From 422694cf2c9b10b9d22f483e49e9a56550fa7ca6 Mon Sep 17 00:00:00 2001
From: DoWake <298666015@qq.com>
Date: Sun, 19 May 2024 22:42:06 +0800
Subject: [PATCH] feat: Add PHP Codes for chapter_computational_complexity

---
 .../iteration.php                             |  76 ++++++++
 .../recursion.php                             |  80 ++++++++
 .../space_complexity.php                      | 117 +++++++++++
 .../time_complexity.php                       | 184 ++++++++++++++++++
 .../worst_best_time_complexity.php            |  42 ++++
 5 files changed, 499 insertions(+)
 create mode 100644 codes/php/chapter_computational_complexity/iteration.php
 create mode 100644 codes/php/chapter_computational_complexity/recursion.php
 create mode 100644 codes/php/chapter_computational_complexity/space_complexity.php
 create mode 100644 codes/php/chapter_computational_complexity/time_complexity.php
 create mode 100644 codes/php/chapter_computational_complexity/worst_best_time_complexity.php

diff --git a/codes/php/chapter_computational_complexity/iteration.php b/codes/php/chapter_computational_complexity/iteration.php
new file mode 100644
index 000000000..14c880a65
--- /dev/null
+++ b/codes/php/chapter_computational_complexity/iteration.php
@@ -0,0 +1,76 @@
+<?php
+
+/**
+ * File: iteration.php
+ * Created Time: 2024-05-19
+ * Author: DoWake (admin@mengxing.cc)
+ */
+
+/* for 循环 */
+function forLoop($n)
+{
+  $res = 0;
+  // 循环求和 1, 2, ..., n-1, n
+  for ($i = 1; $i <= $n; $i++) {
+    $res += $i;
+  }
+  return $res;
+}
+
+/* while 循环 */
+function whileLoop($n)
+{
+  $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 $res;
+}
+
+/* while 循环（两次更新） */
+function whileLoopII($n)
+{
+  $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 $res;
+}
+
+/* 双层 for 循环 */
+function nestedForLoop($n)
+{
+  $res = '';
+  // 循环 i = 1, 2, ..., n-1, n
+  for ($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;
+$res = 0;
+
+$res = forLoop($n);
+echo "\nfor 循环的求和结果 res = {$res}" . PHP_EOL;
+
+$res = whileLoop($n);
+echo "\nwhile 循环的求和结果 res = {$res}" . PHP_EOL;
+
+$res = whileLoopII($n);
+echo "\nwhile 循环（两次更新）求和结果 res = {$res}" . PHP_EOL;
+
+$resStr = nestedForLoop($n);
+echo "\n双层 for 循环的遍历结果 {$resStr}" . PHP_EOL;
diff --git a/codes/php/chapter_computational_complexity/recursion.php b/codes/php/chapter_computational_complexity/recursion.php
new file mode 100644
index 000000000..b297ace87
--- /dev/null
+++ b/codes/php/chapter_computational_complexity/recursion.php
@@ -0,0 +1,80 @@
+<?php
+
+/**
+ * File: recursion.php
+ * Created Time: 2024-05-19
+ * Author: DoWake (admin@mengxing.cc)
+ */
+
+/* 递归 */
+function recur($n)
+{
+  // 终止条件
+  if ($n === 1) {
+    return 1;
+  }
+  // 递：递归调用
+  $res = recur($n - 1);
+  // 归：返回结果
+  return $n + $res;
+}
+
+/* 使用迭代模拟递归 */
+function forLoopRecur($n)
+{
+  // 使用一个显式的栈来模拟系统调用栈
+  $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 $res;
+}
+
+/* 尾递归 */
+function tailRecur($n, $res)
+{
+  // 终止条件
+  if ($n === 0) {
+    return $res;
+  }
+  // 尾递归调用
+  return tailRecur($n - 1, $res + $n);
+}
+
+/* 斐波那契数列：递归 */
+function fib($n)
+{
+  // 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)
+  $res = fib($n - 1) + fib($n - 2);
+  // 返回结果 f(n)
+  return $res;
+}
+
+/* Driver Code */
+$n = 5;
+$res = 0;
+
+$res = recur($n);
+echo "\n递归函数的求和结果 res = {$res}" . PHP_EOL;
+
+$res = forLoopRecur($n);
+echo "\n使用迭代模拟递归求和结果 res = {$res}" . PHP_EOL;
+
+$res = tailRecur($n, 0);
+echo "\n尾递归函数的求和结果 res = {$res}" . PHP_EOL;
+
+$res = fib($n);
