Merge pull request #2168 from Rey-han-24/main

feat: implement BFS solution for Jump Game III (#1306)

Author: hackdartstorm

exercises/1000_programs/medium/1306_jump_game_iii.py

@@ -0,0 +1,36 @@
+def canReach(arr: list[int], start: int) -> bool:
+    # 1. Initialize the queue with our starting position
+    queue = [start]
+    # 2. Keep track of visited indices so we don't get stuck in a loop
+    visited = set()
+    
+    while queue:
+        # Get the current position
+        curr = queue.pop(0)
+        
+        # SUCCESS: We found a zero!
+        if arr[curr] == 0:
+            return True
+            
+        # Mark current as visited
+        visited.add(curr)
+        
+        # Calculate possible jumps
+        for next_pos in [curr + arr[curr], curr - arr[curr]]:
+            # Check if the jump is within the array bounds and not visited
+            if 0 <= next_pos < len(arr) and next_pos not in visited:
+                queue.append(next_pos)
+                
+    # If the queue is empty and we never hit 0, it's impossible
+    return False
+
+# --- Test Cases ---
+if __name__ == "__main__":
+    # Test 1: Should be True (can reach index 5 or 6)
+    print(f"Test 1: {canReach([4,2,3,0,3,1,2], 5)}") 
+    
+    # Test 2: Should be True (start is already 0)
+    print(f"Test 2: {canReach([4,2,3,0,3,1,2], 0)}") 
+    
+    # Test 3: Should be False (cannot reach 0)
+    print(f"Test 3: {canReach([3,0,2,1,2], 2)}")