add php code

codes/php/chapter_computational_complexity/iteration.php

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+<?php
+/**
+ * File: iteration.php
+ * Created Time: 2025-11-06
+ * Author: Leo Mu (whatissrc@gmail.com)
+ */
+
+namespace chapter_computational_complexity;
+
+class iteration
+{
+    /* for 循环 */
+    public static function forLoop($n): int
+    {
+        $res = 0;
+        // 循环求和 1, 2, ..., n-1, n
+        for ($i = 1; $i <= $n; $i++) {
+            $res += $i;
+        }
+        return $res;
+    }
+
+    /* while 循环 */
+    public static function whileLoop($n): int
+    {
+        $res = 0;
+        $i = 1; // 初始化条件变量
+        // 循环求和 1, 2, ..., n-1, n
+        while ($i <= $n) {
+            $res += $i;
+            $i++; // 更新条件变量
+        }
+        return $res;
+    }
+
+    /* while 循环（两次更新） */
+    public static function whileLoopII($n): int
+    {
+        $res = 0;
+        $i = 1; // 初始化条件变量
+        // 循环求和 1, 4, 10, ...
+        while ($i <= $n) {
+            $res += $i;
+            // 更新条件变量
+            $i++;
+            $i *= 2;
+        }
+        return $res;
+    }
+
+    /* 双层 for 循环 */
+    public static function nestedForLoop($n): string
+    {
+        $res = '';
+        // 循环 i = 1, 2, ..., n-1, n
+        for ($i = 1; $i <= $n; $i++) {
+            // 循环 j = 1, 2, ..., n-1, n
+            for ($j = 1; $j <= $n; $j++) {
+                $res .= "($i, $j), ";
+            }
+        }
+        return $res;
+    }
+}
+
+/* Driver Code */
+$n = 5;
+
+$res = Iteration::forLoop($n);
+echo "\nfor 循环的求和结果 res = " . $res . "\n";
+
+$res = Iteration::whileLoop($n);
+echo "\nwhile 循环的求和结果 res = " . $res . "\n";
+
+$res = Iteration::whileLoopII($n);
+echo "\nwhile 循环（两次更新）求和结果 res = " . $res . "\n";
+
+$resStr = Iteration::nestedForLoop($n);
+echo "\n双层 for 循环的遍历结果 " . $resStr . "\n";

codes/php/chapter_computational_complexity/recursion.php

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+<?php
+/**
+ * File: recursion.php
+ * Created Time: 2025-11-06
+ * Author: Leo Mu (whatissrc@gmail.com)
+ */
+
+namespace chapter_computational_complexity;
+
+class recursion
+{
+    /* 递归 */
+    public static function recur(int $n): int
+    {
+        // 终止条件
+        if ($n == 1) {
+            return 1;
+        }
+        // 递：递归调用
+        $res = self::recur($n - 1);
+        // 归：返回结果
+        return $n + $res;
+    }
+
+    /* 使用迭代模拟递归 */
+    public static function forLoopRecur(int $n): int
+    {
+        // 使用一个显式的数组来模拟系统调用栈
+        $stack = [];
+        $res = 0;
+        // 递：递归调用
+        for ($i = $n; $i > 0; $i--) {
+            // 通过"入栈操作"模拟"递"
+            array_push($stack, $i);
+        }
+        // 归：返回结果
+        while (!empty($stack)) {
+            // 通过"出栈操作"模拟"归"
+            $res += array_pop($stack);
+        }
+        // res = 1+2+3+...+n
+        return $res;
+    }
+
+    /* 尾递归 */
+    public static function tailRecur(int $n, int $res): int
+    {
+        // 终止条件
+        if ($n == 0) {
+            return $res;
+        }
+        // 尾递归调用
+        return self::tailRecur($n - 1, $res + $n);
+    }
+
+    /* 斐波那契数列：递归 */
+    public static function fib(int $n): int
+    {
+        // 终止条件 f(1) = 0, f(2) = 1
+        if ($n == 1 || $n == 2) {
+            return $n - 1;
+        }
+        // 递归调用 f(n) = f(n-1) + f(n-2)
+        $res = self::fib($n - 1) + self::fib($n - 2);
+        // 返回结果 f(n)
+        return $res;
+    }
+
+
+}
+
+/* Driver Code */
+$n = 5;
+$res = 0;
+Recursion::recur($n);
+echo "\n递归函数的求和结果 res = {$res}\n";
+
+$res = Recursion::forLoopRecur($n);
+echo "\n使用迭代模拟递归求和结果 res = {$res}\n";
+
+$res = Recursion::tailRecur($n, 0);
+echo "\n尾递归函数的求和结果 res = {$res}\n";
+
+$res = Recursion::fib($n);
+echo "\n斐波那契数列的第 {$n} 项为 {$res}\n";

