docs: English JsonRpcBundle docs, REST and MCP Bundle sections, package cards
en/articles/from-tg/series/algorithm-complexity/o-n3.md
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# O(n³) — cubic complexity
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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.
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## Example: multiplying two matrices
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```php
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function matrixMultiplication($matrixA, $matrixB) {
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$rowsA = count($matrixA);
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$colsA = count($matrixA[0]);
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$colsB = count($matrixB[0]);
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$result = [];
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for ($i = 0; $i < $rowsA; $i++) {
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for ($j = 0; $j < $colsB; $j++) {
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$result[$i][$j] = 0;
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for ($k = 0; $k < $colsA; $k++) {
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$result[$i][$j] += $matrixA[$i][$k] * $matrixB[$k][$j];
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}
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}
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}
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return $result;
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}
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```
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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).
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:::warning
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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).
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:::
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← [Previous: O(n²) — quadratic complexity](/articles/from-tg/series/algorithm-complexity/o-n2) · [Whole series](/articles/from-tg/series/algorithm-complexity) · [Next: O(2ⁿ) — exponential complexity →](/articles/from-tg/series/algorithm-complexity/o-2n)
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---
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*First published in Ukrainian in the Telegram channel [“Created to die”](https://t.me/php_while_true/45) on June 25, 2025.*