面试题32（三）：之字形打印二叉树

一、题目

请实现一个函数按照之字形顺序打印二叉树，即第一行按照从左到右的顺序打印，第二层按照从右到左的顺序打印，第三行再按照从左到右的顺序打印，其他行以此类推。

二、关键

1.两个栈。

2.两个层的交替。

三、解释

1.解题思路：按之字形顺序打印二叉树需要两个栈。我们在打印某一层节点时，把下一层的子节点保存到相应的栈里。如果当前打印的是奇数层，则先保存左子节点再保存右子节点到第一个栈中。如果当前打印的是偶数层（第二层、第四层等），则先保存右子节点再保存左子节点到第二个栈中。

四、代码

#include <cstdio>
#include "..\Utilities\BinaryTree.h"
#include <stack>

void Print(BinaryTreeNode* pRoot)
{
    if(pRoot == nullptr)
        return;

    std::stack<BinaryTreeNode*> levels[2]; //两个栈
    int current = 0;
    int next = 1;

    levels[current].push(pRoot);
    while(!levels[0].empty() || !levels[1].empty())
    {
        BinaryTreeNode* pNode = levels[current].top();
        levels[current].pop();

        printf("%d ", pNode->m_nValue);

        if(current == 0)
        {
            if(pNode->m_pLeft != nullptr)
                levels[next].push(pNode->m_pLeft);
            if(pNode->m_pRight != nullptr)
                levels[next].push(pNode->m_pRight);
        }
        else
        {
            if(pNode->m_pRight != nullptr)
                levels[next].push(pNode->m_pRight);
            if(pNode->m_pLeft != nullptr)
                levels[next].push(pNode->m_pLeft);
        }
        
        //一层打印完毕
        if(levels[current].empty())
        {
            printf("\n");
            current = 1 - current; //**
            next = 1 - next;   //**
        }
    }
}

// ====================测试代码====================
//            8
//        6      10
//       5 7    9  11
void Test1()
{
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode10 = CreateBinaryTreeNode(10);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode9 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode(11);

    ConnectTreeNodes(pNode8, pNode6, pNode10);
    ConnectTreeNodes(pNode6, pNode5, pNode7);
    ConnectTreeNodes(pNode10, pNode9, pNode11);

    printf("====Test1 Begins: ====\n");
    printf("Expected Result is:\n");
    printf("8 \n");
    printf("10 6 \n");
    printf("5 7 9 11 \n\n");

    printf("Actual Result is: \n");
    Print(pNode8);
    printf("\n");

    DestroyTree(pNode8);
}

//            5
//          4
//        3
//      2
void Test2()
{
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNode5, pNode4, nullptr);
    ConnectTreeNodes(pNode4, pNode3, nullptr);
    ConnectTreeNodes(pNode3, pNode2, nullptr);

    printf("====Test2 Begins: ====\n");
    printf("Expected Result is:\n");
    printf("5 \n");
    printf("4 \n");
    printf("3 \n");
    printf("2 \n\n");

    printf("Actual Result is: \n");
    Print(pNode5);
    printf("\n");

    DestroyTree(pNode5);
}

//        5
//         4
//          3
//           2
void Test3()
{
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);

    ConnectTreeNodes(pNode5, nullptr, pNode4);
    ConnectTreeNodes(pNode4, nullptr, pNode3);
    ConnectTreeNodes(pNode3, nullptr, pNode2);

    printf("====Test3 Begins: ====\n");
    printf("Expected Result is:\n");
    printf("5 \n");
    printf("4 \n");
    printf("3 \n");
    printf("2 \n\n");

    printf("Actual Result is: \n");
    Print(pNode5);
    printf("\n");

    DestroyTree(pNode5);
}

void Test4()
{
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);

    printf("====Test4 Begins: ====\n");
    printf("Expected Result is:\n");
    printf("5 \n\n");

    printf("Actual Result is: \n");
    Print(pNode5);
    printf("\n");

    DestroyTree(pNode5);
}

void Test5()
{
    printf("====Test5 Begins: ====\n");
    printf("Expected Result is:\n");

    printf("Actual Result is: \n");
    Print(nullptr);
    printf("\n");
}

//        100
//        /
//       50   
//         \
//         150
void Test6()
{
    BinaryTreeNode* pNode100 = CreateBinaryTreeNode(100);
    BinaryTreeNode* pNode50 = CreateBinaryTreeNode(50);
    BinaryTreeNode* pNode150 = CreateBinaryTreeNode(150);

    ConnectTreeNodes(pNode100, pNode50, nullptr);
    ConnectTreeNodes(pNode50, nullptr, pNode150);

    printf("====Test6 Begins: ====\n");
    printf("Expected Result is:\n");
    printf("100 \n");
    printf("50 \n");
    printf("150 \n\n");

    printf("Actual Result is: \n");
    Print(pNode100);
    printf("\n");
}

//                8
//        4              12
//     2     6       10      14
//   1  3  5  7     9 11   13  15
void Test7()
{
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode(12);
    BinaryTreeNode* pNode2 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode10 = CreateBinaryTreeNode(10);
    BinaryTreeNode* pNode14 = CreateBinaryTreeNode(14);
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode3 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode9 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode(11);
    BinaryTreeNode* pNode13 = CreateBinaryTreeNode(13);
    BinaryTreeNode* pNode15 = CreateBinaryTreeNode(15);

    ConnectTreeNodes(pNode8, pNode4, pNode12);
    ConnectTreeNodes(pNode4, pNode2, pNode6);
    ConnectTreeNodes(pNode12, pNode10, pNode14);
    ConnectTreeNodes(pNode2, pNode1, pNode3);
    ConnectTreeNodes(pNode6, pNode5, pNode7);
    ConnectTreeNodes(pNode10, pNode9, pNode11);
    ConnectTreeNodes(pNode14, pNode13, pNode15);

    printf("====Test7 Begins: ====\n");
    printf("Expected Result is:\n");
    printf("8 \n");
    printf("12 4 \n");
    printf("2 6 10 14 \n");
    printf("15 13 11 9 7 5 3 1 \n\n");

    printf("Actual Result is: \n");
    Print(pNode8);
    printf("\n");

    DestroyTree(pNode8);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();

    return 0;
}