JZ-C-39-Plus

剑指offer第三十九题-拓展:输入一棵二叉树的根结点,判断该树是不是平衡二叉树(AVL)

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//============================================================================
// Name        : JZ-C-39-Plus.cpp
// Author      : Laughing_Lz
// Version     :
// Copyright   : All Right Reserved
// Description : 39-拓展:输入一棵二叉树的根结点,判断该树是不是平衡二叉树(AVL)
//============================================================================
 
#include <iostream>
#include <stdio.h>
#include "BinaryTree.h"
using namespace std;
 
// ====================方法1====================
/**
 * 代码简洁,但是由于一个结点会被重复遍历多次,所以效率不高
 */
int TreeDepth(BinaryTreeNode* pRoot) {
    if (pRoot == NULL)
        return 0;
 
    int nLeft = TreeDepth(pRoot->m_pLeft);
    int nRight = TreeDepth(pRoot->m_pRight);
 
    return (nLeft > nRight) ? (nLeft + 1) : (nRight + 1);
}
 
bool IsBalanced_Solution1(BinaryTreeNode* pRoot) {
    if (pRoot == NULL)
        return true;
 
    int left = TreeDepth(pRoot->m_pLeft);
    int right = TreeDepth(pRoot->m_pRight);
    int diff = left - right;
    if (diff > 1 || diff < -1)
        return false;
 
    return IsBalanced_Solution1(pRoot->m_pLeft)
            && IsBalanced_Solution1(pRoot->m_pRight);
}
 
// ====================方法2====================
/**
 * 采用后序遍历★方式遍历二叉树的每一个结点,在遍历到一个结点之前就已经遍历了它的左右子树。
 * 一边遍历一边判断每个结点是不是平衡的
 */
bool IsBalanced(BinaryTreeNode* pRoot, int* pDepth);
 
bool IsBalanced_Solution2(BinaryTreeNode* pRoot) {
    int depth = 0;
    return IsBalanced(pRoot, &depth);
}
 
bool IsBalanced(BinaryTreeNode* pRoot, int* pDepth) {
    if (pRoot == NULL) {
        *pDepth = 0;
        return true;
    }
 
    int left, right;
    if (IsBalanced(pRoot->m_pLeft, &left)
            && IsBalanced(pRoot->m_pRight, &right)) {
        int diff = left - right;
        if (diff <= 1 && diff >= -1) {
            *pDepth = 1 + (left > right ? left : right);
            return true;
        }
    }
 
    return false;
}
 
// ====================测试代码====================
void Test(char* testName, BinaryTreeNode* pRoot, bool expected) {
    if (testName != NULL)
        printf("%s begins:\n", testName);
 
    printf("Solution1 begins: ");
    if (IsBalanced_Solution1(pRoot) == expected)
        printf("Passed.\n");
    else
        printf("Failed.\n");
 
    printf("Solution2 begins: ");
    if (IsBalanced_Solution2(pRoot) == expected)
        printf("Passed.\n");
    else
        printf("Failed.\n");
}
 
// 完全二叉树
//             1
//         /      \
//        2        3
//       /\       / \
//      4  5     6   7
void Test1() {
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
 
    ConnectTreeNodes(pNode1, pNode2, pNode3);
    ConnectTreeNodes(pNode2, pNode4, pNode5);
    ConnectTreeNodes(pNode3, pNode6, pNode7);
 
    Test("Test1", pNode1, true);
 
    DestroyTree(pNode1);
}
 
// 不是完全二叉树,但是平衡二叉树
//             1
//         /      \
//        2        3
//       /\         \
//      4  5         6
//        /
//       7
void Test2() {
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
 
    ConnectTreeNodes(pNode1, pNode2, pNode3);
    ConnectTreeNodes(pNode2, pNode4, pNode5);
    ConnectTreeNodes(pNode3, NULL, pNode6);
    ConnectTreeNodes(pNode5, pNode7, NULL);
 
    Test("Test2", pNode1, true);
 
    DestroyTree(pNode1);
}
 
// 不是平衡二叉树
//             1
//         /      \
//        2        3
//       /\
//      4  5
//        /
//       6
void Test3() {
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
 
    ConnectTreeNodes(pNode1, pNode2, pNode3);
    ConnectTreeNodes(pNode2, pNode4, pNode5);
    ConnectTreeNodes(pNode5, pNode6, NULL);
 
    Test("Test3", pNode1, false);
 
    DestroyTree(pNode1);
}
 
//               1
//              /
//             2
//            /
//           3
//          /
//         4
//        /
//       5
void Test4() {
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
 
    ConnectTreeNodes(pNode1, pNode2, NULL);
    ConnectTreeNodes(pNode2, pNode3, NULL);
    ConnectTreeNodes(pNode3, pNode4, NULL);
    ConnectTreeNodes(pNode4, pNode5, NULL);
 
    Test("Test4", pNode1, false);
 
    DestroyTree(pNode1);
}
 
// 1
//  \
//   2
//    \
//     3
//      \
//       4
//        \
//         5
void Test5() {
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
 
    ConnectTreeNodes(pNode1, NULL, pNode2);
    ConnectTreeNodes(pNode2, NULL, pNode3);
    ConnectTreeNodes(pNode3, NULL, pNode4);
    ConnectTreeNodes(pNode4, NULL, pNode5);
 
    Test("Test5", pNode1, false);
 
    DestroyTree(pNode1);
}
 
// 树中只有1个结点
void Test6() {
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    Test("Test6", pNode1, true);
 
    DestroyTree(pNode1);
}
 
// 树中没有结点
void Test7() {
    Test("Test7", NULL, true);
}
 
int main(int argc, char** argv) {
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();
 
    return 0;
}

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