题目大意: 给你一棵n个结点的树,求有多少种染色方案,使得染色过程中染过色的结点始终连成一块. 思路: 树形DP. 设f[x]表示先放x时,x的子树中的染色方案数,y为x的子结点. 则f[x]=prod{f[y]}*(size[x]-1)!/prod{size[y]}. 现在我们改变f[x]的含义,让其表示先放x时,整棵子树的方案数. 考虑根的转移对答案做出的贡献. 假设我们从x转移到y,那么就要把y从x中剔除, 设剔除y后的f[x]为t,则t=f[x]*size[y]*(size[x]-1-s…

[CSAcademy]Cycle Tree 题目大意: 定义环树是一张无向连通的简单图,它的生成方式如下: \(2\)个点\(1\)条边的图是环树: 对任意一个环树,加入\(k\)个点\(a_{1\sim k}\),加入方式为从原图中选择一条边\((u,v)\),连接\((u,a_1),(a_1,a_2)\ldots(a_{k-1},a_k),(a_k,v)\),得到的图也是环树. 给定一个\(n(n\le5\times10^4)\)个点,\(m(m\le10^5)\)条边的环树,求最大独立集大…

An undirected, connected tree with N nodes labelled 0...N-1 and N-1 edges are given. The ith edge connects nodes edges[i][0]and edges[i][1] together. Return a list ans, where ans[i] is the sum of the distances between node i and all other nodes. Exam…

Problem A tree is a connected graph with no cycles. A rooted tree is a tree in which one special vertex is called the root. If there is an edge between X and Y in a rooted tree, we say that Y is a child of X if X is closer to the root than Y (in othe…

An undirected, connected tree with N nodes labelled 0...N-1 and N-1 edges are given. The ith edge connects nodes edges[i][0] and edges[i][1] together. Return a list ans, where ans[i] is the sum of the distances between node i and all other nodes. Exa…

Sum of Distances in Tree An undirected, connected tree with N nodes labelled 0...N-1 and N-1 edges are given. The ith edge connects nodes edges[i][0] and edges[i][1] together. Return a list ans, where ans[i] is the sum of the distances between node i…

There is an undirected connected tree with n nodes labeled from 0 to n - 1 and n - 1 edges. You are given the integer n and the array edges where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree. Return an array…

Problem B: CountdownTime Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://acm.hust.edu.cn/vjudge/contest/view.action?cid=88443#problem/B Description Ann Sister owns a genealogical database service, which maintains family tree history for her clients. W…

Union-Find 算法(中文称并查集算法)是解决动态连通性(Dynamic Conectivity)问题的一种算法,作者以此为实例,讲述了如何分析和改进算法,本节涉及三个算法实现,分别是Quick Find, Quick Union 和 Weighted Quick Union. 动态连通性(Dynamic Connectivity) 动态连通性是计算机图论中的一种数据结构,动态维护图结构中相连接的组信息. 简单的说就是,图中各个点之间是否相连.连接后组成了多少个组等信息.我们称连接在一起就…

[CSAcademy]Find the Tree 题目大意: 交互题. 有一棵\(n(n\le2000)\)个结点的树,但是你并不知道树的形态.你可以调用\({\rm query}(x,y,z)\)(其中\(x,y,z\)互不相同)得到与\(x,y,z\)三点距离之和最小的点\(t\).要求你使用不超过\(25000\)次询问,求出树上的所有边. 保证树的形态随机. 思路: 一开始先随便找两个点\(x,y\),枚举第三个点\(z\),询问\({\rm query}(x,y,z)\),则返回的\(…