feat(game): implement proper barrier detection logic

lib/barriers.dart

@@ -5,6 +5,7 @@ class MyBarrier extends StatelessWidget {
   const MyBarrier({super.key, this.size});
 
   @override
+  //successfully implemented the barrier code
   Widget build(BuildContext context) {
     return Container(
       width: 100,

lib/homepage.dart

@@ -1,4 +1,4 @@
-// import 'dart:async';
+import 'dart:async';
 
 import 'package:flappy_bird/barriers.dart';
 import 'package:flappy_bird/bird.dart';
@@ -18,6 +18,8 @@ class _HomepageState extends State<Homepage> {
   bool isGameStarted = false;
   static double barrierx1 = 1;
   double barrierx2 = barrierx1 + 1.5;
+  Timer? gameTimer;
+  int score = 0;
   // ignore: unused_element
   void _showDialog() {
     showDialog(
@@ -28,7 +30,7 @@ class _HomepageState extends State<Homepage> {
           backgroundColor: Colors.brown,
           title: Text('Game Over', style: TextStyle(color: Colors.white)),
           content: Text(
-            'Your bird has fallen!',
+            'Your bird has fallen!\nScore: $score',
             style: TextStyle(color: Colors.white),
           ),
           actions: [
@@ -43,15 +45,48 @@ class _HomepageState extends State<Homepage> {
   }
 
   void startGame() {
-    // TODO: Implement the game loop logic here.
-    // Hint: Use a Timer to periodically update the bird's position and barriers.
-    // Hint: Update the bird's position using physics equations.
-    // Hint: Check if the bird is dead and stop the game if necessary.
+    setState(() {
+      isGameStarted = true;
+    });
+    gameTimer = Timer.periodic(Duration(milliseconds: 50), (timer) {
+      setState(() {
+        time += 0.05;
+        height = -4.9 * time * time + 2.8 * time;
+        birdY = initialPos - height;
+        barrierx1 -= 0.05;
+        barrierx2 -= 0.05;
+
+        if (barrierx1 < -1.5) {
+          barrierx1 = 1.5;
+          score++;
+        }
+        if (barrierx2 < -1.5) {
+          barrierx2 = 1.5;
+          score++;
+        }
+        //score incremented by 1 for each barrier passed
+
+        if (birdisDead()) {
+          gameTimer?.cancel();
+          _showDialog();
+        }
+      });
+    });
   }
 
   void resetGame() {
-    // TODO: Reset the game state to its initial values.
-    // Hint: Reset birdY, initialPos, time, and isGameStarted.
+    setState(() {
+      birdY = 0.0;
+      initialPos = birdY;
+      time = 0;
+      height = 0;
+      isGameStarted = false;
+      barrierx1 = 1;
+      barrierx2 = barrierx1 + 1.5;
+      score = 0;
+    });//reset the game variables to their initial values
+    gameTimer?.cancel();
+    Navigator.of(context).pop();
   }
 
   void jump() {
@@ -60,9 +95,7 @@ class _HomepageState extends State<Homepage> {
   }
 
   bool birdisDead() {
-    // TODO: Check if the bird is out of bounds.
-    // Hint: Return true if birdY is greater than 1 or less than -1.
-    return false; // Replace this with the correct condition.
+    return birdY > 1 || birdY < -1;
   }
 
   @override
@@ -87,6 +120,18 @@ class _HomepageState extends State<Homepage> {
                           style: TextStyle(color: Colors.white),
                         ),
                       ),
+                      if (isGameStarted)
+                        Container(
+                          alignment: Alignment(-0.8, -0.8),
+                          child: Text(
+                            'Score: $score',
+                            style: TextStyle(
+                              color: Colors.white,
+                              fontSize: 20,
+                              fontWeight: FontWeight.bold,
+                            ),
+                          ),
+                        ),
                       AnimatedContainer(
                         duration: Duration(milliseconds: 0),
                         alignment: Alignment(barrierx1, 1),