From 23b4aa118b413d72dfdbeeeaa766ee2795e84717 Mon Sep 17 00:00:00 2001 From: RiverTwilight Date: Mon, 2 Jan 2023 22:07:48 +0800 Subject: [PATCH] code: added scripts to the doc --- .../time_complexity.md | 229 ++++++++++++++++-- 1 file changed, 205 insertions(+), 24 deletions(-) diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md index bd7cb119..4328dc6b 100644 --- a/docs/chapter_computational_complexity/time_complexity.md +++ b/docs/chapter_computational_complexity/time_complexity.md @@ -416,7 +416,6 @@ $$ } } - ``` === "TypeScript" @@ -432,7 +431,6 @@ $$ } } - ``` === "C" @@ -609,7 +607,6 @@ $$ } } } - ``` === "TypeScript" @@ -629,7 +626,6 @@ $$ } } } - ``` === "C" @@ -778,13 +774,24 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 常数阶 */ + function constant(n) { + let count = 0; + const size = 100000; + for (let i = 0; i < size; i++) count++; + return count; + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + function constant(n: number): number { + let count = 0; + const size = 100000; + for (let i = 0; i < size; i++) count++; + return count; + } ``` === "C" @@ -876,13 +883,23 @@ $$ === "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" - + /* 线性阶 */ + function linear(n: number): number { + let count = 0; + for (let i = 0; i < n; i++) count++; + return count; + } ``` === "C" @@ -980,13 +997,29 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 线性阶（遍历数组） */ + function arrayTraversal(nums) { + let count = 0; + // 循环次数与数组长度成正比 + for (let i = 0; i < nums.length; i++) { + count++; + } + return count; + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 线性阶（遍历数组） */ + function arrayTraversal(nums: number[]) { + let count = 0; + // 循环次数与数组长度成正比 + for (let i = 0; i < nums.length; i++) { + count++; + } + return count; + } ``` === "C" @@ -1093,13 +1126,33 @@ $$ === "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): 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" @@ -1244,13 +1297,47 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 平方阶（冒泡排序） */ + function bubbleSort(nums) { + let count = 0; // 计数器 + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + for (let i = nums.length - 1; i > 0; i--) { + // 内循环：冒泡操作 + for (let j = 0; j < i; j++) { + if (nums[j] > nums[j + 1]) { + // 交换 nums[j] 与 nums[j + 1] + let tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + count += 3; // 元素交换包含 3 个单元操作 + } + } + } + return count; + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 平方阶（冒泡排序） */ + function bubbleSort(nums: number[]): number { + let count = 0; // 计数器 + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + for (let i = nums.length - 1; i > 0; i--) { + // 内循环：冒泡操作 + for (let j = 0; j < i; j++) { + if (nums[j] > nums[j + 1]) { + // 交换 nums[j] 与 nums[j + 1] + let tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + count += 3; // 元素交换包含 3 个单元操作 + } + } + } + return count; + } ``` === "C" @@ -1390,13 +1477,40 @@ $$ === "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): 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" @@ -1495,12 +1609,21 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 指数阶（递归实现） */ + function expRecur(n) { + if (n == 1) return 1; + return expRecur(n - 1) + expRecur(n - 1) + 1; + } ``` === "TypeScript" ```typescript title="time_complexity.ts" + /* 指数阶（递归实现） */ + function expRecur(n: number): number { + if (n == 1) return 1; + return expRecur(n - 1) + expRecur(n - 1) + 1; + } ``` @@ -1598,13 +1721,29 @@ $$ === "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): number { + let count = 0; + while (n > 1) { + n = n / 2; + count++; + } + return count; + } ``` === "C" @@ -1694,13 +1833,21 @@ $$ === "JavaScript" ```js title="time_complexity.js" - + /* 对数阶（递归实现） */ + function logRecur(n) { + if (n <= 1) return 0; + return logRecur(n / 2) + 1; + } ``` === "TypeScript" ```typescript title="time_complexity.ts" - + /* 对数阶（递归实现） */ + function logRecur(n: number): number { + if (n <= 1) return 0; + return logRecur(n / 2) + 1; + } ``` === "C" @@ -1801,13 +1948,29 @@ $$ === "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): 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" @@ -1926,13 +2089,31 @@ $$ === "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): 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"