algorithm - Split a random value into four that sum up to it

Question

I have one value like 24, and I have four textboxes. How can I dynamically generate four values that add up to 24?

All the values must be integers and can't be negative, and the result cannot be 6, 6, 6, 6; they must be different like: 8, 2, 10, 4. (But 5, 6, 6, 7 would be okay.)

Answer 1

For your stated problem, it is possible to generate an array of all possible solutions and then pick one randomly. There are in fact 1,770 possible solutions.

var solutions = [[Int]]()

for i in 1...21 {
    for j in 1...21 {
        for k in 1...21 {
            let l = 24 - (i + j + k)
            if l > 0 && !(i == 6 && j == 6 && k == 6) {
                solutions.append([i, j, k, l])
            }
        }
    }
}

// Now generate 20 solutions
for _ in 1...20 {
    let rval = Int(arc4random_uniform(UInt32(solutions.count)))
    println(solutions[rval])
}

This avoids any bias at the cost of initial setup time and storage.

---

This could be improved by:

• Reducing storage space by only storing the first 3 numbers. The 4th one is always 24 - (sum of first 3)
• Reducing storage space by storing each solution as a single integer: (i * 10000 + j * 100 + k)
• Speeding up the generation of solutions by realizing that each loop doesn't need to go to 21.

---

Here is the solution that stores each solution as a single integer and optimizes the loops:

var solutions = [Int]()

for i in 1...21 {
    for j in 1...22-i {
        for k in 1...23-i-j {
            if !(i == 6 && j == 6 && k == 6) {
                solutions.append(i * 10000 + j * 100 + k)
            }
        }
    }
}

// Now generate 20 solutions
for _ in 1...20 {
    let rval = Int(arc4random_uniform(UInt32(solutions.count)))
    let solution = solutions[rval]

    // unpack the values
    let i = solution / 10000
    let j = (solution % 10000) / 100
    let k = solution % 100
    let l = 24 - (i + j + k)

    // print the solution
    println("([i, j, k, l])")
}