diff --git a/codes/javascript/chapter_computational_complexity/time_complexity.js b/codes/javascript/chapter_computational_complexity/time_complexity.js index 9c877602..803b15c8 100644 --- a/codes/javascript/chapter_computational_complexity/time_complexity.js +++ b/codes/javascript/chapter_computational_complexity/time_complexity.js @@ -3,3 +3,156 @@ * Created Time: 2023-01-02 * Author: RiverTwilight (contact@rene.wang) */ + +class time_complexity { + /* 常数阶 */ + constant(n) { + var count = 0; + const size = 100000; + for (var i = 0; i < size; i++) count++; + return count; + } + + /* 线性阶 */ + linear(n) { + var count = 0; + for (var i = 0; i < n; i++) count++; + return count; + } + + /* 线性阶(遍历数组) */ + arrayTraversal(nums) { + var count = 0; + // 循环次数与数组长度成正比 + nums.forEach(() => { + count++; + }); + } + + /* 平方阶 */ + quadratic(n) { + var count = 0; + // 循环次数与数组长度成平方关系 + for (var i = 0; i < n; i++) { + for (let j = 0; j < n; j++) { + count++; + } + } + return count; + } + + /* 平方阶(冒泡排序) */ + bubbleSort(nums) { + var count = 0; // 计数器 + // 外循环:待排序元素数量为 n-1, n-2, ..., 1 + for (var 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; + } + + /* 指数阶(循环实现) */ + exponential(n) { + var count = 0, + base = 1; + // cell 每轮一分为二,形成数列 1, 2, 4, 8, ..., 2^(n-1) + for (var 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; + } + + /* 指数阶(递归实现) */ + expRecur(n) { + if (n == 1) return 1; + return this.expRecur(n - 1) + this.expRecur(n - 1) + 1; + } + + /* 对数阶(循环实现) */ + logarithmic(n) { + var count = 0; + while (n > 1) { + n = n / 2; + count++; + } + return count; + } + + /* 对数阶(递归实现) */ + logRecur(n) { + if (n <= 1) return 0; + return this.logRecur(n / 2) + 1; + } + + /* 线性对数阶 */ + linearLogRecur(n) { + if (n <= 1) return 1; + var count = this.linearLogRecur(n / 2) + this.linearLogRecur(n / 2); + for (var i = 0; i < n; i++) { + count++; + } + return count; + } + + /* 阶乘阶(递归实现) */ + factorialRecur(n) { + if (n == 0) return 1; + var count = 0; + // 从 1 个分裂出 n 个 + for (var i = 0; i < n; i++) { + count += this.factorialRecur(n - 1); + } + return count; + } +} + +(function main() { + var test = new time_complexity(); + + var n = 8; + console.log("输入数据大小 n = " + n); + + var count = test.constant(n); + console.log("常数阶的计算操作数量 = " + count); + + count = test.linear(n); + console.log("线性阶的计算操作数量 = " + count); + count = test.arrayTraversal(new Array(n)); + console.log("线性阶(遍历数组)的计算操作数量 = " + count); + + count = test.quadratic(n); + console.log("平方阶的计算操作数量 = " + count); + var nums = new Array(n); + for (var i = 0; i < n; i++) nums[i] = n - i; // [n,n-1,...,2,1] + count = test.bubbleSort(nums); + console.log("平方阶(冒泡排序)的计算操作数量 = " + count); + + count = test.exponential(n); + console.log("指数阶(循环实现)的计算操作数量 = " + count); + count = test.expRecur(n); + console.log("指数阶(递归实现)的计算操作数量 = " + count); + + count = test.logarithmic(n); + console.log("对数阶(循环实现)的计算操作数量 = " + count); + count = test.logRecur(n); + console.log("对数阶(递归实现)的计算操作数量 = " + count); + + count = test.linearLogRecur(n); + console.log("线性对数阶(递归实现)的计算操作数量 = " + count); + + count = test.factorialRecur(n); + console.log("阶乘阶(递归实现)的计算操作数量 = " + count); +})(); diff --git a/codes/typescript/chapter_computational_complexity/time_complexity.ts b/codes/typescript/chapter_computational_complexity/time_complexity.ts index 6f0c9737..9c877602 100644 --- a/codes/typescript/chapter_computational_complexity/time_complexity.ts +++ b/codes/typescript/chapter_computational_complexity/time_complexity.ts @@ -1,5 +1,5 @@ /** - * File: time_complexity.ts + * File: time_complexity.js * Created Time: 2023-01-02 * Author: RiverTwilight (contact@rene.wang) */