feat: Configure Vite proxy for API requests and update API URL to use a relative path.

frontend/src/api.js

@@ -1,6 +1,8 @@
 import axios from 'axios';
 
-const API_URL = 'http://localhost:8000';
+// Use relative path '/api' which works with Nginx proxy in Docker
+// and Vite proxy in local development
+const API_URL = '/api';
 
 export const generateCase = async (size, minVal, maxVal) => {
     const response = await axios.post(`${API_URL}/max_subarray/generate`, {

frontend/vite.config.js

@@ -4,4 +4,13 @@ import react from '@vitejs/plugin-react'
 // https://vitejs.dev/config/
 export default defineConfig({
   plugins: [react()],
+  server: {
+    proxy: {
+      '/api': {
+        target: 'http://localhost:8000',
+        changeOrigin: true,
+        rewrite: (path) => path.replace(/^\/api/, '')
+      }
+    }
+  }
 })