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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)
+ */
+
+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
+		for (var i = 0; i < nums.length; i++) {
+			count++;
+		}
+		return 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);
+})();

codes/typescript/chapter_computational_complexity/time_complexity.ts

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+/**
+ * File: time_complexity.js
+ * Created Time: 2023-01-02
+ * Author: RiverTwilight (contact@rene.wang)
+ */