Data Structures

Inorder predecessor and successor

There is BST given with root node with key part as integer only. The structure of each node is as follows:

struct Node
{
    int key;
    struct Node *left, *right ;
}; 

You need to find the inorder successor and predecessor of a given key. In case the given key is not found in BST, then return the two values within which this key will lie.

Following is the algorithm to reach the desired result. Its a recursive method:


Input: root node, key

Output: predecessor node, successor node
1. If root is NULL
      then return
2. if key is found then
    a. If its left subtree is not null
        Then predecessor will be the right most 
        child of left subtree or left child itself.
    b. If its right subtree is not null
        The successor will be the left most child 
        of right subtree or right child itself.
    return
3. If key is smaller then root node
        set the successor as root
        search recursively into left subtree
    else
        set the predecessor as root
        search recursively into right subtree

Following is the implementation of above algorithm:

// C++ program to find predecessor and successor in a BST
#include <iostream>
using namespace std;

// BST Node
struct Node
{
    int key;
    struct Node *left, *right;
};

// This function finds predecessor and successor of key in BST.
// It sets pre and suc as predecessor and successor respectively
void findPreSuc(Node* root, Node*& pre, Node*& suc, int key)
{
    // Base case
    if (root == NULL)  return ;

    // If key is present at root
    if (root->key == key)
    {
        // the maximum value in left subtree is predecessor
        if (root->left != NULL)
        {
            Node* tmp = root->left;
            while (tmp->right)
                tmp = tmp->right;
            pre = tmp ;
        }

        // the minimum value in right subtree is successor
        if (root->right != NULL)
        {
            Node* tmp = root->right ;
            while (tmp->left)
                tmp = tmp->left ;
            suc = tmp ;
        }
        return ;
    }

    // If key is smaller than root's key, go to left subtree
    if (root->key > key)
    {
        suc = root ;
        findPreSuc(root->left, pre, suc, key) ;
    }
    else // go to right subtree
    {
        pre = root ;
        findPreSuc(root->right, pre, suc, key) ;
    }
}

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

/* A utility function to insert a new node with given key in BST */
Node* insert(Node* node, int key)
{
    if (node == NULL) return newNode(key);
    if (key < node->key)
        node->left  = insert(node->left, key);
    else
        node->right = insert(node->right, key);
    return node;
}

// Driver program to test above function
int main()
{
    int key = 65;    //Key to be searched in BST

   /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */
    Node *root = NULL;
    root = insert(root, 50);
    insert(root, 30);
    insert(root, 20);
    insert(root, 40);
    insert(root, 70);
    insert(root, 60);
    insert(root, 80);


    Node* pre = NULL, *suc = NULL;

    findPreSuc(root, pre, suc, key);
    if (pre != NULL)
      cout << "Predecessor is " << pre->key << endl;
    else
      cout << "No Predecessor";

    if (suc != NULL)
      cout << "Successor is " << suc->key;
    else
      cout << "No Successor";
    return 0;
}

# Python program to find predecessor and successor in a BST

# A BST node
class Node:

    # Constructor to create a new node
    def __init__(self, key):
        self.key  = key
        self.left = None
        self.right = None

# This fucntion finds predecessor and successor of key in BST
# It sets pre and suc as predecessor and successor respectively
def findPreSuc(root, key):

    # Base Case
    if root is None:
        return

    # If key is present at root
    if root.key == key:

        # the maximum value in left subtree is predecessor
        if root.left is not None:
            tmp = root.left 
            while(tmp.right):
                tmp = tmp.right 
            findPreSuc.pre = tmp


        # the minimum value in right subtree is successor
        if root.right is not None:
            tmp = root.right
            while(temp.left):
                tmp = tmp.left 
            findPreSuc.suc = tmp 

        return 

    # If key is smaller than root's key, go to left subtree
    if root.key > key :
        findPreSuc.suc = root 
        findPreSuc(root.left, key)

    else: # go to right subtree
        findPreSuc.pre = root
        findPreSuc(root.right, key)

# A utility function to insert a new node in with given key in BST
def insert(node , key):
    if node is None:
        return Node(key)

    if key < node.key:
        node.left = insert(node.left, key)

    else:
        node.right = insert(node.right, key)

    return node


# Driver program to test above function
key = 65 #Key to be searched in BST

""" Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 
"""
root = None
root = insert(root, 50)
insert(root, 30);
insert(root, 20);
insert(root, 40);
insert(root, 70);
insert(root, 60);
insert(root, 80);

# Static variables of the function findPreSuc 
findPreSuc.pre = None
findPreSuc.suc = None

findPreSuc(root, key)

if findPreSuc.pre is not None:
    print "Predecessor is", findPreSuc.pre.key

else:
    print "No Predecessor"

if findPreSuc.suc is not None:
    print "Successor is", findPreSuc.suc.key
else:
    print "No Successor"

Output:

Predecessor is 60
Successor is 70


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