Wednesday, February 11, 2026

A Special Number - Sum of whose digits is divisible by 4 (Super Easy)

Index of "Algorithms: Design and Analysis"
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Problem
    
A number 
 is said to be special if the sum of its digits is divisible by 4.

For a given integer 
, find a number 
 such that:

 is a special number
 is minimum possible
Input format

The first line contains an integer 
 denoting the number of test cases.
For each test case:
The first line contains an integer 
.
Output format

For each test case, print a number 
 that satisfies the above conditions in a new line.

Constraints


 

Sample Input
2
432
99
Sample Output
435
103
Time Limit: 1
Memory Limit: 256
Source Limit:
Explanation
For first test case:

n = 435, sum of digits is 12 which is divisible by 4.
For second test case:

n = 103, sum of digits is 4 which is divisible by 4.

My Code

def solve(n):
    found = False
    while not found:
        s = sum(map(int, str(n)))
        if s % 4 == 0:
            found = True
            return n
        n += 1

T = int(input())

for _ in range(T):
    n = int(input())
    out_ = solve(n)
    print (out_)

ChatGPT's Thoughts

User: Explain the solution to this problem in layman terms. Give clear descriptions of what this problem is trying to teach/assess, what design pattern, what problem solving trick/technique.

Let’s break this down very clearly and simply.

🧩 What is the problem asking?

A number is special if:

The sum of its digits is divisible by 4.

You are given a number a.

You must find a number n such that:

n ≥ a
Sum of digits of n is divisible by 4
n is the smallest possible number satisfying the above

🧠 What is this problem really testing?

This problem tests:

1️⃣ Digit manipulation

You must calculate sum of digits.

2️⃣ Divisibility property

You must check if sum % 4 == 0.

3️⃣ Greedy / incremental search

You start from a and move upward until you find the first valid number.

4️⃣ Observational reasoning

Since a ≤ 1000, brute force is perfectly safe.

🎯 Key Insight

If a number is not valid, just check the next number.

Why is this safe?

Because:

Maximum a is only 1000
At worst you check 3 numbers ahead
Within 4 consecutive numbers, one will satisfy divisibility by 4 (because modulo cycles)

So this is a simple linear scan problem.

🔍 Step-by-step in Layman Terms

Suppose:

ini
a = 432

Sum of digits:


4 + 3 + 2 = 9

9 is NOT divisible by 4.

Try next:


433 → 4+3+3 = 10

Not divisible by 4.


434 → 11

Not divisible by 4.


435 → 12

12 % 4 = 0 ✅

So answer = 435.

🧠 Why this works quickly

Because divisibility by 4 depends only on:

bash
(sum of digits) % 4

And modulo cycles every 4 increments.

So you'll find answer in at most 3–4 steps.

🧠 What Design Pattern Is Used?

This is:

✔ Brute Force with Small Constraints

✔ Incremental Search (Greedy Forward Scan)

You stop as soon as condition becomes true.

🧠 What Trick Is Being Used?

The trick is:

Instead of trying to construct digits, just check numbers one by one.

Because constraints are small.

This is a classic competitive programming lesson:

Always check constraints before overthinking.

🧠 Time Complexity

Worst case:

Check 3–4 numbers per test case

If T = 10⁵
Total operations ≈ 4 × 10⁵ → very fast.

Time complexity: O(T)

💡 Summary of What This Problem Teaches

Digit sum manipulation
Modulo arithmetic
Greedy thinking
Recognizing small constraints allow brute force
Don’t over-engineer simple problems

If you want, I can now:

Show optimized mathematical reasoning (without loop)
Provide Python code
Show why answer always exists within 4 steps
Or convert this into an interview-style explanation 😊

survival8

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