Best First Search (Informed Search) - GeeksforGeeks

12 Apr, 2022
Prerequisites : BFS, DFS In BFS and DFS, when we are at a node, we can consider any of the adjacent as 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.
We use a priority queue or heap to store costs of nodes which have lowest evaluation function value. So the implementation is a variation of BFS, we just need to change Queue to PriorityQueue. 
// This pseudocode is adapted from below 
// source:
// https://courses.cs.washington.edu/
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
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 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++
Python3
// 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 source, 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, source));    int s = source;    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;}
from queue import PriorityQueuev = 14graph = [[] for i in range(v)] # Function For Implementing Best First Search# Gives output path having lowest cost  def best_first_search(source, target, n):    visited = [False] * n    visited = True    pq = PriorityQueue()    pq.put((0, source))    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 = 0target = 9best_first_search(source, target, v) # This code is contributed by Jyotheeswar Ganne
0 1 3 2 8 9 
Analysis : 
worst case time complexity for Best First Search is O(n * Log n) where n is number of nodes. In 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.
Performance of the algorithm depends on how well the cost or evaluation function is designed.
Special case of Best first search :
   1. Greedy Best first search algorithm
   2. A* search algorithm
Related Article: A* Search Algorithm This article is contributed by Shambhavi Singh. If you like GeeksforGeeks 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 GeeksforGeeks main page and help other Geeks. 
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