/*
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 rand() outputs (rand() % 49):
12, 3, 40, 25, 7, 33
After adding +1 (because the code uses 1 + rand() % (n - 1)):
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 generate_random_sum(int $n, int $k): array {
if ($k <= 0 || $n < $k) {
// k positive integers must sum to n → minimum sum is k
throw new InvalidArgumentException("Invalid n or k");
}
$cuts = [];
// Generate (k - 1) random cut points in [1, n - 1]
for ($i = 0; $i < $k - 1; $i++) {
$cuts[] = random_int(1, $n - 1);
}
// Sort the cut points so we can compute segment lengths
sort($cuts);
$result = [];
$prev = 0;
// Convert cut points into segment lengths
foreach ($cuts as $c) {
$result[] = $c - $prev;
$prev = $c;
}
// Last segment: from last cut to n
$result[] = $n - $prev;
return $result;
}
$n = 50; // total sum
$k = 7; // number of random parts
$parts = generate_random_sum($n, $k);
echo "Random parts that sum to $n:\n";
foreach ($parts as $x) {
echo $x . " ";
}
echo "\n";
// Verify sum
echo "Sum = " . array_sum($parts) . "\n";
/*
run:
Random parts that sum to 50:
7 4 12 3 9 6 9
Sum = 50
*/
