Sum of All Numbers in an Array (Recursive)¶

Description¶

Write a recursive function that takes an array of numbers and returns the sum of all its elements.

Approach 1: Recursion from End¶

• Time Complexity: O(n) - The function calls itself for each element in the array.
• Space Complexity: O(n) - Each function call adds a frame to the call stack.

This function works by breaking the problem down: the sum of an array is the last element plus the sum of the rest of the array. - Base Case: When the index reaches 0, it returns the first element. This is the base case that stops the recursion. - Recursive Step: For any other index, it returns the number at the current index plus the result of the recursive call for the subarray before it (index - 1).

function sumOfNNumbers(numbers: number[], index: number): number {
  // Base Case: If we're at the first element, just return it.
  if (index === 0) {
    return numbers[0];
  }

  // Recursive Step: Return the current element plus the sum of the elements before it.
  return numbers[index] + sumOfNNumbers(numbers, index - 1);
}

const test1 = [10, 2, 5, 10, 3];
console.log(sumOfNNumbers(test1, test1.length - 1)); // 30

const test2 = [1, 2, 3, 4, 5];
console.log(sumOfNNumbers(test2, test2.length - 1)); // 15