# [Leetcode 701] Insert into a Binary Search Tree

Description:

You are given the `root` node of a binary search tree (BST) and a `value` to insert into the tree. Return the root node of the BST after the insertion. It is guaranteed that the new value does not exist in the original BST.

Notice that there may exist multiple valid ways for the insertion, as long as the tree remains a BST after insertion. You can return any of them.

Example 1:

`Input: root = [4,2,7,1,3], val = 5Output: [4,2,7,1,3,5]Explanation: Another accepted tree is:`

Example 2:

`Input: root = [40,20,60,10,30,50,70], val = 25Output: [40,20,60,10,30,50,70,null,null,25]`

Example 3:

`Input: root = [4,2,7,1,3,null,null,null,null,null,null], val = 5Output: [4,2,7,1,3,5]`

Constraints:

• The number of nodes in the tree will be in the range `[0, 104]`.
• `-108 <= Node.val <= 108`
• All the values `Node.val` are unique.
• `-108 <= val <= 108`
• It’s guaranteed that `val` does not exist in the original BST.

C code solution (recursive):

`/** * Definition for a binary tree node. * struct TreeNode { *     int val; *     struct TreeNode *left; *     struct TreeNode *right; * }; */struct TreeNode* insertIntoBST(struct TreeNode* root, int val){        struct TreeNode* newNode = (struct TreeNode*)malloc(sizeof(struct TreeNode));    newNode->val = val;    newNode->left = NULL;    newNode->right = NULL;        if(!root){        return newNode;    }        if(val < root->val)        root->left = insertIntoBST(root->left, val);    else if(val > root->val)        root->right = insertIntoBST(root->right, val);        return root;}`

C code solution (iterative):

`struct TreeNode* insertIntoBST(struct TreeNode* root, int val){        struct TreeNode* newNode = (struct TreeNode*)malloc(sizeof(struct TreeNode));    newNode->val = val;    newNode->left = NULL;    newNode->right = NULL;        if(!root){        return newNode;    }            struct TreeNode* prev;    struct TreeNode* curr = root;    int is_left = 0;    //trace to the bottom node    while(curr){        if(val < curr->val){            prev = curr;            curr = curr->left;            is_left = 1;        }        else{            prev = curr;            curr = curr->right;            is_left = 0;        }    }    //decide the node should be at left or right of the bottom node    if(is_left)        prev->left = newNode;    else        prev->right = newNode;        return root;}`

A very clean code solution:

`struct TreeNode* insertIntoBST(struct TreeNode* root, int val){        struct TreeNode* newNode = (struct TreeNode*)malloc(sizeof(struct TreeNode));    newNode->val = val;    newNode->left = NULL;    newNode->right = NULL;        if(!root){        return newNode;    }        struct TreeNode** pp = &root;        while (*pp != NULL) {        if (val > (*pp)->val)            pp = &(*pp)->right;        else            pp = &(*pp)->left;    }        *pp = newNode;        return root;}`

Hi I am Samuel