Merge pull request #196 from RiverTwilight/patch-1

code: added Typescript and Javascript examples

codes/javascript/chapter_computational_complexity/time_complexity.js

@@ -0,0 +1,155 @@
+/**
+ * File: time_complexity.js
+ * Created Time: 2023-01-02
+ * Author: RiverTwilight (contact@rene.wang)
+ */
+
+/* 常数阶 */
+function constant(n) {
+    let count = 0;
+    const size = 100000;
+    for (let i = 0; i < size; i++) count++;
+    return count;
+}
+
+/* 线性阶 */
+function linear(n) {
+    let count = 0;
+    for (let i = 0; i < n; i++) count++;
+    return count;
+}
+
+/* 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;
+}
+
+/* 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;
+}
+
+/* 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;
+}
+
+/* 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;
+}
+
+/* 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) {
+    let 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;
+    let count = linearLogRecur(n / 2) + linearLogRecur(n / 2);
+    for (let i = 0; i < n; i++) {
+        count++;
+    }
+    return count;
+}
+
+/* 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;
+}
+
+/* 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
+const n = 8;
+console.log("输入数据大小 n = " + n);
+
+let count = constant(n);
+console.log("常数阶的计算操作数量 = " + count);
+
+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);
+
+count = quadratic(n);
+console.log("平方阶的计算操作数量 = " + count);
+let nums = new Array(n);
+for (let 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);
+
+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);
+
+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);
+
+count = linearLogRecur(n);
+console.log("线性对数阶（递归实现）的计算操作数量 = " + count);
+
+count = factorialRecur(n);
+console.log("阶乘阶（递归实现）的计算操作数量 = " + count);

codes/javascript/chapter_computational_complexity/worst_best_time_complexity.js

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+/*
+ * File: worst_best_time_complexity.js
+ * Created Time: 2023-01-05
+ * Author: RiverTwilight (contact@rene.wang)
+ */
+
+/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
+function randomNumbers(n) {
+    let nums = Array(n);
+    // 生成数组 nums = { 1, 2, 3, ..., n }
+    for (let i = 0; i < n; i++) {
+        nums[i] = i + 1;
+    }
+    // 随机打乱数组元素
+    for (let i = 0; i < n; i++) {
+        let r = Math.floor(Math.random() * (i + 1));
+        let temp = nums[i];
+        nums[i] = nums[r];
+        nums[r] = temp;
+    }
+    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;
+}
+
+/* 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.join(", ") + "]"
+        );
+        console.log("数字 1 的索引为 " + index);
+    }
+}