In a social network, an individual person is a node. Between two people there is an undirected edge because they are mutual friends. When one person tells another person a story, they both know the story. Given timestamp as the time two people meet, timestamp can be seen as the weight of the edge. This post is about depth first search in weighted graph, with timestamp as the weight associated with the edge.
A weighted graph can be represented as a adjacency list. The data structure HashMap is used. The keys are all people who spread the story. The values are the edges from a person (key) to his neighbors. The edges contains the timestamps when two people meet and tell the story. We are going to find out all people who know the story by checking the timestamp.
Depth first search uses recursion here. The timestamp’s initial value is 0. It is passed as a parameter of DFS recursive method. In the method, the input timestamp is compared with the timestamp stored within the edge. If the input time is smaller than the edge’s timestamp, that means these two people have the opportunity to tell the story when they meet. This neighbor will be in the group who know the story. Otherwise, he is excluded. At the end, we can find all people who know the story.
Google Interview Question :
When a person who knows it meets any other person, they immediately share the story with them. Initially, only person 1 knows the story. Given a list of meetings between people in a form of (person_1_id, person_2_id, timestamp) construct a list of the persons who will know the story at the very end.
Example: [(1, 2, 100), (3,4, 200), (1,3, 300), (2,5, 400)], 1 // The events could be out of order.
Person 2 will learn the story at the moment 100, person 3 — at the moment 300, person 5 — in the moment 400. Person 4 will never learn the story. So the answer is [1, 2, 3, 5].
Eg2: [(1, 2, 100), (2, 3, 100), (4, 5, 100)], 2
where the first parameter is array of the Persons meet at particular timestamp, second parameter is the PersonId who knows the story first.
Output: [1, 2, 3].
Java
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import java.util.*; class Graph<T> { static class GraphNode<T> { T person2; int timestamp; //Time O(1), Space O(1) public GraphNode(T val, int ts) { person2 = val; this.timestamp = ts; } //Time O(1), Space O(1) public String toString() { return person2 + " " + timestamp; } } private Map<T, ArrayList<GraphNode<T>>> adj = new HashMap<>(); //Add edges, bi-direction, Time O(1), Space O(1) public void tellFriend(T src, T dest, int ts) { //add edge from src to dest adj.putIfAbsent(src, new ArrayList<GraphNode<T>>()); GraphNode<T> newNode = new GraphNode<>(dest, ts); adj.get(src).add(newNode); //add edge from dest to src adj.putIfAbsent(dest, new ArrayList<GraphNode<T>>()); newNode = new GraphNode<>(src, ts); adj.get(dest).add(newNode); } //DFS wrapper, call dfsUtil, Time O(V+E), Space O(V) //V is total number of people, E is number of connections public void dfs(T src) { Map<T, Boolean> visited = new HashMap<>();//memoization for (T key: adj.keySet()) visited.put(key, false); Set<T> group = new HashSet<>(); //output result group.add(src); dfsUtil(src, visited, 0, group); System.out.println("People who know story: " + group); } //DFS + memoization, recursion, Time O(V+E), Space O(V) private void dfsUtil(T v, Map<T,Boolean> visited, int time1, Set<T> group) { visited.put(v, true); for(GraphNode<T> ne: adj.get(v)) { T dest = ne.person2; int time2 = ne.timestamp; if (time1 <= time2 ) group.add(dest); if (!visited.get(dest)) dfsUtil(dest, visited, time2, group); } } //print graph in adjacency list, Time O(n) Space O(1) public void printGraph() { System.out.println("graph:"); for (T key: adj.keySet()) { System.out.println(key + "-" + adj.get(key)); } } } public class PeopleWhoKnowStoryByTimeStamp { public static void main(String args[]) { //case1: [(1, 2, 100), (3,4, 200), (1,3, 300), (2,5, 400)], 1 Graph<Integer> g = new Graph<>(); g.tellFriend(1, 2, 100); g.tellFriend(3, 4, 200); g.tellFriend(1, 3, 300); g.tellFriend(2, 5, 400); g.printGraph(); g.dfs(1); //case 2 [(1, 2, 100), (2, 3, 100), (4, 5, 100)], 2 Graph<Integer> g2 = new Graph<>(); g2.tellFriend(1, 2, 100); g2.tellFriend(2, 3, 100); g2.tellFriend(4, 5, 100); g2.printGraph(); g2.dfs(2); } } |
JavaScript
