In BFS and DFS, when we are at a node, we can consider any of the adjacent as the next node. So both BFS and DFS blindly explore paths without considering any cost function.
The idea of Best First Search is to use an evaluation function to decide which adjacent is most promising and then explore.
Best First Search falls under the category of Heuristic Search or Informed Search.
Implementation of Best First Search:
We use a priority queue or heap to store the costs of nodes that have the lowest evaluation function value. So the implementation is a variation of BFS, we just need to change Queue to PriorityQueue.
// Pseudocode for Best First Search
Best-First-Search(Graph g, Node start)
1) Create an empty PriorityQueue
PriorityQueue pq;
2) Insert "start" in pq.
pq.insert(start)
3) Until PriorityQueue is empty
u = PriorityQueue.DeleteMin
If u is the goal
Exit
Else
Foreach neighbor v of u
If v "Unvisited"
Mark v "Visited"
pq.insert(v)
Mark u "Examined"
End procedure
Illustration:
Let us consider the below example:
- We start from source “S” and search for goal “I” using given costs and Best First search.
- pq initially contains S
- We remove S from pq and process unvisited neighbors of S to pq.
- pq now contains {A, C, B} (C is put before B because C has lesser cost)
- We remove A from pq and process unvisited neighbors of A to pq.
- pq now contains {C, B, E, D}
- We remove C from pq and process unvisited neighbors of C to pq.
- pq now contains {B, H, E, D}
- We remove B from pq and process unvisited neighbors of B to pq.
- pq now contains {H, E, D, F, G}
- We remove H from pq.
- Since our goal “I” is a neighbor of H, we return.
Below is the implementation of the above idea:
C++
// C++ program to implement Best First Search using priority// queue#include <bits/stdc++.h>using namespace std;typedef pair<int, int> pi;vector<vector<pi> > graph;// Function for adding edges to graphvoid addedge(int x, int y, int cost){ graph[x].push_back(make_pair(cost, y)); graph[y].push_back(make_pair(cost, x));}// Function For Implementing Best First Search// Gives output path having lowest costvoid best_first_search(int actual_Src, int target, int n){ vector<bool> visited(n, false); // MIN HEAP priority queue priority_queue<pi, vector<pi>, greater<pi> > pq; // sorting in pq gets done by first value of pair pq.push(make_pair(0, actual_Src)); int s = actual_Src; visited[s] = true; while (!pq.empty()) { int x = pq.top().second; // Displaying the path having lowest cost cout << x << " "; pq.pop(); if (x == target) break; for (int i = 0; i < graph[x].size(); i++) { if (!visited[graph[x][i].second]) { visited[graph[x][i].second] = true; pq.push(make_pair(graph[x][i].first,graph[x][i].second)); } } }}// Driver code to test above methodsint main(){ // No. of Nodes int v = 14; graph.resize(v); // The nodes shown in above example(by alphabets) are // implemented using integers addedge(x,y,cost); addedge(0, 1, 3); addedge(0, 2, 6); addedge(0, 3, 5); addedge(1, 4, 9); addedge(1, 5, 8); addedge(2, 6, 12); addedge(2, 7, 14); addedge(3, 8, 7); addedge(8, 9, 5); addedge(8, 10, 6); addedge(9, 11, 1); addedge(9, 12, 10); addedge(9, 13, 2); int source = 0; int target = 9; // Function call best_first_search(source, target, v); return 0;} |
Java