+echo "\n斐波那契数列的第 {$n} 项为 {$res}" . PHP_EOL;
diff --git a/codes/php/chapter_computational_complexity/space_complexity.php b/codes/php/chapter_computational_complexity/space_complexity.php
new file mode 100644
index 000000000..d35f8ede6
--- /dev/null
+++ b/codes/php/chapter_computational_complexity/space_complexity.php
@@ -0,0 +1,117 @@
+<?php
+
+/**
+ * File: space_complexity.php
+ * Created Time: 2024-05-19
+ * Author: DoWake (admin@mengxing.cc)
+ */
+
+require_once '../utils/ListNode.php';
+require_once '../utils/TreeNode.php';
+require_once '../utils/PrintUtil.php';
+
+/* 函数 */
+function func()
+{
+  // 执行某些操作
+  return 0;
+}
+
+/* 常数阶 */
+function spaceConstant($n)
+{
+  // 常量、变量、对象占用 O(1) 空间
+  define('A', 0);
+  $b = 0;
+  $nums = array_fill(0, 10000, 0);
+  $node = new ListNode(0);
+  // 循环中的变量占用 O(1) 空间
+  for ($i = 0; $i < $n; $i++) {
+    $c = 0;
+  }
+  // 循环中的函数占用 O(1) 空间
+  for ($i = 0; $i < $n; $i++) {
+    func();
+  }
+}
+
+/* 线性阶 */
+function linear($n)
+{
+  // 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++) {
+    $nodes[] = new ListNode($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($i);
+  }
+}
+
+/* 线性阶（递归实现） */
+function linearRecur($n)
+{
+  echo "递归 n = {$n}" . PHP_EOL;
+  if ($n === 1) {
+    return;
+  }
+  linearRecur($n - 1);
+}
+
+/* 平方阶 */
+function quadratic($n)
+{
+  // 矩阵占用 O(n^2) 空间
+  $numMatrix = array_fill(0, $n, 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[] = $tmp;
+  }
+}
+
+/* 平方阶（递归实现） */
+function quadraticRecur($n)
+{
+  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($nums) . PHP_EOL;
+  return quadraticRecur($n - 1);
+}
+
+/* 指数阶（建立满二叉树） */
+function buildTree($n)
+{
+  if ($n === 0) {
+    return null;
+  }
+  $root = new TreeNode(0);
+  $root->left = buildTree($n - 1);
+  $root->right = buildTree($n - 1);
+  return $root;
+}
+
+/* Driver Code */
+$n = 5;
+// 常数阶
+spaceConstant($n);
+// 线性阶
+linear($n);
+linearRecur($n);
+// 平方阶
+quadratic($n);
+quadraticRecur($n);
+// 指数阶
+$root = buildTree($n);
+PrintUtil::printTree($root);
diff --git a/codes/php/chapter_computational_complexity/time_complexity.php b/codes/php/chapter_computational_complexity/time_complexity.php
new file mode 100644
index 000000000..3ad09025e
--- /dev/null
+++ b/codes/php/chapter_computational_complexity/time_complexity.php
@@ -0,0 +1,184 @@
+<?php
+
+/**
+ * File: time_complexity.php
+ * Created Time: 2024-05-19
+ * Author: DoWake (admin@mengxing.cc)
+ */
+
+
+/* 常数阶 */
+function timeConstant($n)
+{
+  $count = 0;
+  $size = 100000;
+  for ($i = 0; $i < $size; $i++) {
+    $count++;
+  }
+  return $count;
+}
+
+/* 线性阶 */
+function linear($n)
+{
+  $count = 0;
+  for ($i = 0; $i < $n; $i++) {
+    $count++;
+  }
+  return $count;
+}
+
+/* 线性阶（遍历数组） */
+function arrayTraversal($nums)
+{
+  $count = 0;
+  // 循环次数与数组长度成正比
+  foreach ($nums as $num) {
+    $count++;
+  }
+  return $count;
+}
+
+/* 平方阶 */
+function quadratic($n)
+{
+  $count = 0;
+  // 循环次数与数据大小 n 成平方关系
+  for ($i = 0; $i < $n; $i++) {
+    for ($j = 0; $j < $n; $j++) {
+      $count++;
+    }
+  }
+  return $count;
+}
+
+/* 平方阶（冒泡排序） */
+function bubbleSort($nums)
+{
+  $count = 0; // 计数器
+  // 外循环：未排序区间为 [0, i]
+  for ($i = count($nums) - 1; $i > 0; $i--) {
+    // 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端
+    for ($j = 0; $j < $i; $j++) {
+      if ($nums[$j] > $nums[$j + 1]) {
+        // 交换 nums[j] 与 nums[j + 1]
+        $tmp = $nums[$j];
+        $nums[$j] = $nums[$j + 1];
+        $nums[$j + 1] = $tmp;
