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package class12;
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public class Code04_IsFull {
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public static class Node {
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public int value;
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public Node left;
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public Node right;
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public Node(int data) {
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this.value = data;
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}
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}
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// 第一种方法
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// 收集整棵树的高度h，和节点数n
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// 只有满二叉树满足 : 2 ^ h - 1 == n
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public static boolean isFull1(Node head) {
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if (head == null) {
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return true;
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}
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Info1 all = process1(head);
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return (1 << all.height) - 1 == all.nodes;
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}
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public static class Info1 {
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public int height;
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public int nodes;
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public Info1(int h, int n) {
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height = h;
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nodes = n;
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}
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}
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public static Info1 process1(Node head) {
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if (head == null) {
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return new Info1(0, 0);
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}
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Info1 leftInfo = process1(head.left);
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Info1 rightInfo = process1(head.right);
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int height = Math.max(leftInfo.height, rightInfo.height) + 1;
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int nodes = leftInfo.nodes + rightInfo.nodes + 1;
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return new Info1(height, nodes);
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}
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// 第二种方法
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// 收集子树是否是满二叉树
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// 收集子树的高度
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// 左树满 && 右树满 && 左右树高度一样 -> 整棵树是满的
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public static boolean isFull2(Node head) {
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if (head == null) {
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return true;
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}
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return process2(head).isFull;
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}
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public static class Info2 {
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public boolean isFull;
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public int height;
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public Info2(boolean f, int h) {
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isFull = f;
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height = h;
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}
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}
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public static Info2 process2(Node h) {
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if (h == null) {
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return new Info2(true, 0);
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}
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Info2 leftInfo = process2(h.left);
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Info2 rightInfo = process2(h.right);
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boolean isFull = leftInfo.isFull && rightInfo.isFull && leftInfo.height == rightInfo.height;
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int height = Math.max(leftInfo.height, rightInfo.height) + 1;
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return new Info2(isFull, height);
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}
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// for test
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public static Node generateRandomBST(int maxLevel, int maxValue) {
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return generate(1, maxLevel, maxValue);
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}
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// for test
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public static Node generate(int level, int maxLevel, int maxValue) {
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if (level > maxLevel || Math.random() < 0.5) {
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return null;
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}
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Node head = new Node((int) (Math.random() * maxValue));
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head.left = generate(level + 1, maxLevel, maxValue);
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head.right = generate(level + 1, maxLevel, maxValue);
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return head;
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}
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public static void main(String[] args) {
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int maxLevel = 5;
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int maxValue = 100;
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int testTimes = 1000000;
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System.out.println("测试开始");
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for (int i = 0; i < testTimes; i++) {
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Node head = generateRandomBST(maxLevel, maxValue);
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if (isFull1(head) != isFull2(head)) {
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System.out.println("出错了!");
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}
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}
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System.out.println("测试结束");
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}
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}
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