Given a binary tree, print all root-to-leaf paths

For the below example tree, all root-to-leaf paths are:
10 –> 8 –> 3
10 –> 8 –> 5
10 –> 2 –> 2

Algorithm:
Use a path array path[] to store current root to leaf path. Traverse from root to all leaves in top-down fashion. While traversing, store data of all nodes in current path in array path[]. When we reach a leaf node, print the path array.

C

#include<stdio.h>
#include<stdlib.h>
 
/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node
{
   int data;
   struct node* left;
   struct node* right;
};

/* Prototypes for funtions needed in printPaths() */ 
void printPathsRecur(struct node* node, int path[], int pathLen);
void printArray(int ints[], int len);

/*Given a binary tree, print out all of its root-to-leaf
 paths, one per line. Uses a recursive helper to do the work.*/
void printPaths(struct node* node) 
{
  int path[1000];
  printPathsRecur(node, path, 0);
}

/* Recursive helper function -- given a node, and an array containing
 the path from the root node up to but not including this node,
 print out all the root-leaf paths.*/
void printPathsRecur(struct node* node, int path[], int pathLen) 
{
  if (node==NULL) 
    return;

  /* append this node to the path array */
  path[pathLen] = node->data;
  pathLen++;

  /* it's a leaf, so print the path that led to here  */
  if (node->left==NULL && node->right==NULL) 
  {
    printArray(path, pathLen);
  }
  else 
  {
    /* otherwise try both subtrees */
    printPathsRecur(node->left, path, pathLen);
    printPathsRecur(node->right, path, pathLen);
  }
}


/* UTILITY FUNCTIONS */
/* Utility that prints out an array on a line. */
void printArray(int ints[], int len) 
{
  int i;
  for (i=0; i<len; i++) 
  {
    printf("%d ", ints[i]);
  }
  printf("\n");
}    

/* utility that allocates a new node with the
   given data and NULL left and right pointers. */   
struct node* newnode(int data)
{
  struct node* node = (struct node*)
                       malloc(sizeof(struct node));
  node->data = data;
  node->left = NULL;
  node->right = NULL;
 
  return(node);
}
 
/* Driver program to test above functions*/
int main()
{ 
 
  /* Constructed binary tree is
            10
          /   \
        8      2
      /  \    /
    3     5  2
  */
  struct node *root = newnode(10);
  root->left        = newnode(8);
  root->right       = newnode(2);
  root->left->left  = newnode(3);
  root->left->right = newnode(5);
  root->right->left = newnode(2);
 
  printPaths(root);
 
  getchar();
  return 0;
}

Java

// Java program to print all the node to leaf path
 
/* A binary tree node has data, pointer to left child
   and a pointer to right child */
class Node 
{
    int data;
    Node left, right;
 
    Node(int item) 
    {
        data = item;
        left = right = null;
    }
}
 
class BinaryTree 
{
    Node root;
     
    /*Given a binary tree, print out all of its root-to-leaf
      paths, one per line. Uses a recursive helper to do 
      the work.*/
    void printPaths(Node node) 
    {
        int path[] = new int[1000];
        printPathsRecur(node, path, 0);
    }
 
    /* Recursive helper function -- given a node, and an array
       containing the path from the root node up to but not 
       including this node, print out all the root-leaf paths.*/
    void printPathsRecur(Node node, int path[], int pathLen) 
    {
        if (node == null)
            return;
 
        /* append this node to the path array */
        path[pathLen] = node.data;
        pathLen++;
 
        /* it's a leaf, so print the path that led to here  */
        if (node.left == null && node.right == null)
            printArray(path, pathLen);
        else 
        {
            /* otherwise try both subtrees */
            printPathsRecur(node.left, path, pathLen);
            printPathsRecur(node.right, path, pathLen);
        }
    }
 
    /* Utility function that prints out an array on a line. */
    void printArray(int ints[], int len) 
    {
        int i;
        for (i = 0; i < len; i++) 
        {
            System.out.print(ints[i] + " ");
        }
        System.out.println("");
    }
 
    // driver program to test above functions
    public static void main(String args[]) 
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(10);
        tree.root.left = new Node(8);
        tree.root.right = new Node(2);
        tree.root.left.left = new Node(3);
        tree.root.left.right = new Node(5);
        tree.root.right.left = new Node(2);
        
        /* Let us test the built tree by printing Insorder traversal */
        tree.printPaths(tree.root);
    }
}

// This code has been contributed by Mayank Jaiswal


Output :
10 8 3 
10 8 5 
10 2 2 

Time Complexity: O(n2) where n is number of nodes.

References:
http://cslibrary.stanford.edu/110/BinaryTrees.html

Please write comments if you find any bug in above codes/algorithms, or find other ways to solve the same problem.

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