From 2a47d31191f3712ef961ef2380b162efdbebf6eb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=83=AD=E7=AB=8Blee?= Date: Wed, 21 Dec 2022 16:40:15 +0800 Subject: [PATCH] Update time_complexity.md MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 增加对应的 js 和 ts 代码，方便前端学习的同学阅读代码。 --- .../time_complexity.md | 411 ++++++++++++++++-- 1 file changed, 383 insertions(+), 28 deletions(-) diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md index a482c7ae1..8bc92a194 100644 --- a/docs/chapter_computational_complexity/time_complexity.md +++ b/docs/chapter_computational_complexity/time_complexity.md @@ -79,13 +79,31 @@ $$ === "JavaScript" ```js title="" - + // 在某运行平台下 + function algorithm(n){ + let a = 2 // 1 ns + a = a + 1 // 1 ns + a = a * 2 // 10 ns + // 循环 n 次 + for(let i = 0; i < n; i++){ // 1 ns + a = a + i // 5 ns + } + } ``` === "TypeScript" ```typescript title="" - + // 在某运行平台下 + function algorithm(n: number): void { + let a = 2 // 1 ns + a = a + 1 // 1 ns + a = a * 2 // 10 ns + // 循环 n 次 + for (let i = 0; i < n; i++) { // 1 ns + a = a + i // 5 ns + } + } ``` === "C" @@ -194,13 +212,47 @@ $$ === "JavaScript" ```js title="" + // 算法 A 时间复杂度：常数阶 + function algorithmA(n) { + console.log(0); + } + // 算法 B 时间复杂度：线性阶 + function algorithmB(n) { + for (let i = 0; i < n; i++) { + console.log(0); + } + } + + // 算法 C 时间复杂度：常数阶 + function algorithmC(n) { + for (let i = 0; i < 1000000; i++) { + console.log(0); + } + } ``` === "TypeScript" ```typescript title="" + // 算法 A 时间复杂度：常数阶 + function algorithmA(n: number) { + console.log(0) + } + // 算法 A 时间复杂度：常数阶 + function algorithmB(n: number) { + for (let i = 0; i < n; i++) { + console.log(0) + } + } + + // 算法 C 时间复杂度：常数阶 + function algorithmC(n: number) { + for (let i = 0; i < 1000000; i++) { + console.log(0) + } + } ``` === "C" @@ -292,13 +344,31 @@ $$ === "JavaScript" ```js title="" - + function algorithm(n) { + let a = 1 // +1 + a = a + 1 // +1 + a = a * 2 // +1 + // 循环 n 次 + for (let i = 0; i < n; i++) { + // +1（每轮都执行 i ++） + console.log(0) // +1 + } + } ``` === "TypeScript" ```typescript title="" - + function algorithm(n: number) { + let a = 1 // +1 + a = a + 1 // +1 + a = a * 2 // +1 + // 循环 n 次 + for (let i = 0; i < n; i++) { + // +1（每轮都执行 i ++） + console.log(0) // +1 + } + } ``` === "C" @@ -439,13 +509,39 @@ $$ === "JavaScript" ```js title="" - + function algorithm(n) { + let a = 1 // +0（技巧 1） + a = a + n // +0（技巧 1） + // +n（技巧 2） + for (let i = 0; i < 5 * n + 1; i++) { + console.log(0) + } + // +n*n（技巧 3） + for (let i = 0; i < 2 * n; i++) { + for (let j = 0; j < n + 1; j++) { + console.log(0) + } + } + } ``` === "TypeScript" ```typescript title="" - + function algorithm(n: number) { + let a = 1 // +0（技巧 1） + a = a + n // +0（技巧 1） + // +n（技巧 2） + for (let i = 0; i < 5 * n + 1; i++) { + console.log(0) + } + // +n*n（技巧 3） + for (let i = 0; i < 2 * n; i++) { + for (let j = 0; j < n + 1; j++) { + console.log(0) + } + } + } ``` === "C" @@ -558,13 +654,29 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 常数阶 */ + function constant(n) { + let count = 0 + const size = 100000 + for (let i = 0; i < size; i++) { + count++ + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 常数阶 */ + function constant(n: number): number { + let count = 0 + const size = 100000 + for (let i = 0; i < size; i++) { + count++ + } + return count + } ``` === "C" @@ -634,13 +746,26 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 线性阶 */ + function linear(n) { + let count = 0 + for (let i = 0; i < n; i++) { + count++ + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + function linear(n: number): number { + let count = 0 + for (let i = 0; i < n; i++) { + count++ + } + return count + } ``` === "C" @@ -718,13 +843,29 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 线性阶（遍历数组） */ + function arrayTraversal(nums) { + let count = 0 + // 循环次数与数组长度成正比 + for (let num of nums) { + count++ + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 线性阶（遍历数组） */ + function arrayTraversal(nums: number[]) { + let count = 0 + // 循环次数与数组长度成正比 + for (let num of nums) { + count++ + } + return count + } ``` === "C" @@ -807,13 +948,33 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 平方阶 */ + function quadratic(n) { + let count = 0 + // 循环次数与数组长度成平方关系 + for (let i = 0; i < n; i++) { + for (let j = 0; j < n; j++) { + count++ + } + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 平方阶 */ + function quadratic(n: number) { + let count = 0 + // 循环次数与数组长度成平方关系 + for (let i = 0; i < n; i++) { + for (let j = 0; j < n; j++) { + count++ + } + } + return count + } ``` === "C" @@ -929,13 +1090,47 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 平方阶（冒泡排序） */ + function bubbleSort(nums) { + let count = 0 // 计数器 + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + for (let i = nums.length - 1; i > 0; i--) { + // 内循环：冒泡操作 + for (let j = 0; j < i; j++) { + if (nums[j] > nums[j + 1]) { + // 交换 nums[j] 与 nums[j + 1] + let tmp = nums[j] + nums[j] = nums[j + 1] + nums[j + 1] = tmp + count += 3 // 元素交换包含 3 个单元操作 + } + } + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 