codes/php/chapter_computational_complexity/space_complexity.php

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+<?php
+/**
+ * File: space_complexity.php
+ * Created Time: 2025-11-06
+ * Author: Leo Mu (whatissrc@gmail.com)
+ */
+
+namespace chapter_computational_complexity;
+class space_complexity
+{
+    /* 函数 */
+    public static function functionMethod(): int
+    {
+        // 执行某些操作
+        return 0;
+    }
+
+    /* 常数阶 */
+    public static function constant(int $n): void
+    {
+        // 常量、变量、对象占用 O(1) 空间
+        $a = 0;
+        $b = 0;
+        $nums = array_fill(0, 10000, 0);
+        // 循环中的变量占用 O(1) 空间
+        for ($i = 0; $i < $n; $i++) {
+            $c = 0;
+        }
+        // 循环中的函数占用 O(1) 空间
+        for ($i = 0; $i < $n; $i++) {
+            self::functionMethod();
+        }
+    }
+
+    /* 线性阶 */
+    public static function linear(int $n): void
+    {
+        // 长度为 n 的数组占用 O(n) 空间
+        $nums = array_fill(0, $n, 0);
+        // 长度为 n 的列表占用 O(n) 空间
+        $nodes = [];
+        for ($i = 0; $i < $n; $i++) {
+            $nodes[] = ['val' => $i];
+        }
+        // 长度为 n 的哈希表占用 O(n) 空间
+        $map = [];
+        for ($i = 0; $i < $n; $i++) {
+            $map[$i] = strval($i);
+        }
+    }
+
+    /* 线性阶（递归实现）*/
+    public static function linearRecur(int $n): void
+    {
+        echo "递归 n = " . $n . "\n";
+        if ($n == 1) {
+            return;
+        }
+        self::linearRecur($n - 1);
+    }
+
+    /* 平方阶 */
+    public static function quadratic(int $n): void
+    {
+        // 矩阵占用 O(n^2) 空间
+        $numMatrix = [];
+        for ($i = 0; $i < $n; $i++) {
+            $numMatrix[$i] = array_fill(0, $n, 0);
+        }
+        // 二维列表占用 O(n^2) 空间
+        $numList = [];
+        for ($i = 0; $i < $n; $i++) {
+            $tmp = [];
+            for ($j = 0; $j < $n; $j++) {
+                $tmp[] = 0;
+            }
+            $numList[] = $tmp;
+        }
+    }
+
+    /* 平方阶（递归实现） */
+    public static function quadraticRecur(int $n): int
+    {
+        if ($n <= 0) {
+            return 0;
+        }
+        // 数组 nums 长度为 n, n-1, ..., 2, 1
+        $nums = array_fill(0, $n, 0);
+        echo "递归 n = " . $n . " 中的 nums 长度 = " . count($nums) . "\n";
+        return self::quadraticRecur($n - 1);
+    }
+
+    /* 指数阶（建立满二叉树）*/
+    public static function buildTree(int $n)
+    {
+        if ($n == 0) {
+            return null;
+        }
+        $root = ['val' => 0, 'left' => null, 'right' => null];
+        $root['left'] = self::buildTree($n - 1);
+        $root['right'] = self::buildTree($n - 1);
+        return $root;
+    }
+}
+
+/* Driver Code */
+$n = 5;
+// 常数阶
+space_complexity::constant($n);
+// 线性阶
+space_complexity::linear($n);
+space_complexity::linearRecur($n);
+// 平方阶
+space_complexity::quadratic($n);
+space_complexity::quadraticRecur($n);
+// 指数阶
+$root = space_complexity::buildTree($n);
+echo "指数阶（建立满二叉树）完成\n";