+        $count += 3; // 元素交换包含 3 个单元操作
+      }
+    }
+  }
+  return $count;
+}
+
+/* 指数阶（循环实现） */
+function exponential($n)
+{
+  $count = 0;
+  $base = 1;
+  // 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+  for ($i = 0; $i < $n; $i++) {
+    for ($j = 0; $j < $base; $j++) {
+      $count++;
+    }
+    $base *= 2;
+  }
+  // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+  return $count;
+}
+
+/* 指数阶（递归实现） */
+function expRecur($n)
+{
+  if ($n === 1) {
+    return 1;
+  }
+  return expRecur($n - 1) + expRecur($n - 1) + 1;
+}
+
+/* 对数阶（循环实现） */
+function logarithmic($n)
+{
+  $count = 0;
+  while ($n > 1) {
+    $n = $n / 2;
+    $count++;
+  }
+  return $count;
+}
+
+/* 对数阶（递归实现） */
+function logRecur($n)
+{
+  if ($n <= 1) {
+    return 0;
+  }
+  return logRecur($n / 2) + 1;
+}
+
+/* 线性对数阶 */
+function linearLogRecur($n)
+{
+  if ($n <= 1) {
+    return 1;
+  }
+  $count = linearLogRecur($n / 2) + linearLogRecur($n / 2);
+  for ($i = 0; $i < $n; $i++) {
+    $count++;
+  }
+  return $count;
+}
+
+/* 阶乘阶（递归实现） */
+function factorialRecur($n)
+{
+  if ($n === 0) {
+    return 1;
+  }
+  $count = 0;
+  // 从 1 个分裂出 n 个
+  for ($i = 0; $i < $n; $i++) {
+    $count += factorialRecur($n - 1);
+  }
+  return $count;
+}
+
+/* Driver Code */
+// 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势
+$n = 8;
+echo "输入数据大小 n = {$n}" . PHP_EOL;
+
+$count = timeConstant($n);
+echo "常数阶的操作数量 = {$count}" . PHP_EOL;
+
+$count = linear($n);
+echo "线性阶的操作数量 = {$count}" . PHP_EOL;
+$count = arrayTraversal(array_fill(0, $n, 0));
+echo "线性阶（遍历数组）的操作数量 = {$count}" . PHP_EOL;
+
+$count = quadratic($n);
+echo "平方阶的操作数量 = {$count}" . PHP_EOL;
+$nums = [];
+for ($i = 0; $i < $n; $i++) {
+  $nums[$i] = $n - $i; // [n,n-1,...,2,1]
+}
+$count = bubbleSort($nums);
+echo "平方阶（冒泡排序）的操作数量 = {$count}" . PHP_EOL;
+
+$count = exponential($n);
+echo "指数阶（循环实现）的操作数量 = {$count}" . PHP_EOL;
+$count = expRecur($n);
+echo "指数阶（递归实现）的操作数量 = {$count}" . PHP_EOL;
+
+$count = logarithmic($n);
+echo "对数阶（循环实现）的操作数量 = {$count}" . PHP_EOL;
+
+$count = logRecur($n);
+echo "对数阶（递归实现）的操作数量 = {$count}" . PHP_EOL;
+
+$count = linearLogRecur($n);
+echo "线性对数阶（递归实现）的操作数量 = {$count}" . PHP_EOL;
+
+$count = factorialRecur($n);
+echo "阶乘阶（递归实现）的操作数量 = {$count}" . PHP_EOL;
diff --git a/codes/php/chapter_computational_complexity/worst_best_time_complexity.php b/codes/php/chapter_computational_complexity/worst_best_time_complexity.php
new file mode 100644
index 000000000..94079bc8a
--- /dev/null
+++ b/codes/php/chapter_computational_complexity/worst_best_time_complexity.php
@@ -0,0 +1,42 @@
+<?php
+
+/**
+ * File: worst_best_time_complexity.php
+ * Created Time: 2024-05-19
+ * Author: DoWake (admin@mengxing.cc)
+ */
+
+/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
+function randomNumbers($n)
+{
+  $nums = [];
+  // 生成数组 nums = { 1, 2, 3, ..., n }
+  for ($i = 0; $i < $n; $i++) {
+    $nums[$i] = $i + 1;
+  }
+  // 随机打乱数组元素
+  shuffle($nums);
+  return $nums;
+}
+
+/* 查找数组 nums 中数字 1 所在索引 */
+function findOne($nums)
+{
+  foreach ($nums as $key => $value) {
+    // 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)
+    // 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)
+    if ($value === 1) {
+      return $key;
+    }
+  }
+  return -1;
+}
+
+/* Driver Code */
+for ($i = 0; $i < 10; $i++) {
+  $n = 100;
+  $nums = randomNumbers($n);
+  $index = findOne($nums);
+  echo "\n数组 [ 1, 2, ..., n ] 被打乱后 = [" . join(', ', $nums) . "]" . PHP_EOL;
+  echo "数字 1 的索引为 {$index}" . PHP_EOL;
+}