剑指Offer面试题:23.二叉树中和为某一值的路径

一、题目:二叉树中和为某一值的路径

题目:输入一棵二叉树和一个整数,打印出二叉树中结点值的和为输入整数的所有路径。从树的根结点开始往下一直到叶结点所经过的结点形成一条路径。例如输入下图中二叉树和整数22,则打印出两条路径,第一条路径包含结点10、12,第二条路径包含结点10、5和7。

  二叉树结点的定义如下:

    public class BinaryTreeNode
    {
        public int Data { get; set; }
        public BinaryTreeNode leftChild { get; set; }
        public BinaryTreeNode rightChild { get; set; }

        public BinaryTreeNode(int data)
        {
            this.Data = data;
        }

        public BinaryTreeNode(int data, BinaryTreeNode left, BinaryTreeNode right)
        {
            this.Data = data;
            this.leftChild = left;
            this.rightChild = right;
        }
    }

二、解题思路

2.1 核心步骤

  首先,通过下图了解遍历上图中的二叉树的过程:

  通过上图可以总结出规律:

  (1)当用前序遍历的方式访问到某一结点时,我们把该结点添加到路径上,并累加该结点的值。

  (2)如果该结点为叶结点并且路径中结点值的和刚好等于输入的整数,则当前的路径符合要求,我们把它打印出来。如果当前结点不是叶结点,则继续访问它的子结点。

  (3)当前结点访问结束后,递归函数将自动回到它的父结点。这里要注意的是:在函数退出之前要在路径上删除当前结点并减去当前结点的值,以确保返回父结点时路径刚好是从根结点到父结点的路径。

2.2 代码实现

    public static void FindPath(BinaryTreeNode root, int expectedSum)
    {
        if (root == null)
        {
            return;
        }

        int currentSum = 0;
        List<int> path = new List<int>();
        FindPath(root, expectedSum, path, ref currentSum);
    }

    private static void FindPath(BinaryTreeNode root, int expectedSum, List<int> path, ref int currentSum)
    {
        currentSum += root.Data;
        path.Add(root.Data);
        // 如果是叶结点,并且路径上结点的和等于输入的值
        // 打印出这条路径
        bool isLeaf = root.leftChild == null && root.rightChild == null;
        if (isLeaf && currentSum == expectedSum)
        {
            foreach (int data in path)
            {
                Console.Write("{0}\t", data);
            }
            Console.WriteLine();
        }

        // 如果不是叶结点,则遍历它的子结点
        if (root.leftChild != null)
        {
            FindPath(root.leftChild, expectedSum, path, ref currentSum);
        }

        if (root.rightChild != null)
        {
            FindPath(root.rightChild, expectedSum, path, ref currentSum);
        }

        // 在返回到父结点之前,在路径上删除当前结点,
        // 并在currentSum中减去当前结点的值
        path.Remove(root.Data);
        currentSum -= root.Data;
    }

三、单元测试

3.1 测试用例

  (1)辅助方法的封装

    private static void TestPortal(string testName, BinaryTreeNode root, int expectedSum)
    {
        if (!string.IsNullOrEmpty(testName))
        {
            Console.WriteLine("{0} begins:", testName);
        }

        FindPath(root, expectedSum);

        Console.WriteLine();
    }

    private static void SetSubTreeNode(BinaryTreeNode root, BinaryTreeNode lChild, BinaryTreeNode rChild)
    {
        if (root == null)
        {
            return;
        }

        root.leftChild = lChild;
        root.rightChild = rChild;
    }

    private static void ClearUpTreeNode(BinaryTreeNode root)
    {
        if (root != null)
        {
            BinaryTreeNode left = root.leftChild;
            BinaryTreeNode right = root.rightChild;

            root = null;

            ClearUpTreeNode(left);
            ClearUpTreeNode(right);
        }
    }
View Code

  (2)功能、特殊输入测试

    //            10
    //         /      \
    //        5        12
    //       /\        
    //      4  7     
    // 有两条路径上的结点和为22
    public static void Test1()
    {
        BinaryTreeNode node10 = new BinaryTreeNode(10);
        BinaryTreeNode node5 = new BinaryTreeNode(5);
        BinaryTreeNode node12 = new BinaryTreeNode(12);
        BinaryTreeNode node4 = new BinaryTreeNode(4);
        BinaryTreeNode node7 = new BinaryTreeNode(7);

        SetSubTreeNode(node10, node5, node12);
        SetSubTreeNode(node5, node4, node7);

        Console.WriteLine("Two paths should be found in Test1.");
        TestPortal("Test1", node10, 22);

        ClearUpTreeNode(node10);
    }

    //            10
    //         /      \
    //        5        12
    //       /\        
    //      4  7     
    // 没有路径上的结点和为15
    public static void Test2()
    {
        BinaryTreeNode node10 = new BinaryTreeNode(10);
        BinaryTreeNode node5 = new BinaryTreeNode(5);
        BinaryTreeNode node12 = new BinaryTreeNode(12);
        BinaryTreeNode node4 = new BinaryTreeNode(4);
        BinaryTreeNode node7 = new BinaryTreeNode(7);

        SetSubTreeNode(node10, node5, node12);
        SetSubTreeNode(node5, node4, node7);

        Console.WriteLine("No paths should be found in Test2.");
        TestPortal("Test2", node10, 15);

        ClearUpTreeNode(node10);
    }

    //               5
    //              /
    //             4
    //            /
    //           3
    //          /
    //         2
    //        /
    //       1
    // 有一条路径上面的结点和为15
    public static void Test3()
    {
        BinaryTreeNode node5 = new BinaryTreeNode(5);
        BinaryTreeNode node4 = new BinaryTreeNode(4);
        BinaryTreeNode node3 = new BinaryTreeNode(3);
        BinaryTreeNode node2 = new BinaryTreeNode(2);
        BinaryTreeNode node1 = new BinaryTreeNode(1);

        node5.leftChild = node4;
        node4.leftChild = node3;
        node3.leftChild = node2;
        node2.leftChild = node1;

        Console.WriteLine("One path should be found in Test3.");
        TestPortal("Test3", node5, 15);

        ClearUpTreeNode(node5);
    }

    // 1
    //  \
    //   2
    //    \
    //     3
    //      \
    //       4
    //        \
    //         5
    // 没有路径上面的结点和为16
    public static void Test4()
    {
        BinaryTreeNode node1 = new BinaryTreeNode(1);
        BinaryTreeNode node2 = new BinaryTreeNode(2);
        BinaryTreeNode node3 = new BinaryTreeNode(3);
        BinaryTreeNode node4 = new BinaryTreeNode(4);
        BinaryTreeNode node5 = new BinaryTreeNode(5);

        node1.leftChild = node2;
        node2.leftChild = node3;
        node3.leftChild = node4;
        node4.leftChild = node5;

        Console.WriteLine("No paths should be found in Test4.");
        TestPortal("Test4", node1, 16);

        ClearUpTreeNode(node1);
    }

    // 树中只有1个结点
    public static void Test5()
    {
        BinaryTreeNode node1 = new BinaryTreeNode(1);

        Console.WriteLine("One paths should be found in Test5.");
        TestPortal("Test5", node1, 1);

        ClearUpTreeNode(node1);
    }

    // 树中没有结点
    public static void Test6()
    {
        Console.WriteLine("No paths should be found in Test6.");
        TestPortal("Test6", null, 0);
    }

3.2 测试结果

 

posted @ 2015-09-06 23:40 Edison Chou 阅读(...) 评论(...) 编辑 收藏