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codes/java/chapter_computational_complexity/space_complexity/space_complexity_types.java

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+package chapter_computational_complexity.space_complexity;
+
+import include.*;
+import java.util.*;
+
+public class space_complexity_types {
+    /* 函数 */
+    static int function() {
+        // do something
+        return 0;
+    }
+    
+    /* 常数阶 */
+    static void constant(int n) {
+        // 常量、变量、对象占用 O(1) 空间
+        final int a = 0;
+        int b = 0;
+        int[] nums = new int[10000];
+        ListNode node = new ListNode(0);
+        // 循环中的变量占用 O(1) 空间
+        for (int i = 0; i < n; i++) {
+            int c = 0;
+        }
+        // 循环中的函数占用 O(1) 空间
+        for (int i = 0; i < n; i++) {
+            function();
+        }
+    }
+
+    /* 线性阶 */
+    static void linear(int n) {
+        // 长度为 n 的数组占用 O(n) 空间
+        int[] nums = new int[n];
+        // 长度为 n 的列表占用 O(n) 空间
+        List<ListNode> nodes = new ArrayList<>();
+        for (int i = 0; i < n; i++) {
+            nodes.add(new ListNode(i));
+        }
+        // 长度为 n 的哈希表占用 O(n) 空间
+        Map<Integer, String> map = new HashMap<>();
+        for (int i = 0; i < n; i++) {
+            map.put(i, String.valueOf(i));
+        }
+    }
+
+    /* 线性阶（递归实现） */
+    static void linearRecur(int n) {
+        System.out.println("递归 n = " + n);
+        if (n == 1) return;
+        linearRecur(n - 1);
+    }
+
+    /* 平方阶 */
+    static void quadratic(int n) {
+        // 矩阵占用 O(n^2) 空间
+        int numMatrix[][] = new int[n][n];
+        // 二维列表占用 O(n^2) 空间
+        List<List<Integer>> numList = new ArrayList<>();
+        for (int i = 0; i < n; i++) {
+            List<Integer> tmp = new ArrayList<>();
+            for (int j = 0; j < n; j++) {
+                tmp.add(0);
+            }
+            numList.add(tmp);
+        }
+    }
+
+    /* 平方阶（递归实现） */
+    static int quadraticRecur(int n) {
+        if (n <= 0) return 0;
+        int[] nums = new int[n];
+        System.out.println("递归 n = " + n + " 中的 nums 长度 = " + nums.length);
+        return quadraticRecur(n - 1);
+    }
+
+    /* 指数阶（建立满二叉树） */
+    static TreeNode buildTree(int n) {
+        if (n == 0) return null;
+        TreeNode root = new TreeNode(0);
+        root.left = buildTree(n - 1);
+        root.right = buildTree(n - 1);
+        return root;
+    }
+
+    /* Driver Code */
+    public static void main(String[] args) {
+        int n = 5;
+        // 常数阶
+        constant(n);
+        // 线性阶
+        linear(n);
+        linearRecur(n);
+        // 平方阶
+        quadratic(n);
+        quadraticRecur(n);
+        // 指数阶
+        TreeNode tree = buildTree(n);
+        PrintUtil.printTree(tree);
+    }
+}

codes/java/chapter_computational_complexity/space_time_tradeoff/leetcode_two_sum.java

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+package chapter_computational_complexity.space_time_tradeoff;
+
+import java.util.*;
+
+class solution_brute_force {
+    public int[] twoSum(int[] nums, int target) {
+        int size = nums.length;
+        for (int i = 0; i < size - 1; i++) {
+            for (int j = i + 1; j < size; j++) {
+                if (nums[i] + nums[j] == target)
+                    return new int[] { i, j };
+            }
+        }
+        return new int[0];
+    }
+}
+
+class solution_hash_map {
+    public int[] twoSum(int[] nums, int target) {
+        int size = nums.length;
+        Map<Integer, Integer> dic = new HashMap<>();
+        for (int i = 0; i < size; i++) {
+            if (dic.containsKey(target - nums[i])) {
+                return new int[] { dic.get(target - nums[i]), i };
+            }
+            dic.put(nums[i], i);
+        }
+        return new int[0];
+    }
+}
+
+public class leetcode_two_sum {
+    public static void main(String[] args) {
+        // ======= Test Case =======
+        int[] nums = { 2,7,11,15 };
+        int target = 9;
+        
+        // ====== Driver Code ======
+        solution_brute_force slt1 = new solution_brute_force();
+        int[] res = slt1.twoSum(nums, target);
+        System.out.println(Arrays.toString(res));
+
+        solution_hash_map slt2 = new solution_hash_map();
+        res = slt2.twoSum(nums, target);
+        System.out.println(Arrays.toString(res));
+    }
+}

codes/java/chapter_computational_complexity/time_complexity/time_complexity_types.java

