对一棵树的垂直遍历

http://www.geeksforgeeks.org/print-binary-tree-vertical-order/

借助 hashMap实现

#include <iostream>
#include <map>
#include <algorithm>
#include <vector>
using namespace std;

// A node of binary tree
struct Node
{
    int data;
    struct Node *left, *right;
};

// A utility function to create a new Binary Tree node
Node* newNode(int data)
{
    Node *temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}

// A utility function to find min and max distances with respect
// to root.
void findMinMax(Node *node, int *min, int *max, int hd)
{
    // Base case
    if (node == NULL) return;

    // Update min and max
    if (hd < *min) *min = hd;
    else if (hd > *max) *max = hd;

    // Recur for left and right subtrees
    findMinMax(node->left, min, max, hd-1);
    findMinMax(node->right, min, max, hd+1);
}

// A utility function to print all nodes on a given line_no.
// hd is horizontal distance of current node with respect to root.
void printVerticalLine(Node *node, int line_no, int hd)
{
    // Base case
    if (node == NULL) return;
    // If this node is on the given line number
    if (hd == line_no)
        cout << node->data << " ";

    // Recur for left and right subtrees
    printVerticalLine(node->left, line_no, hd-1);
    printVerticalLine(node->right, line_no, hd+1);
}

// The main function that prints a given binary tree in
// vertical order
void verticalOrder(Node *root)
{
    // Find min and max distances with resepect to root
    int min = 0, max = 0;
    findMinMax(root, &min, &max, 0);

    // Iterate through all possible vertical lines starting
    // from the leftmost line and print nodes line by line
    for (int line_no = min; line_no <= max; line_no++)
    {
        printVerticalLine(root, line_no, 0);
        cout << endl;
    }
}


void VerticalHashMap(Node *node, int hd, map<int, int>& hM)
{
    if (node == NULL) return;

    if (hM.end() == hM.find(hd))
        hM.insert(map<int, int>::value_type(hd, node->data));
    else {
        hM.at(hd) += node->data;
    }

    VerticalHashMap(node->left, hd-1, hM);
    VerticalHashMap(node->right, hd+1, hM);
}

void printVerticalSum(Node* root) 
{
    map<int, int> hM;
    VerticalHashMap(root, 0, hM);

    for (auto tmp : hM) {
        cout << tmp.second << endl;
    }
}


// Driver program to test above functions
int main()
{
    // Create binary tree shown in above figure
    Node *root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    root->right->left->right = newNode(8);
    root->right->right->right = newNode(9);

    cout << "Vertical order traversal is \n";
    verticalOrder(root);
    cout << "Vertical sum is \n";
    printVerticalSum(root);
    system("pause");
    return 0;
}