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class GraphNode { //Time O(1), Space O(1) constructor(val, ts) { this.person2 = val; this.timestamp = ts; } //Time O(1), Space O(1) toString() { return this.person2 + " " + this.timestamp; } } class Graph { //Time O(1), Space O(1) constructor() { this.adj = new Map(); } //add edge, bi-direction, Time O(1), Space O(1) tellFriend(src, dest, ts) { //add edge from src to dest if (!this.adj.has(src)) this.adj.set(src, new Array()); var newNode = new GraphNode(dest, ts); this.adj.get(src).push(newNode); //add edge from dest to src if (!this.adj.has(dest)) this.adj.set(dest, new Array()); newNode = new GraphNode(src, ts); this.adj.get(dest).push(newNode); } //DFS wrapper, call dfsUtil, Time O(V+E), Space O(V) //V is total number of people, E is number of connections dfs(src) { var visited = new Map();//memoization for (let key of this.adj.keys()) visited.set(key, false); var group = new Set(); //output result group.add(src); this.dfsUtil(src, visited, 0, group); console.log("People who know story: " + Array.from(group.values())); } //DFS + memoization, recursion, Time O(V+E), Space O(V) dfsUtil(v, visited, time1, group) { visited.set(v, true); for(let ne of this.adj.get(v)) { let dest = ne.person2; let time2 = ne.timestamp; if (time1 <= time2 ) group.add(dest); if (!visited.get(dest)) this.dfsUtil(dest, visited, time2, group); } } // print graph in adjacency list, Time O(n) Space O(1) printGraph() { console.log("graph:"); for (let key of this.adj.keys()) { console.log(key + "-" + this.adj.get(key)); } } } //case1: [(1, 2, 100), (3,4, 200), (1,3, 300), (2,5, 400)], 1 let g = new Graph(); g.tellFriend(1, 2, 100); g.tellFriend(3, 4, 200); g.tellFriend(1, 3, 300); g.tellFriend(2, 5, 400); g.printGraph(); g.dfs(1); //case 2 [(1, 2, 100), (2, 3, 100), (4, 5, 100)], 2 let g2 = new Graph(); g2.tellFriend(1, 2, 100); g2.tellFriend(2, 3, 100); g2.tellFriend(4, 5, 100); g2.printGraph(); g2.dfs(2); |
Python
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class GraphNode : #Time O(1), Space O(1) def __init__(self, val, ts): self.person2 = val self.timestamp = ts #Time O(1), Space O(1) def __str__(self): return str(self.person2) + " " + str(self.timestamp) class Graph : #Time O(1), Space O(1) def __init__(self): self.adj = {} #add edge, bi-direction, Time O(1), Space O(1) def tellFriend(self, src, dest, ts) : #add edge from src to dest if src not in self.adj: self.adj[src]= [] newNode = GraphNode(dest, ts) self.adj[src].append(newNode) #add edge from dest to src if dest not in self.adj: self.adj[dest]= [] newNode = GraphNode(src, ts) self.adj[dest].append(newNode) #DFS wrapper, call dfsUtil, Time O(V+E), Space O(V) #V is total number of people, E is number of connections def dfs(self, src) : visited = {} # memoization for key in self.adj: visited[key]= False group = set() # output result group.add(src) self.dfsUtil(src, visited, 0, group) print("People who know story: " + str(group)) #DFS + memoization, recursion, Time O(V+E), Space O(V) def dfsUtil(self, v, visited, time1, group) : visited[v] = True for ne in self.adj[v]: dest = ne.person2 time2 = ne.timestamp if time1 <= time2 : group.add(dest) if visited[dest] == False: self.dfsUtil(dest, visited, time2, group) # print graph in adjacency list, Time O(n) Space O(1) def printGraph(self) : print("graph:") for key in self.adj: line = str(key) +"-" array = self.adj[key] for i in array: line += str(i) +", " print (line) # case1: [(1, 2, 100), (3,4, 200), (1,3, 300), (2,5, 400)], 1 g = Graph(); g.tellFriend(1, 2, 100) g.tellFriend(3, 4, 200) g.tellFriend(1, 3, 300) g.tellFriend(2, 5, 400) g.printGraph() g.dfs(1) #case 2 [(1, 2, 100), (2, 3, 100), (4, 5, 100)], 2 g2 = Graph(); g2.tellFriend(1, 2, 100) g2.tellFriend(2, 3, 100) g2.tellFriend(4, 5, 100) g2.printGraph() g2.dfs(2) |
Doodle
Output:
graph:
1-[2 100, 3 300]
2-[1 100, 5 400]
3-[4 200, 1 300]
4-[3 200]
5-[2 400]
People who know story: [1, 2, 3, 5]
graph:
1-[2 100]
2-[1 100, 3 100]
3-[2 100]
4-[5 100]
5-[4 100]
People who know story: [1, 2, 3]
O Notation:
Time complexity: O(V+E)
Space complexity: O(V)
V is total number of people, E is number of connections
The weighted graph is represented as adjacency list. Depth first search uses recursion. The weight will be passed as parameter in the DFS recursive method. Inside the method, the input weight is compared with the weight associated with the edge. If the input is smaller than the edge’s weight, that means these edge is eligible to visit. Otherwise, the edge is excluded. At the end, you will get the visited edges based on the weight comparison.
Download PeopleWhoKnowStoryByTimeStamp.java
Download PeopleWhoKnowStoryByTimeStamp.js
Download PeopleWhoKnowStoryByTimeStamp.py
