Memoization with fibonacci seq

src/memoization/README.md

@@ -0,0 +1,43 @@
+# Fibonacci Function
+
+This module provides a function to compute the nth Fibonacci number using memoization to optimize performance.
+
+## Function
+
+### `fibonacci(position: number): number`
+
+#### Description
+
+Computes the nth Fibonacci number using memoization to optimize performance.
+
+#### Parameters
+
+- `position` (number): The position in the Fibonacci sequence to compute. If a non-negative integer is provided, it will default to 0.
+
+#### Returns
+
+- `number`: The nth Fibonacci number.
+
+#### Example
+
+```typescript
+import { fibonacci } from './index'
+
+console.log(fibonacci(0)) // returns 0
+console.log(fibonacci(1)) // returns 1
+console.log(fibonacci(5)) // returns 5
+console.log(fibonacci(10)) // returns 55
+```
+
+## Usage
+
+1. Import the `fibonacci` function from the module.
+2. Call the function with the desired position in the Fibonacci sequence.
+
+## Notes
+
+- The function uses memoization to store previously computed Fibonacci numbers, which significantly improves performance for large values of `n`.
+
+## License
+
+This project is licensed under the MIT License.

src/memoization/index.ts

@@ -1,10 +1,24 @@
-const memo: { [key: number]: number } = {}
+const memo: number[] = []
 
-export const fibonacci = (n: number): number => {
-  if (n <= 0) return 0
-  if (n === 1) return 1
-  if (memo[n]) return memo[n]
+/**
+ * Computes the nth Fibonacci number using memoization to optimize performance.
+ *
+ * @param {number} n - The position in the Fibonacci sequence to compute. If a non-negative integer is provided, it will default to 0.
+ * @returns {number} - The nth Fibonacci number.
+ *
+ * @example
+ * ```typescript
+ * fibonacci(0); // returns 0
+ * fibonacci(1); // returns 1
+ * fibonacci(5); // returns 5
+ * fibonacci(10); // returns 55
+ * ```
+ */
+export const fibonacci = (position: number): number => {
+  if (position <= 0) return 0
+  if (position === 1) return 1
+  if (memo[position]) return memo[position]
 
-  memo[n] = fibonacci(n - 1) + fibonacci(n - 2)
-  return memo[n]
+  memo[position] = fibonacci(position - 1) + fibonacci(position - 2)
+  return memo[position]
 }