Bi directional dijkstra (#7982)

* Added Bi-Directional Dijkstra

* Added Bi-Directional Dijkstra

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Added doctest and type hints

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Rename Bi_directional_Dijkstra.py to bi_directional_dijkstra.py

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update bi_directional_dijkstra.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

graphs/bi_directional_dijkstra.py

@@ -0,0 +1,130 @@
+"""
+Bi-directional Dijkstra's algorithm.
+
+A bi-directional approach is an efficient and
+less time consuming optimization for Dijkstra's
+searching algorithm
+
+Reference: shorturl.at/exHM7
+"""
+
+# Author: Swayam Singh (https://github.com/practice404)
+
+
+from queue import PriorityQueue
+from typing import Any
+
+import numpy as np
+
+
+def bidirectional_dij(
+    source: str, destination: str, graph_forward: dict, graph_backward: dict
+) -> int:
+    """
+    Bi-directional Dijkstra's algorithm.
+
+    Returns:
+        shortest_path_distance (int): length of the shortest path.
+
+    Warnings:
+        If the destination is not reachable, function returns -1
+
+    >>> bidirectional_dij("E", "F", graph_fwd, graph_bwd)
+    3
+    """
+    shortest_path_distance = -1
+
+    visited_forward = set()
+    visited_backward = set()
+    cst_fwd = {source: 0}
+    cst_bwd = {destination: 0}
+    parent_forward = {source: None}
+    parent_backward = {destination: None}
+    queue_forward: PriorityQueue[Any] = PriorityQueue()
+    queue_backward: PriorityQueue[Any] = PriorityQueue()
+
+    shortest_distance = np.inf
+
+    queue_forward.put((0, source))
+    queue_backward.put((0, destination))
+
+    if source == destination:
+        return 0
+
+    while queue_forward and queue_backward:
+        while not queue_forward.empty():
+            _, v_fwd = queue_forward.get()
+
+            if v_fwd not in visited_forward:
+                break
+        else:
+            break
+        visited_forward.add(v_fwd)
+
+        while not queue_backward.empty():
+            _, v_bwd = queue_backward.get()
+
+            if v_bwd not in visited_backward:
+                break
+        else:
+            break
+        visited_backward.add(v_bwd)
+
+        # forward pass and relaxation
+        for nxt_fwd, d_forward in graph_forward[v_fwd]:
+            if nxt_fwd in visited_forward:
+                continue
+            old_cost_f = cst_fwd.get(nxt_fwd, np.inf)
+            new_cost_f = cst_fwd[v_fwd] + d_forward
+            if new_cost_f < old_cost_f:
+                queue_forward.put((new_cost_f, nxt_fwd))
+                cst_fwd[nxt_fwd] = new_cost_f
+                parent_forward[nxt_fwd] = v_fwd
+            if nxt_fwd in visited_backward:
+                if cst_fwd[v_fwd] + d_forward + cst_bwd[nxt_fwd] < shortest_distance:
+                    shortest_distance = cst_fwd[v_fwd] + d_forward + cst_bwd[nxt_fwd]
+
+        # backward pass and relaxation
+        for nxt_bwd, d_backward in graph_backward[v_bwd]:
+            if nxt_bwd in visited_backward:
+                continue
+            old_cost_b = cst_bwd.get(nxt_bwd, np.inf)
+            new_cost_b = cst_bwd[v_bwd] + d_backward
+            if new_cost_b < old_cost_b:
+                queue_backward.put((new_cost_b, nxt_bwd))
+                cst_bwd[nxt_bwd] = new_cost_b
+                parent_backward[nxt_bwd] = v_bwd
+
+            if nxt_bwd in visited_forward:
+                if cst_bwd[v_bwd] + d_backward + cst_fwd[nxt_bwd] < shortest_distance:
+                    shortest_distance = cst_bwd[v_bwd] + d_backward + cst_fwd[nxt_bwd]
+
+        if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
+            break
+
+    if shortest_distance != np.inf:
+        shortest_path_distance = shortest_distance
+    return shortest_path_distance
+
+
+graph_fwd = {
+    "B": [["C", 1]],
+    "C": [["D", 1]],
+    "D": [["F", 1]],
+    "E": [["B", 1], ["G", 2]],
+    "F": [],
+    "G": [["F", 1]],
+}
+graph_bwd = {
+    "B": [["E", 1]],
+    "C": [["B", 1]],
+    "D": [["C", 1]],
+    "F": [["D", 1], ["G", 1]],
+    "E": [[None, np.inf]],
+    "G": [["E", 2]],
+}
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()