1. Introduction to Maxflow

Min-cut pb

• input: edge-weighted digraph G, each edge e has weight("capacity") c[e]>=0, a source vertex s, a target vertex t.
• def. an **st-cut **(A,B) is a partition of vertices into 2 disjoint sets A and B, with s in set A and …

1. Shortest Paths APIs

context: directe, weighted graphs.

shortest path variants

in terms of vertices:

• source-sink: form one vertex to another
• single source: from one vertex to all others (considered in this lecture)
• all pairs

constraints on edge weights:

• nonnegative weights
• arbitary weights
• eculidean

cycles:

• no directed cycles
• no negative …

1. Introduction to MSTs

Given: undirected connecte graph G with positive edge weights.
def. **Spanning tree **T
is a subgraph of G, that is both tree (connected, acyclic) and spanning(all vertices are included).

⇒ Goal: find a spanning tree with minimum weight sum.

2. Greedy Algorithm

assumptions for simplification:

• edge …

1. Intro to digraphs

Has profound differences wrt undirected graphs.

def: digraph
* edges: have directions
* vertex: distinguish indeg and outdeg

digraph pbs:

• path/shortest path
• topological sort: Can you draw a digraph so that all edges point upwards?
• strong connectivity: Is there a directed path between all pairs of vertices …

1. Intro to graphs

Graph: vertices connected by edges.

terminology:

• path: sequence of vertices connected by edges
• cycle: path with same starting and ending vertex
• two vertices are connected: if there is a path between

ex of graph problems:

• path: or connectivity
• shortest path
• cycle
• Euler tour (ouii..)
• Hamilton tour …

weighted graph的最短路径问题有三个非常有名的算法, 分别以三个大牛的名字命名, 今天用尽量简洁的篇幅一一介绍.

简单起见(这回只写伪代码好了), 对于图的定义如下:

• node …

今天总结一下也许是搜索问题里最重要的算法: DFS !

由于树可以看成是一个graph, 这里还是只写对于graph的DFS算法. Graph类的定义还是用每一个节点保存邻居信息:

public class GraphNode{      
    int val;      
    List<GraphNode> neighbors …

除了上次介绍的minhash方法以外, 还有一种常见的hash方法, 叫做simHash. 这里做简要介绍.
这个hash函数的背景和上次一样, 还是考虑把文本抽象为ngram的集合:

然后相似度依 …

今天总结一下广度优先搜索(BFS). BFS是树/图的遍历的常用算法之一, 对于没有边权重的图来说可以计算最短路径.
由于树的BFS只是图的BFS的一种特殊情况, 而 …

Here is a mindmap of the common algorithms and data structures, it can give an overview of the algorithmic terms.

I shall update its content later on. And maybe write some blog entries on some of the items.

This mindmap is drawn using xmind.