Minimize coins with overpay and change
Company: Snowflake
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Technical Screen
You have an unlimited number of coins with denominations:
- `1, 5, 10, 50, 100, 200`
You need to pay exactly `n` units to another person. You are allowed to **overpay**, and the other person will always be able to give you **exact change** (they also have unlimited coins).
Define the **total coins used** as:
- the number of coins you give to pay, **plus**
- the number of coins you receive back as change.
Return the **minimum possible total number of coins** needed to complete the transaction.
### Input
- A single integer `n`.
### Output
- A single integer: the minimum total number of coins exchanged.
### Example
**Input:**
```
41
```
**Output:**
```
3
```
**Explanation:** Pay `50 + 1` (2 coins) and receive `10` as change (1 coin), total `2 + 1 = 3`.
### Constraints
- Assume `0 ≤ n ≤ 10^9`.
- Both payer and receiver have unlimited coins of each denomination.
Quick Answer: This question evaluates algorithmic optimization and combinatorial reasoning in the coin-change domain, measuring proficiency with efficient numeric manipulation, counting strategies, and handling of fixed coin denominations.
You have an unlimited number of coins with denominations 1, 5, 10, 50, 100, and 200. You need to pay exactly n units to another person. You are allowed to overpay, and the other person can always give you exact change using the same coin denominations.
The total number of coins used is:
- the number of coins you give, plus
- the number of coins you receive back as change.
Return the minimum possible total number of coins exchanged.
Constraints
- 0 <= n <= 10^9
- Both payer and receiver have unlimited coins of denominations 1, 5, 10, 50, 100, 200
Examples
Input: (0,)
Expected Output: 0
Explanation: No payment is needed, so no coins are exchanged.
Input: (41,)
Expected Output: 3
Explanation: Pay 51 using coins 50 + 1 (2 coins) and receive 10 as change (1 coin), for a total of 3.
Input: (49,)
Expected Output: 2
Explanation: Pay 50 with one coin and receive 1 as change with one coin, total 2.
Input: (159,)
Expected Output: 4
Explanation: Pay 160 using 100 + 50 + 10 (3 coins) and receive 1 as change (1 coin), total 4.