/*
Generate k random positive integers that sum to n.
Algorithm (stick-breaking / random composition):
------------------------------------------------
1. We choose (k - 1) random "cut points" in the range [1, n - 1].
These represent where we "break" the integer n into k parts.
2. Sort the cut points.
3. Compute the differences between consecutive points
(including 0 and n as boundaries). These differences
are the k positive integers that sum to n.
This produces a uniformly random composition of n.
*/
/*
Paper Run (Dry Run) of the Random-Sum Program
---------------------------------------------
Input:
n = 50
k = 7
We need (k - 1) = 6 random cut points in the range [1, 49].
Simulated random outputs (Math.random() * 49):
12, 3, 40, 25, 7, 33
After adding +1 (because the code uses 1 + random):
cuts = {13, 4, 41, 26, 8, 34}
Step 1: Sort the cut points
cuts → {4, 8, 13, 26, 34, 41}
Step 2: Convert cut points into segment lengths
prev = 0
out[0] = 4 - 0 = 4
prev = 4
out[1] = 8 - 4 = 4
prev = 8
out[2] = 13 - 8 = 5
prev = 13
out[3] = 26 - 13 = 13
prev = 26
out[4] = 34 - 26 = 8
prev = 34
out[5] = 41 - 34 = 7
prev = 41
out[6] = 50 - 41 = 9 (final segment)
Final result:
parts = {4, 4, 5, 13, 8, 7, 9}
Verification:
4 + 4 + 5 + 13 + 8 + 7 + 9 = 50
Output:
Random parts that sum to 50:
4 4 5 13 8 7 9
Sum = 50
*/
function generateRandomSum(n: number, k: number): number[] {
if (k <= 0 || n < k) {
// k positive integers must sum to n → minimum sum is k
throw new Error("Invalid n or k");
}
const cuts: number[] = [];
// Generate (k - 1) random cut points in [1, n - 1]
for (let i: number = 0; i < k - 1; i++) {
const cut: number = 1 + Math.floor(Math.random() * (n - 1));
cuts.push(cut);
}
// Sort the cut points so we can compute segment lengths
cuts.sort((a: number, b: number) => a - b);
const result: number[] = [];
let prev: number = 0;
// Convert cut points into segment lengths
for (const c of cuts) {
result.push(c - prev);
prev = c;
}
// Last segment: from last cut to n
result.push(n - prev);
return result;
}
// Main execution
const n: number = 50; // total sum
const k: number = 7; // number of random parts
const parts: number[] = generateRandomSum(n, k);
console.log(`Random parts that sum to ${n}:`);
console.log(parts.join(" "));
// Verify sum
const sum: number = parts.reduce((a: number, b: number) => a + b, 0);
console.log("Sum =", sum);
/*
run:
Random parts that sum to 50:
8 4 0 10 11 3 14
Sum = 50
*/
