Add Dijkstra's shortest path algorithm with example and README update

Algorithms/dijkstra.py

@@ -0,0 +1,44 @@
+import heapq
+
+def dijkstra(graph, start):
+    """
+    Dijkstra's algorithm to find shortest paths from start node to all other nodes.
+
+    Parameters:
+    graph : dict - adjacency list {node: [(neighbor, weight), ...]}
+    start : starting node
+
+    Returns:
+    distances : dict - shortest distance from start to each node
+    """
+
+    distances = {node: float('inf') for node in graph}
+    distances[start] = 0
+
+    priority_queue = [(0, start)]  # (distance, node)
+
+    while priority_queue:
+        current_distance, current_node = heapq.heappop(priority_queue)
+
+        if current_distance > distances[current_node]:
+            continue
+
+        for neighbor, weight in graph[current_node]:
+            distance = current_distance + weight
+
+            if distance < distances[neighbor]:
+                distances[neighbor] = distance
+                heapq.heappush(priority_queue, (distance, neighbor))
+
+    return distances
+
+# Example usage:
+if __name__ == "__main__":
+    graph = {
+        'A': [('B', 1), ('C', 4)],
+        'B': [('A', 1), ('C', 2), ('D', 5)],
+        'C': [('A', 4), ('B', 2), ('D', 1)],
+        'D': [('B', 5), ('C', 1)]
+    }
+    start_node = 'A'
+    print("Shortest distances:", dijkstra(graph, start_node))