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+package chapter_computational_complexity.time_complexity;
+
+public class time_complexity_types {
+    /* 常数阶 */
+    static int constant(int n) {
+        int count = 0;
+        int size = 100000;
+        for (int i = 0; i < size; i++)
+            count++;
+        return count;
+    }
+
+    /* 线性阶 */
+    static int linear(int n) {
+        int count = 0;
+        for (int i = 0; i < n; i++)
+            count++;
+        return count;
+    }
+    
+    /* 线性阶（遍历数组） */
+    static int arrayTraversal(int[] nums) {
+        int count = 0;
+        // 循环次数与数组长度成正比
+        for (int num : nums) {
+            // System.out.println(num);
+            count++;
+        }
+        return count;
+    }
+
+    /* 平方阶 */
+    static int quadratic(int n) {
+        int count = 0;
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                count++;
+            }
+        }
+        return count;
+    }
+
+    /* 平方阶（冒泡排序） */
+    static void bubbleSort(int[] nums) {
+        int n = nums.length;
+        for (int i = 0; i < n - 1; i++) {
+            for (int j = 0; j < n - 1 - i; j++) {
+                if (nums[j] > nums[j + 1]) {
+                    // 交换 nums[j] 和 nums[j + 1]
+                    int tmp = nums[j];
+                    nums[j] = nums[j + 1];
+                    nums[j + 1] = tmp;
+                }
+            }
+        }
+    }
+
+    /* 指数阶（循环实现） */
+    static int exponential(int n) {
+        int count = 0, base = 1;
+        // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+        for (int i = 0; i < n; i++) {
+            for (int 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） */
+    static int expRecur(int n) {
+        if (n == 1) return 1;
+        return expRecur(n - 1) + expRecur(n - 1) + 1;
+    }
+
+    /* 对数阶（循环实现） */
+    static int logarithmic(float n) {
+        int count = 0;
+        while (n > 1) {
+            n = n / 2;
+            count++;
+        }
+        return count;
+    }
+
+    /* 对数阶（递归实现） */
+    static int logRecur(float n) {
+        if (n <= 1) return 0;
+        return logRecur(n / 2) + 1;
+    }
+
+    /* 线性对数阶 */
+    static int linearLogRecur(float n) {
+        if (n <= 1) return 1;
+        int count = linearLogRecur(n / 2) + 
+                    linearLogRecur(n / 2);
+        for (int i = 0; i < n; i++) {
+            count++;
+        }
+        return count;
+    }
+
+    /* 阶乘阶（递归实现） */
+    static int factorialRecur(int n) {
+        if (n == 0) return 1;
+        int count = 0;
+        // 从 1 个分裂出 n 个
+        for (int i = 0; i < n; i++) {
+            count += factorialRecur(n - 1);
+        }
+        return count;
+    }
+
+    /* Driver Code */
+    public static void main(String[] args) {
+        // 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
+        int n = 8;
+        System.out.println("输入数据大小 n = " + n);
+
+        int count = constant(n);
+        System.out.println("常数阶的计算操作数量 = " + count);
+
+        count = linear(n);
+        System.out.println("线性阶的计算操作数量 = " + count);
+        count = arrayTraversal(new int[n]);
+        System.out.println("线性阶（遍历数组）的计算操作数量 = " + count);
+
+        count = quadratic(n);
+        System.out.println("平方阶的计算操作数量 = " + count);
+
+        count = exponential(n);
+        System.out.println("指数阶（循环实现）的计算操作数量 = " + count);
+        count = expRecur(n);
+        System.out.println("指数阶（递归实现）的计算操作数量 = " + count);
+
+        count = logarithmic((float) n);
+        System.out.println("对数阶（循环实现）的计算操作数量 = " + count);
+        count = logRecur((float) n);
+        System.out.println("对数阶（递归实现）的计算操作数量 = " + count);
+
+        count = linearLogRecur((float) n);
+        System.out.println("线性对数阶（递归实现）的计算操作数量 = " + count);
+
+        count = factorialRecur(n);
+        System.out.println("阶乘阶（递归实现）的计算操作数量 = " + count);
+    }
+}

codes/java/chapter_computational_complexity/time_complexity/worst_best_time_complexity.java

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+package chapter_computational_complexity.time_complexity;
+
+import java.util.*;
+
+public class worst_best_time_complexity {
+    /* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
+    static int[] randomNumbers(int n) {
+        Integer[] nums = new Integer[n];
+        // 生成数组 nums = { 1, 2, 3, ..., n }
+        for (int i = 0; i < n; i++) {
+            nums[i] = i + 1;
+        }
+        // 随机打乱数组元素
+        Collections.shuffle(Arrays.asList(nums));
+        // Integer[] -> int[]
+        int[] res = new int[n];
+        for (int i = 0; i < n; i++) {
+            res[i] = nums[i];
+        }
+        return res;
+    }
+
+    /* 查找数组 nums 中数字 1 所在索引 */
+    static int findOne(int[] nums) {
+        for (int i = 0; i < nums.length; i++) {
+            if (nums[i] == 1)
+                return i;
+        }
+        return -1;
+    }
+    
+    /* Driver Code */
+    public static void main(String[] args) {
+        for (int i = 0; i < 10; i++) {
+            int n = 100;
+            int[] nums = randomNumbers(n);
+            int index = findOne(nums);
+            System.out.println("\n数组 [ 1, 2, ..., n ] 被打乱后 = " + Arrays.toString(nums));
+            System.out.println("数字 1 的索引为 " + index);
+        }
+    }
+}