Breadth-First Search — VisualAlgorithms Docs

How it works

Breadth-First Search explores the grid in expanding rings: it visits every neighbour of the start, then every neighbour of those, and so on, using a FIFO queue. The first time it reaches the goal it has found a shortest path in terms of number of steps.

Because it expands uniformly in all directions, BFS guarantees the fewest-edges path on an unweighted grid.

Implementation

      
 function bfsPathfind(grid, start, end, allowDiag) {
  const visited = new Set([key(start[0], start[1])]);
  const prev = new Map();
  const queue = [[start[0], start[1]]];
  while (queue.length) {
    const __pattern1 = queue.shift();
    const cr = __pattern1[0];
    const cc = __pattern1[1];
    visitNode(cr, cc);
    if (cr === end[0] && cc === end[1]) {
      reconstructPath(prev, start, end);
      return;
    }
    for (const [nr, nc] of getNeighbors(grid, cr, cc, allowDiag)) {
      const neighborKey = key(nr, nc);
      if (visited.has(neighborKey)) continue;
      visited.add(neighborKey);
      prev.set(neighborKey, [cr, cc]);
      queue.push([nr, nc]);
      pushFrontier(nr, nc);
    }
  }
  reportNoPath();
} def bfsPathfind(grid, start, end, allowDiag):
    visited = Set([key(start[0], start[1])])
    prev = Map()
    queue = [[start[0], start[1]]]
    while queue.length:
        __pattern1 = queue.shift()
        cr = __pattern1[0]
        cc = __pattern1[1]
        visitNode(cr, cc)
        if ((cr == end[0]) and (cc == end[1])):
            reconstructPath(prev, start, end)
            return
        for nr, nc in getNeighbors(grid, cr, cc, allowDiag):
            neighborKey = key(nr, nc)
            if visited.has(neighborKey):
                continue
            visited.add(neighborKey)
            prev.set(neighborKey, [cr, cc])
            queue.push([nr, nc])
            pushFrontier(nr, nc)
    reportNoPath() #include <vector>
#include <algorithm>
void bfsPathfind(int grid, int start, int end, int allowDiag) {
    auto visited = Set([key(start[0], start[1])]);
    auto prev = Map();
    auto queue = [[start[0], start[1]]];
    while(queue.length) {
        auto __pattern1 = queue.shift();
        auto cr = __pattern1[0];
        auto cc = __pattern1[1];
        visitNode(cr, cc);
        if(((cr == end[0]) && (cc == end[1]))) {
            reconstructPath(prev, start, end);
            return;
        }
        for(auto& [nr, nc] : getNeighbors(grid, cr, cc, allowDiag)) {
            auto neighborKey = key(nr, nc);
            if(visited.has(neighborKey)) {
                continue;
            }
            visited.add(neighborKey);
            prev.set(neighborKey, [cr, cc]);
            queue.push([nr, nc]);
            pushFrontier(nr, nc);
        }
    }
    reportNoPath();
} public void bfsPathfind(int grid, int start, int end, int allowDiag) {
    var visited = Set([key(start[0], start[1])]);
    var prev = Map();
    var queue = [[start[0], start[1]]];
    while(queue.length) {
        var __pattern1 = queue.shift();
        var cr = __pattern1[0];
        var cc = __pattern1[1];
        visitNode(cr, cc);
        if(((cr == end[0]) && (cc == end[1]))) {
            reconstructPath(prev, start, end);
            return;
        }
        foreach(var (nr, nc) in getNeighbors(grid, cr, cc, allowDiag)) {
            var neighborKey = key(nr, nc);
            if(visited.has(neighborKey)) {
                continue;
            }
            visited.add(neighborKey);
            prev.set(neighborKey, [cr, cc]);
            queue.push([nr, nc]);
            pushFrontier(nr, nc);
        }
    }
    reportNoPath();
} #include <stdio.h>
void bfsPathfind(int grid, int start, int end, int allowDiag) {
    var visited = Set([key(start[0], start[1])]);
    var prev = Map();
    var queue = [[start[0], start[1]]];
    while(queue.length) {
        var __pattern1 = queue.shift();
        var cr = __pattern1[0];
        var cc = __pattern1[1];
        visitNode(cr, cc);
        if(((cr == end[0]) && (cc == end[1]))) {
            reconstructPath(prev, start, end);
            return;
        }
        for(int _fod_i = 0; _fod_i < getNeighbors(grid, cr, cc, allowDiag)_len; _fod_i++) {
            int nr = getNeighbors(grid, cr, cc, allowDiag)[_fod_i][0];
            int nc = getNeighbors(grid, cr, cc, allowDiag)[_fod_i][1];
            var neighborKey = key(nr, nc);
            if(visited.has(neighborKey)) {
                continue;
            }
            visited.add(neighborKey);
            prev.set(neighborKey, [cr, cc]);
            queue.push([nr, nc]);
            pushFrontier(nr, nc);
        }
    }
    reportNoPath();
} 

Advantages

Guarantees the shortest path on unweighted grids.
Simple, predictable, and complete — it always finds a path if one exists.

Disadvantages

Ignores edge weights, so it is not suitable for weighted terrain.
Explores many cells; A* is far more focused when a heuristic is available.

When to use it

Use BFS for shortest paths on uniform-cost grids, flood fills, and reachability checks.