// Java program to implement Best First Search using priority// queueimport java.util.ArrayList;import java.util.PriorityQueue;public class GFG{ static ArrayList<ArrayList<edge> > adj = new ArrayList<>(); // Function for adding edges to graph static class edge implements Comparable<edge> { int v, cost; edge(int v, int cost) { this.v = v; this.cost = cost; } @Override public int compareTo(edge o) { if (o.cost < cost) { return 1; } else return -1; } } public GFG(int v) { for (int i = 0; i < v; i++) { adj.add(new ArrayList<>()); } } // Function For Implementing Best First Search // Gives output path having lowest cost static void best_first_search(int source, int target, int v) { // MIN HEAP priority queue PriorityQueue<edge> pq = new PriorityQueue<>(); boolean visited[] = new boolean[v]; visited = true; // sorting in pq gets done by first value of pair pq.add(new edge(source, -1)); while (!pq.isEmpty()) { int x = pq.poll().v; // Displaying the path having lowest cost System.out.print(x + " "); if (target == x) { break; } for (edge adjacentNodeEdge : adj.get(x)) { if (!visited[adjacentNodeEdge.v]) { visited[adjacentNodeEdge.v] = true; pq.add(adjacentNodeEdge); } } } } void addedge(int u, int v, int cost) { adj.get(u).add(new edge(v, cost)); adj.get(v).add(new edge(u, cost)); } // Driver code to test above methods public static void main(String args[]) { // No. of Nodes int v = 14; // The nodes shown in above example(by alphabets) are // implemented using integers addedge(x,y,cost); GFG graph = new GFG(v); graph.addedge(0, 1, 3); graph.addedge(0, 2, 6); graph.addedge(0, 3, 5); graph.addedge(1, 4, 9); graph.addedge(1, 5, 8); graph.addedge(2, 6, 12); graph.addedge(2, 7, 14); graph.addedge(3, 8, 7); graph.addedge(8, 9, 5); graph.addedge(8, 10, 6); graph.addedge(9, 11, 1); graph.addedge(9, 12, 10); graph.addedge(9, 13, 2); int source = 0; int target = 9; // Function call best_first_search(source, target, v); }}// This code is contributed by Prithi_Dey |
Python3
from queue import PriorityQueuev = 14graph = [[] for i in range(v)]# Function For Implementing Best First Search# Gives output path having lowest costdef best_first_search(actual_Src, target, n): visited = [False] * n pq = PriorityQueue() pq.put((0, actual_Src)) visited[actual_Src] = True while pq.empty() == False: u = pq.get()[1] # Displaying the path having lowest cost print(u, end=" ") if u == target: break for v, c in graph[u]: if visited[v] == False: visited[v] = True pq.put((c, v)) print()# Function for adding edges to graphdef addedge(x, y, cost): graph[x].append((y, cost)) graph[y].append((x, cost))# The nodes shown in above example(by alphabets) are# implemented using integers addedge(x,y,cost);addedge(0, 1, 3)addedge(0, 2, 6)addedge(0, 3, 5)addedge(1, 4, 9)addedge(1, 5, 8)addedge(2, 6, 12)addedge(2, 7, 14)addedge(3, 8, 7)addedge(8, 9, 5)addedge(8, 10, 6)addedge(9, 11, 1)addedge(9, 12, 10)addedge(9, 13, 2)source = 0target = 9best_first_search(source, target, v)# This code is contributed by Jyotheeswar Ganne |
C#
using System;using System.Collections.Generic;using System.Collections;// C# program to implement Best First Search using priority// queueclass HelloWorld { public static LinkedList<Tuple<int, int>>[] graph; // Function for adding edges to graph public static void addedge(int x, int y, int cost) { graph[x].AddLast(new Tuple<int, int>(cost, y)); graph[y].AddLast(new Tuple<int, int>(cost, x)); } // Function for finding the minimum weight element. public static Tuple<int,int> get_min(LinkedList<Tuple<int,int>> pq){ // Assuming the maximum wt can be of 1e5. Tuple<int,int> curr_min = new Tuple<int,int>(100000, 100000); foreach(var ele in pq){ if(ele.Item1 == curr_min.Item1){ if(ele.Item2 < curr_min.Item2){ curr_min = ele; } } else{ if(ele.Item1 < curr_min.Item1){ curr_min = ele; } } } return curr_min; } // Function For Implementing Best First Search // Gives output path having lowest cost public static void best_first_search(int actual_Src, int target, int