CODING JOURNEY DAY 2

🚀 Day 2 of My Coding Journey | GeeksforGeeks

Hello developers 👋
This is Sabarish M S from Government College of Engineering, Salem, Tamil Nadu, India 🇮🇳.
Continuing my coding journey with GeeksforGeeks, here’s my Day 2 progress.

🔹 Problem Statement

You are given two very large integers in the form of strings:

a → base

b → exponent

Your task is to find the last digit of aᵇ.

🔹 Examples

Input:
a = "3", b = "10"
Output:
9
Explanation:
3¹⁰ = 59049 → last digit is 9

Input:
a = "6", b = "2"
Output:
6
Explanation:
6² = 36 → last digit is 6

🔹 Constraints

1 ≤ |a|, |b| ≤ 1000

a and b are very large, so they cannot be converted to integers

🔹 Key Insight (Mathematical Optimization)

The last digit of powers repeats in cycles of 4.

For example:

2 → 2, 4, 8, 6 (cycle length = 4)

3 → 3, 9, 7, 1

7 → 7, 9, 3, 1

So instead of calculating aᵇ, we only need:

👉 last digit of a
👉 b % 4

🔹** Solution Approach**

Handle base cases:

If b = "0" → result is 1

If a = "0" → result is 0

Extract the last digit of a

Compute b % 4 manually (since b is a string)

If b % 4 == 0, treat it as 4

Compute power manually (no Math.pow)

Return result % 10

🔹 Why This Approach?

✅ Handles very large numbers
✅ Avoids overflow
✅ No floating-point operations
✅ Interview-friendly logic
✅ Time Complexity: O(|b|)
✅ Space Complexity: O(1)

🔹 What I Learned Today

How to work with huge numbers using strings

Importance of pattern recognition in math problems

Why optimization matters more than brute force

How interviewers expect logic over libraries