How do you test code that uses performance and backtracking?

Testing code that utilizes performance and backtracking can be challenging, but it is essential for ensuring efficiency and correctness in algorithms. One effective approach is to analyze the algorithm's time and space complexity, and use profiling tools or custom benchmarks to assess performance. Additionally, unit tests can help validate the functionality of the backtracking logic.

Here’s an example of a simple backtracking algorithm in PHP that solves the N-Queens problem, along with a way to test its performance:


        <?php
        function solveNQueens($n) {
            $board = array_fill(0, $n, array_fill(0, $n, '.'));
            $result = [];
            backtrack($board, 0, $n, $result);
            return $result;
        }

        function backtrack(&$board, $row, $n, &$result) {
            if ($row == $n) {
                $result[] = array_map('implode', $board);
                return;
            }
            for ($col = 0; $col < $n; $col++) {
                if (isSafe($board, $row, $col, $n)) {
                    $board[$row][$col] = 'Q';
                    backtrack($board, $row + 1, $n, $result);
                    $board[$row][$col] = '.'; // backtrack
                }
            }
        }

        function isSafe($board, $row, $col, $n) {
            // Check the column and the diagonals
            for ($i = 0; $i < $row; $i++) {
                if ($board[$i][$col] == 'Q') {
                    return false;
                }
            }
            for ($i = $row - 1, $j = $col - 1; $i >= 0 && $j >= 0; $i--, $j--) {
                if ($board[$i][$j] == 'Q') {
                    return false;
                }
            }
            for ($i = $row - 1, $j = $col + 1; $i >= 0 && $j < $n; $i--, $j++) {
                if ($board[$i][$j] == 'Q') {
                    return false;
                }
            }
            return true;
        }

        // Performance Test
        $start = microtime(true);
        $result = solveNQueens(8);
        $end = microtime(true);
        echo "Solved in: " . ($end - $start) . " seconds";
        ?>

How do you test code that uses performance and backtracking?

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How do you test code that uses performance and backtracking?

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