hello-algo/codes/javascript/chapter_computational_complexity/time_complexity.js

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/**
* File: time_complexity.js
* Created Time: 2023-01-02
* Author: RiverTwilight (contact@rene.wang)
*/
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/* 常数阶 */
function constant(n) {
var count = 0;
const size = 100000;
for (var i = 0; i < size; i++) count++;
return count;
}
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/* 线性阶 */
function linear(n) {
var count = 0;
for (var i = 0; i < n; i++) count++;
return count;
}
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/* 线性阶(遍历数组) */
function arrayTraversal(nums) {
var count = 0;
// 循环次数与数组长度成正比
for (var i = 0; i < nums.length; i++) {
count++;
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}
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return count;
}
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/* 平方阶 */
function 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++;
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}
}
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return count;
}
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/* 平方阶(冒泡排序) */
function 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
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}
}
}
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return count;
}
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/* 指数阶(循环实现) */
function 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++;
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}
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base *= 2;
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}
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// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
return count;
}
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/* 指数阶(递归实现) */
function expRecur(n) {
if (n == 1) return 1;
return expRecur(n - 1) + expRecur(n - 1) + 1;
}
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/* 对数阶(循环实现) */
function logarithmic(n) {
var count = 0;
while (n > 1) {
n = n / 2;
count++;
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}
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return count;
}
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/* 对数阶(递归实现) */
function logRecur(n) {
if (n <= 1) return 0;
return logRecur(n / 2) + 1;
}
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/* 线性对数阶 */
function linearLogRecur(n) {
if (n <= 1) return 1;
var count = linearLogRecur(n / 2) + linearLogRecur(n / 2);
for (var i = 0; i < n; i++) {
count++;
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}
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return count;
}
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/* 阶乘阶(递归实现) */
function 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 += factorialRecur(n - 1);
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}
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return count;
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}
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var n = 8;
console.log("输入数据大小 n = " + n);
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var count = constant(n);
console.log("常数阶的计算操作数量 = " + count);
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count = linear(n);
console.log("线性阶的计算操作数量 = " + count);
count = arrayTraversal(new Array(n));
console.log("线性阶(遍历数组)的计算操作数量 = " + count);
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count = 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 = bubbleSort(nums);
console.log("平方阶(冒泡排序)的计算操作数量 = " + count);
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count = exponential(n);
console.log("指数阶(循环实现)的计算操作数量 = " + count);
count = expRecur(n);
console.log("指数阶(递归实现)的计算操作数量 = " + count);
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count = logarithmic(n);
console.log("对数阶(循环实现)的计算操作数量 = " + count);
count = logRecur(n);
console.log("对数阶(递归实现)的计算操作数量 = " + count);
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count = linearLogRecur(n);
console.log("线性对数阶(递归实现)的计算操作数量 = " + count);
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count = factorialRecur(n);
console.log("阶乘阶(递归实现)的计算操作数量 = " + count);