Dijkstra's Algorithm — VisualAlgorithms Docs

How it works

Dijkstra's algorithm grows a set of finalized nodes outward from the start, always finalizing the unvisited node with the smallest known distance next (using a priority queue). It relaxes each neighbour's tentative distance as it goes.

On a grid with non-negative weights it finds the true lowest-cost path, generalizing BFS to weighted terrain.

Implementation

      
 function dijkstraPathfind(grid, start, end, allowDiag) {
  const rows = grid.length;
  const cols = grid[0].length;
  const dist = Matrix(rows, cols, Infinity);
  const visited = new Set();
  const prev = new Map();
  const heap = PriorityQueue("priority");
  dist[start[0]][start[1]] = 0;
  priorityQueuePush(heap, {
    priority: 0,
    row: start[0],
    col: start[1]
  });
  while (priorityQueueSize(heap)) {
    const __pattern1 = priorityQueuePop(heap);
    const cr = __pattern1.row;
    const cc = __pattern1.col;
    const currentKey = key(cr, cc);
    if (visited.has(currentKey)) continue;
    visited.add(currentKey);
    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;
      const nd = dist[cr][cc] + stepCost(grid, cr, cc, nr, nc);
      if (nd < dist[nr][nc]) {
        dist[nr][nc] = nd;
        prev.set(neighborKey, [cr, cc]);
        priorityQueuePush(heap, {
          priority: nd,
          row: nr,
          col: nc
        });
        pushFrontier(nr, nc);
      }
    }
  }
  reportNoPath();
} def dijkstraPathfind(grid, start, end, allowDiag):
    rows = grid.length
    cols = grid[0].length
    dist = Matrix(rows, cols, Infinity)
    visited = Set()
    prev = Map()
    heap = PriorityQueue("priority")
    dist[start[0]][start[1]] = 0
    priorityQueuePush(heap, {priority: 0, row: start[0], col: start[1]})
    while priorityQueueSize(heap):
        __pattern1 = priorityQueuePop(heap)
        cr = __pattern1.row
        cc = __pattern1.col
        currentKey = key(cr, cc)
        if visited.has(currentKey):
            continue
        visited.add(currentKey)
        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
            nd = (dist[cr][cc] + stepCost(grid, cr, cc, nr, nc))
            if (nd < dist[nr][nc]):
                dist[nr][nc] = nd
                prev.set(neighborKey, [cr, cc])
                priorityQueuePush(heap, {priority: nd, row: nr, col: nc})
                pushFrontier(nr, nc)
    reportNoPath() #include <vector>
#include <algorithm>
void dijkstraPathfind(int grid, int start, int end, int allowDiag) {
    auto rows = grid.length;
    auto cols = grid[0].length;
    auto dist = Matrix(rows, cols, Infinity);
    auto visited = Set();
    auto prev = Map();
    auto heap = PriorityQueue("priority");
    dist[start[0]][start[1]] = 0;
    priorityQueuePush(heap, {priority: 0, row: start[0], col: start[1]});
    while(priorityQueueSize(heap)) {
        auto __pattern1 = priorityQueuePop(heap);
        auto cr = __pattern1.row;
        auto cc = __pattern1.col;
        auto currentKey = key(cr, cc);
        if(visited.has(currentKey)) {
            continue;
        }
        visited.add(currentKey);
        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;
            }
            auto nd = (dist[cr][cc] + stepCost(grid, cr, cc, nr, nc));
            if((nd < dist[nr][nc])) {
                dist[nr][nc] = nd;
                prev.set(neighborKey, [cr, cc]);
                priorityQueuePush(heap, {priority: nd, row: nr, col: nc});
                pushFrontier(nr, nc);
            }
        }
    }
    reportNoPath();
} public void dijkstraPathfind(int grid, int start, int end, int allowDiag) {
    var rows = grid.length;
    var cols = grid[0].length;
    var dist = Matrix(rows, cols, Infinity);
    var visited = Set();
    var prev = Map();
    var heap = PriorityQueue("priority");
    dist[start[0]][start[1]] = 0;
    priorityQueuePush(heap, {priority: 0, row: start[0], col: start[1]});
    while(priorityQueueSize(heap)) {
        var __pattern1 = priorityQueuePop(heap);
        var cr = __pattern1.row;
        var cc = __pattern1.col;
        var currentKey = key(cr, cc);
        if(visited.has(currentKey)) {
            continue;
        }
        visited.add(currentKey);
        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;
            }
            var nd = (dist[cr][cc] + stepCost(grid, cr, cc, nr, nc));
            if((nd < dist[nr][nc])) {
                dist[nr][nc] = nd;
                prev.set(neighborKey, [cr, cc]);
                priorityQueuePush(heap, {priority: nd, row: nr, col: nc});
                pushFrontier(nr, nc);
            }
        }
    }
    reportNoPath();
} #include <stdio.h>
void dijkstraPathfind(int grid, int start, int end, int allowDiag) {
    var rows = grid.length;
    var cols = grid[0].length;
    var dist = Matrix(rows, cols, Infinity);
    var visited = Set();
    var prev = Map();
    var heap = PriorityQueue("priority");
    dist[start[0]][start[1]] = 0;
    priorityQueuePush(heap, {priority: 0, row: start[0], col: start[1]});
    while(priorityQueueSize(heap)) {
        var __pattern1 = priorityQueuePop(heap);
        var cr = __pattern1.row;
        var cc = __pattern1.col;
        var currentKey = key(cr, cc);
        if(visited.has(currentKey)) {
            continue;
        }
        visited.add(currentKey);
        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;
            }
            var nd = (dist[cr][cc] + stepCost(grid, cr, cc, nr, nc));
            if((nd < dist[nr][nc])) {
                dist[nr][nc] = nd;
                prev.set(neighborKey, [cr, cc]);
                priorityQueuePush(heap, {priority: nd, row: nr, col: nc});
                pushFrontier(nr, nc);
            }
        }
    }
    reportNoPath();
} 

Advantages

Finds the optimal lowest-cost path on graphs with non-negative weights.
Handles weighted terrain that BFS cannot.

Disadvantages

Expands in all directions without goal awareness, so it visits more nodes than A*.
Does not support negative edge weights.

When to use it

Use it for weighted shortest paths when you have no admissible heuristic; add a heuristic and it becomes A*.