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en/articles/from-tg/series/algorithm-complexity/o-n3.md
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O(n³) — cubic complexity
Things are getting really serious now. Algorithms with O(n³) use three nested loops. This means that as the data grows, the execution time grows cubically.
Example: multiplying two matrices
function matrixMultiplication($matrixA, $matrixB) {
$rowsA = count($matrixA);
$colsA = count($matrixA[0]);
$colsB = count($matrixB[0]);
$result = [];
for ($i = 0; $i < $rowsA; $i++) {
for ($j = 0; $j < $colsB; $j++) {
$result[$i][$j] = 0;
for ($k = 0; $k < $colsA; $k++) {
$result[$i][$j] += $matrixA[$i][$k] * $matrixB[$k][$j];
}
}
}
return $result;
}
Sounds academic, but it happens more often than you'd think: in calculations, graph building, searching for combinations. Anything that needs to compare triples of data or three-dimensional structures is a candidate for O(n³).
This is a critical point already. If you can avoid code like this — avoid it. You can often find ways to bring it down to O(n²) or even O(n log n).
First published in Ukrainian in the Telegram channel “Created to die” on June 25, 2025.