Maximize Eight-Dollar Shares without Giving Anyone Four
Company: MongoDB
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
Distribute all `money` dollars among `children` children. Each child must receive at least one dollar, and no child may receive exactly four dollars. Return the maximum number of children who can receive exactly eight dollars. Return `-1` if no valid distribution exists.
```cpp
class Solution {
public:
int distMoney(int money, int children);
};
```
### Examples
**Example 1:**
```text
Input: money = 10, children = 3
Output: 1
Explanation: Give the children 8, 1, and 1 dollars. Two eight-dollar shares already exceed the total.
```
**Example 2:**
```text
Input: money = 12, children = 2
Output: 0
Explanation: Giving one child 8 would leave the forbidden amount 4 for the other. Giving 6 to each child is valid.
```
### Constraints
- `1 <= money <= 200`.
- `2 <= children <= 30`.
### Clarifying Questions
- Can money be left over? No; all must be distributed.
- May a child get more than eight dollars? Yes.
- Is four dollars forbidden even when nobody gets eight? Yes.
- Does an answer of zero mean impossible? No; it means a valid distribution exists but none can give a child exactly eight.
```hint Check the boundary
Check the difference between leaving money undistributed and giving a child more than eight dollars.
```
Overview: Distribute all money while giving each child at least one dollar and never four, maximizing the number who receive exactly eight.