AlgoViz

Sum of First N Numbers

Easy

n plus the sum of everything below

Problem

Return the sum 1 + 2 + ... + N using recursion.

In simple words

Add n to the sum of the first n-1 numbers, bottoming out at 0.

The idea

sum(n) is n + sum(n-1), with sum(0) = 0. Trusting the recursive call to be correct for the smaller case is the mental move that makes recursion usable — you never need to unroll the whole thing in your head.

The trick

  • Base case sum(0) = 0.
  • The closed form n(n+1)/2 is O(1) — recursion here is for the lesson, not the speed.

This one walks through the worked example rather than tracing the algorithm frame by frame — a full walkthrough is still to be drawn. The code and the idea below are the real solution.

5
0

Step 1 of 2. Here's the example — n = 5 Values: 5.

1/2
Optimal
timeO(n)spaceO(n)
1f(n):2  if n==0: return 03  return n + f(n-1)

Input

array
[5]

Output

answer

Check yourself

3 quick questions about this walkthrough. A wrong answer costs nothing.

Examples

Example 1

Input:
n = 5
Output:
15
Explanation:
1+2+3+4+5 = 15.

Example 2

Input:
n = 10
Output:
55
Explanation:
1+...+10 = 55.

Example 3

Input:
n = 1
Output:
1
Explanation:
Just 1.

Practice this problem:GeeksforGeeks(opens in a new tab)

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