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++ 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 graph void 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 cost void 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 methods int 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 program to implement Best First Search using priority // queue import 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 |
from queue import PriorityQueue
v = 14
graph = [[] for i in range (v)]
# Function For Implementing Best First Search # Gives output path having lowest cost def 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 graph def 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 = 0
target = 9
best_first_search(source, target, v) # This code is contributed by Jyotheeswar Ganne |
using System;
using System.Collections.Generic;
using System.Collections;
// C# program to implement Best First Search using priority // queue class 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. |
<script> // javascript program to implement Best First Search using priority // queue // Function for adding edges to graph function 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 cost function 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 Nodes let 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 call best_first_search(source, target, v); // The code is contributed by Nidhi goel. </script> |
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