平方阶（冒泡排序） */ + function bubbleSort(nums: number[]) { + let count = 0 // 计数器 + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + for (let i = nums.length - 1; i > 0; i--) { + // 内循环：冒泡操作 + for (let j = 0; j < i; j++) { + if (nums[j] > nums[j + 1]) { + // 交换 nums[j] 与 nums[j + 1] + let tmp = nums[j] + nums[j] = nums[j + 1] + nums[j + 1] = tmp + count += 3 // 元素交换包含 3 个单元操作 + } + } + } + return count + } ``` === "C" @@ -1030,13 +1225,39 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 指数阶（循环实现） */ + function exponential(n) { + let count = 0, + base = 1 + // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1) + for (let i = 0; i < n; i++) { + for (let j = 0; j < base; j++) { + count++ + } + base *= 2 + } + // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1 + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 指数阶（循环实现） */ + function exponential(n: number) { + let count = 0, + base = 1 + // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1) + for (let i = 0; i < n; i++) { + for (let j = 0; j < base; j++) { + count++ + } + base *= 2 + } + // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1 + return count + } ``` === "C" @@ -1101,13 +1322,21 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 指数阶（递归实现）*/ + function expRecur(n) { + if (n == 1) return 1 + return expRecur(n - 1) + expRecur(n - 1) + 1 + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 指数阶（递归实现）*/ + function expRecur(n: number) { + if (n == 1) return 1 + return expRecur(n - 1) + expRecur(n - 1) + 1 + } ``` === "C" @@ -1187,13 +1416,29 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 对数阶（循环实现） */ + function logarithmic(n) { + let count = 0 + while (n > 1) { + n = n / 2 + count++ + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 对数阶（循环实现） */ + function logarithmic(n: number) { + let count = 0 + while (n > 1) { + n = n / 2 + count++ + } + return count + } ``` === "C" @@ -1258,13 +1503,21 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 对数阶（递归实现）*/ + function logRecur(n) { + if (n <= 1) return 0 + return logRecur(n / 2) + 1 + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 对数阶（递归实现）*/ + function logRecur(n: number) { + if (n <= 1) return 0 + return logRecur(n / 2) + 1 + } ``` === "C" @@ -1348,13 +1601,29 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 线性对数阶 */ + function linearLogRecur(n) { + if (n <= 1) return 1 + let count = linearLogRecur(n / 2) + linearLogRecur(n / 2) + for (let i = 0; i < n; i++) { + count++ + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 线性对数阶 */ + function linearLogRecur(n: number) { + if (n <= 1) return 1 + let count = linearLogRecur(n / 2) + linearLogRecur(n / 2) + for (let i = 0; i < n; i++) { + count++ + } + return count + } ``` === "C" @@ -1446,13 +1715,31 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 阶乘阶（递归实现） */ + function factorialRecur(n) { + if (n == 0) return 1 + let count = 0 + // 从 1 个分裂出 n 个 + for (let i = 0; i < n; i++) { + count += factorialRecur(n - 1) + } + return count + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 阶乘阶（递归实现） */ + function factorialRecur(n: number) { + if (n == 0) return 1 + let count = 0 + // 从 1 个分裂出 n 个 + for (let i = 0; i < n; i++) { + count += factorialRecur(n - 1) + } + return count + } ``` === "C" @@ -1634,13 +1921,81 @@ $$ === "JavaScript" ```js title="worst_best_time_complexity.js" + /* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */ + function randomNumbers(n) { + // 生成数组 nums = { 1, 2, 3, ..., n } + let nums = [...Array(n).keys()].map(i => i + 1); + shuffle(nums); + return nums; + } + /* 查找数组 nums 中数字 1 所在索引 */ + function findOne(nums) { + for (let i = 0; i < nums.length; i++) { + if (nums[i] === 1) return i; + } + return -1; + } + + /* 随机打乱数组元素 */ + function shuffle(arr) { + let n = arr.length; + for (let i = 0; i < n; i++) { + let j = Math.floor(Math.random() * n); + [arr[i], arr[j]] = [arr[j], arr[i]]; + } + } + + /* Driver Code */ + ;(function main() { + for (let i = 0; i < 10; i++) { + let n = 100; + let nums = randomNumbers(n); + let index = findOne(nums); + console.log("\n数组 [ 1, 2, ..., n ] 被打乱后 =", nums); + console.log("数字 1 的索引为", index); + } + })() ``` === "TypeScript" ```typescript title="worst_best_time_complexity.ts" + /* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */ + function randomNumbers(n: number): number[] { + // 生成数组 nums = { 1, 2, 3, ..., n } + let nums = [...Array(n).keys()].map((i) => i + 1) + shuffle(nums) + return nums + } + /* 查找数组 nums 中数字 1 所在索引 */ + function findOne(nums: number[]): number { + for (let i = 0; i < nums.length; i++) { + if (nums[i] === 1) return i + } + return -1 + } + + /* 随机打乱数组元素 */ + function shuffle(arr: number[]) { + let n = arr.length + for (let i = 0; i < n; i++) { + let j = Math.floor(Math.random() * n) + ;[arr[i], arr[j]] = [arr[j], arr[i]] + } + } + + /* Driver Code */ + ;(function main() { + for (let i = 0; i < 10; i++) { + let n = 100 + let nums = randomNumbers(n) + let index = findOne(nums) + console.log('\n数组 [ 1, 2, ..., n ] 被打乱后 =', nums) + console.log('数字 1 的索引为', index) + } + })() ``` === "C"