栈多数是用来做为基本的工具使用,二叉树多用来作为已排序元素列表的存储,B 树用在存储中,本文介绍的 Graph 多数是为了解决现实问题(说到底,所有的数据结构都是这个目的),如:网络布局.任务安排等. 图的基本概念 示例 顶点(Vertex) 上图的 1.2.3.4.5.6 就是顶点. 邻接(Adjoin) 如果 A 和 B 通过定向边相连,且方向为 A -> B,则 B 为 A 的邻接,如果相连的边是没有方向的,则 A 和 B 互为邻接.…

地址:http://codeforces.com/problemset/problem/165/D 题目: D. Beard Graph time limit per test 4 seconds memory limit per test 256 megabytes input standard input output standard output Let's define a non-oriented connected graph of n vertices and n - 1 edg…

［抄题］: Given an undirected graph, return true if and only if it is bipartite. Recall that a graph is bipartite if we can split it's set of nodes into two independent subsets A and B such that every edge in the graph has one node in A and another node…

Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree. For example: Given n = 5 and edges = [[0, 1], [0, 2], [0, 3], [1, 4]], return tru…

Question: Detect cycle in a directed graph Answer: Depth First Traversal can be used to detect cycle in a Graph. DFS for a connected graph produces a tree. There is a cycle in a graph only if there is a back edge present in the graph. A back edge is…

Generative Graph Models 第八章传统的图生成方法> The previous parts of this book introduced a wide variety of methods for learning representations of graphs. In this final part of the book, we will discuss a distinct but closely related task: the problem of > g…

论文信息 论文标题:Towards Deeper Graph Neural Networks论文作者:Meng Liu, Hongyang Gao, Shuiwang Ji论文来源:2020, KDD论文地址:download 论文代码:download 1 Introduction 问题引入: 图卷积是领域聚合的代表,这些邻域聚合方法中的一层只考虑近邻,当进一步深入以实现更大的接受域时,性能会下降,这种性能恶化归因于过平滑问题( over-smoothing),即当感受域增大时,在传播和更新过…

For a undirected graph with tree characteristics, we can choose any node as the root. The result graph is then a rooted tree. Among all possible rooted trees, those with minimum height are called minimum height trees (MHTs). Given such a graph, write…

图论的常见题目有两类,一类是求两点间最短距离,另一类是拓扑排序,两种写起来都很烦. 求最短路径: 127. Word Ladder Given two words (beginWord and endWord), and a dictionary's word list, find the length of shortest transformation sequence from beginWord to endWord, such that: Only one letter can be…

C. Digit Tree time limit per test:3 seconds memory limit per test:256 megabytes input:standard input output:standard output ZS the Coder has a large tree. It can be represented as an undirected connected graph of n vertices numbered from 0 to n - 1 a…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5458 Problem Description Given an undirected connected graph G with n nodes and m edges, with possibly repeated edges and/or loops. The stability of connectedness between node u and node v is defined by…

这个东西先放在这吧.做过的以后会用#号标示出来 1.burnside定理,polya计数法    这个大家可以看brudildi的<组合数学>,那本书的这一章写的很详细也很容易理解.最好能完全看懂了,理解了再去做题,不要只记个公式.    *简单题:(直接用套公式就可以了)    pku2409 Let it Bead      #http://acm.pku.edu.cn/JudgeOnline/problem?id=2409    pku2154 Color   #http://acm.p…

动态规划 动态规划 容易: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 不易: , , , , , , , , , , , , , , , , , , , , , , , , 推荐: , , , , , , , , , , , , , , , , , , , , , , , , Jury Compromise False co…

题目:这里 题意: 感觉并不能表达清楚题意,所以 Problem Description In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two nodes are connected by exactly one path. In other words, any connected graph without simple cycles is a…