LeetCode 258 - Add Digits | C++ Solution | Digital Root Formula O(1)

✅ LeetCode 258 - Add Digits | Digital Root Math Trick | O(1) C++ Solution

🔥 Solve LeetCode 258 - Add Digits in CONSTANT TIME using the famous Digital Root formula — no loops needed!

📌 Problem Statement:
Given an integer num, repeatedly add all its digits until the result has only one digit, and return it.

🧩 What You'll Learn:
✔ What is Digital Root in mathematics
✔ Loop/Simulation approach (naive)
✔ O(1) Mathematical formula using modulo
✔ Why the formula (n-1)%9 + 1 works
✔ Time Complexity: O(1) | Space Complexity: O(1)

🛠️ Approach - Step by Step:
STEP 1 → If num == 0, return 0
STEP 2 → Digital root formula: 1 + (num - 1) % 9
STEP 3 → This is based on the property of numbers in base 10
STEP 4 → Every number's digital root cycles 1-9
STEP 5 → Handle special case num == 0 separately
STEP 6 → Return (num % 9 == 0) ? 9 : num % 9

⏱️ Timestamps:
0:00 - Problem Statement
1:00 - Naive Loop Simulation
2:30 - Digital Root Concept
4:00 - Mathematical Formula Derivation
6:00 - C++ O(1) Code
7:30 - Complexity Analysis

💻 Difficulty: Easy
🏷️ Topics: Math, Simulation, Number Theory

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Видео LeetCode 258 - Add Digits | C++ Solution | Digital Root Formula O(1) канала JALAK PALAN