Given a Binary Tree where each node has following structure, write a function to populate next pointer for all nodes. The next pointer for every node should be set to point to inorder successor.

struct node
{
  int data;
  struct node* left;
  struct node* right;
  struct node* next;
}

Initially, all next pointers have NULL values. Your function should fill these next pointers so that they point to inorder successor.

Solution (Use Reverse Inorder Traversal)
Traverse the given tree in reverse inorder traversal and keep track of previously visited node. When a node is being visited, assign previously visited node as next.

#include <stdio.h>
#include <stdlib.h>

struct node
{
    int data;
    struct node *left;
    struct node *right;
    struct node *next;
};

/* Set next of p and all descendents of p by traversing them in reverse Inorder */
void populateNext(struct node* p)
{
    // The first visited node will be the rightmost node
    // next of the rightmost node will be NULL
    static struct node *next = NULL;

    if (p)
    {
        // First set the next pointer in right subtree
        populateNext(p->right);

        // Set the next as previously visited node in reverse Inorder
        p->next = next;

        // Change the prev for subsequent node
        next = p;

        // Finally, set the next pointer in right subtree
        populateNext(p->left);
    }
}

/* UTILITY FUNCTIONS */
/* Helper function 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;
    node->next = NULL;

    return(node);
}

/* Driver program to test above functions*/
int main()
{

    /* Constructed binary tree is
              10
            /   \
          8      12
        /
      3
    */
    struct node *root = newnode(10);
    root->left        = newnode(8);
    root->right       = newnode(12);
    root->left->left  = newnode(3);

    // Populates nextRight pointer in all nodes
    populateNext(root);

    // Let us see the populated values
    struct node *ptr = root->left->left;
    while(ptr)
    {
        // -1 is printed if there is no successor
        printf("Next of %d is %d \n", ptr->data, ptr->next? ptr->next->data: -1);
        ptr = ptr->next;
    }

    return 0;
}

We can avoid the use of static variable by passing reference to next as paramater. 

// An implementation that doesn't use static variable

// A wrapper over populateNextRecur
void populateNext(struct node *root)
{
    // The first visited node will be the rightmost node
    // next of the rightmost node will be NULL
    struct node *next = NULL;

    populateNextRecur(root, &next);
}

/* Set next of all descendents of p by traversing them in reverse Inorder */
void populateNextRecur(struct node* p, struct node **next_ref)
{
    if (p)
    {
        // First set the next pointer in right subtree
        populateNextRecur(p->right, next_ref);

        // Set the next as previously visited node in reverse Inorder
        p->next = *next_ref;

        // Change the prev for subsequent node
        *next_ref = p;

        // Finally, set the next pointer in right subtree
        populateNextRecur(p->left, next_ref);
    }
}

Time Complexity: O(n)

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