# Inorder predecessor and successor for a given key in BST

I recently encountered with a question in an interview at e-commerce company. The interviewer asked the following question:

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.

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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 the above algorithm:

## C++

 `// C++ program to find predecessor and successor in a BST ` `#include ` `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

 `# 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 function 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"` ` `  `# This code is contributed by Nikhil Kumar Singh(nickzuck_007) `

Output:

```Predecessor is 60
Successor is 70```

Another Approach :
We can also find the inorder successor and inorder predecessor using inorder traversal . Check if the current node is smaller than the given key for predecessor and for successor, check if it is greater than the given key . If it is greater than the given key then, check if it is smaller than the already stored value in successor then, update it . At last, get the predecessor and successor stored in q(successor) and p(predecessor).

## C++

 `// CPP code for inorder succesor  ` `// and predecessor of tree ` `#include ` `#include ` ` `  `using` `namespace` `std; ` ` `  `struct` `Node ` `{ ` `    ``int` `data; ` `    ``Node* left,*right; ` `}; ` `  `  `// Function to return data ` `Node* getnode(``int` `info) ` `{ ` `    ``Node* p = (Node*)``malloc``(``sizeof``(Node)); ` `    ``p->data = info; ` `    ``p->right = NULL; ` `    ``p->left = NULL; ` `    ``return` `p; ` `} ` ` `  `/* ` `since inorder traversal results in ` `ascending order visit to node , we ` `can store the values of the largest ` `no which is smaller than a (predecessor) ` `and smallest no which is large than ` `a (succesor) using inorder traversal ` `*/` `void` `find_p_s(Node* root,``int` `a,  ` `              ``Node** p, Node** q) ` `{ ` `    ``// If root is null return  ` `    ``if``(!root) ` `        ``return` `; ` `         `  `    ``// traverse the left subtree     ` `    ``find_p_s(root->left, a, p, q); ` `     `  `    ``// root data is greater than a ` `    ``if``(root&&root->data > a) ` `    ``{ ` `         `  `        ``// q stores the node whose data is greater ` `        ``// than a and is smaller than the previously ` `        ``// stored data in *q which is sucessor ` `        ``if``((!*q) || (*q) && (*q)->data > root->data) ` `                ``*q = root; ` `    ``} ` `     `  `    ``// if the root data is smaller than ` `    ``// store it in p which is predecessor ` `    ``else` `if``(root && root->data < a) ` `    ``{ ` `        ``*p = root; ` `    ``} ` `     `  `    ``// traverse the right subtree ` `    ``find_p_s(root->right, a, p, q); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``Node* root1 = getnode(50); ` `    ``root1->left = getnode(20); ` `    ``root1->right = getnode(60); ` `    ``root1->left->left = getnode(10); ` `    ``root1->left->right = getnode(30); ` `    ``root1->right->left = getnode(55); ` `    ``root1->right->right = getnode(70); ` `    ``Node* p = NULL, *q = NULL; ` `  `  `    ``find_p_s(root1, 55, &p, &q); ` `     `  `    ``if``(p) ` `        ``cout << p->data; ` `    ``if``(q) ` `        ``cout << ``" "` `<< q->data; ` `    ``return` `0; ` `} `

## Python3

 `""" Python3 code for inorder succesor  ` `and predecessor of tree """` ` `  `# A Binary Tree Node  ` `# Utility function to create a new tree node  ` `class` `getnode:  ` ` `  `    ``# Constructor to create a new node  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `"""  ` `since inorder traversal results in  ` `ascendingorder visit to node , we  ` `can store the values of the largest  ` `o which is smaller than a (predecessor)  ` `and smallest no which is large than  ` `a (succesor) using inorder traversal  ` `"""` `def` `find_p_s(root, a, p, q):  ` ` `  `    ``# If root is None return  ` `    ``if``(``not` `root): ` `        ``return` `         `  `    ``# traverse the left subtree      ` `    ``find_p_s(root.left, a, p, q)  ` `     `  `    ``# root data is greater than a  ` `    ``if``(root ``and` `root.data > a): ` `         `  `        ``# q stores the node whose data is greater  ` `        ``# than a and is smaller than the previously  ` `        ``# stored data in *q which is sucessor  ` `        ``if``((``not` `q[``0``]) ``or` `q[``0``] ``and`  `                ``q[``0``].data > root.data): ` `            ``q[``0``] ``=` `root ` `             `  `    ``# if the root data is smaller than  ` `    ``# store it in p which is predecessor  ` `    ``elif``(root ``and` `root.data < a): ` `        ``p[``0``]``=` `root  ` `     `  `    ``# traverse the right subtree  ` `    ``find_p_s(root.right, a, p, q) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``:  ` ` `  `    ``root1 ``=` `getnode(``50``)  ` `    ``root1.left ``=` `getnode(``20``)  ` `    ``root1.right ``=` `getnode(``60``)  ` `    ``root1.left.left ``=` `getnode(``10``)  ` `    ``root1.left.right ``=` `getnode(``30``)  ` `    ``root1.right.left ``=` `getnode(``55``)  ` `    ``root1.right.right ``=` `getnode(``70``)  ` `    ``p ``=` `[``None``] ` `    ``q ``=` `[``None``]  ` `     `  `    ``find_p_s(root1, ``55``, p, q)  ` `     `  `    ``if``(p[``0``]) : ` `        ``print``(p[``0``].data, end ``=` `"") ` `    ``if``(q[``0``]) : ` `        ``print``("", q[``0``].data) ` ` `  `# This code is contributed by  ` `# SHUBHAMSINGH10 `

Output :

```50 60
```

Thanks Shweta for suggesting this method.