n) { int[] visited = new int[n]; for(int i = 0; i < n; i++){ visited[i] = 0; } // MIN HEAP priority queue LinkedList<Tuple<int, int>> pq = new LinkedList<Tuple<int,int>>(); // sorting in pq gets done by first value of pair pq.AddLast(new Tuple<int, int> (0, actual_Src)); int s = actual_Src; visited[s] = 1; while (pq.Count > 0) { Tuple<int,int> curr_min = get_min(pq); int x = curr_min.Item2; pq.Remove(curr_min); Console.Write(x + " "); // Displaying the path having lowest cost if (x == target) break; LinkedList<Tuple<int,int>> list = graph[x]; foreach(var val in list) { if (visited[val.Item2] == 0) { visited[val.Item2] = 1; pq.AddLast(new Tuple<int,int>(val.Item1, val.Item2)); } } } } static void Main() { // No. of Nodes int v = 14; graph = new LinkedList<Tuple<int, int>>[v]; for (int i = 0; i < graph.Length; ++i){ graph[i] = new LinkedList<Tuple<int, int>>(); } // The nodes shown in above example(by alphabets) are // implemented using integers addedge(x,y,cost); addedge(0, 1, 3); addedge(0, 2, 6); addedge(0, 3, 5); addedge(1, 4, 9); addedge(1, 5, 8); addedge(2, 6, 12); addedge(2, 7, 14); addedge(3, 8, 7); addedge(8, 9, 5); addedge(8, 10, 6); addedge(9, 11, 1); addedge(9, 12, 10); addedge(9, 13, 2); int source = 0; int target = 9; // Function call best_first_search(source, target, v); }}// The code is contributed by Nidhi goel. |
Javascript
<script>// javascript program to implement Best First Search using priority// queue// Function for adding edges to graphfunction addedge(x, y, cost){ graph[x].push([cost, y]); graph[y].push([cost, x]);}// Function For Implementing Best First Search// Gives output path having lowest costfunction best_first_search(actual_Src, target, n){ let visited = new Array(n).fill(false); // MIN HEAP priority queue let pq = []; // sorting in pq gets done by first value of pair pq.push([0, actual_Src]); let s = actual_Src; visited[s] = true; while (pq.length > 0) { let x = pq[0][1]; // Displaying the path having lowest cost document.write(x + " "); pq.shift(); if (x == target) break; for (let i = 0; i < graph[x].length; i++) { if (visited[graph[x][i][1]] == 0) { visited[graph[x][i][1]] = true; pq.push([graph[x][i][0],graph[x][i][1]]); pq.sort((a, b)=>{ if(a[0] != b[0]){ return a[0]-b[0]; } return a[1]-b[1]; }); } } }}// Driver code to test above methods// No. of Nodeslet v = 14;let graph = new Array(v);for(let i = 0; i < v; i++){ graph[i] = new Array(0);}// The nodes shown in above example(by alphabets) are// implemented using integers addedge(x,y,cost);addedge(0, 1, 3);addedge(0, 2, 6);addedge(0, 3, 5);addedge(1, 4, 9);addedge(1, 5, 8);addedge(2, 6, 12);addedge(2, 7, 14);addedge(3, 8, 7);addedge(8, 9, 5);addedge(8, 10, 6);addedge(9, 11, 1);addedge(9, 12, 10);addedge(9, 13, 2);let source = 0;let target = 9;// Function callbest_first_search(source, target, v);// The code is contributed by Nidhi goel. </script> |
Output
0 1 3 2 8 9
Analysis :
- The worst-case time complexity for Best First Search is O(n * log n) where n is the number of nodes. In the worst case, we may have to visit all nodes before we reach goal. Note that priority queue is implemented using Min(or Max) Heap, and insert and remove operations take O(log n) time.
- The performance of the algorithm depends on how well the cost or evaluation function is designed.
Special cases of Best first search:
- Greedy Best first search algorithm
- A* search algorithm
This article is contributed by Shambhavi Singh. If you like neveropen and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the neveropen main page and help other Geeks.
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