# Golang program to find floor and ceil in binary search tree

A binary search tree (BST) is a type of binary tree where every node has at most two children, commonly referred to as the left child and the right child.

In this Golang article, we will learn how to find floor and ceil in binary search tree using recursion and iterative method. The binary search tree is a useful data structure for efficient searching, insertion, and deletion of elements.

## Syntax

func ceil(root *Node, val int) int {…}


The ceil() function is used to find the ceil value in the binary search tree.

func floor(root *Node, val int) int {…}


The floor() function is used to find the floor value in the binary search tree.

func floorCeil(root *Node, key int) (int, int) {…}


The floorCeil() function is used to find the floor and ceil value in the binary search tree recursively.

## Algorithm

• Step 1 − First, we need to import the fmt package.

• Step 2 − Then, initialize a node struct and assign three variables in it. The first variable stores the integer value, while the second and third pointer variable stores the address to the left and right node respectively.

• Step 3 − Now, create aninsert() function that takes a node and a value to insert. This function inserts the node value into the appropriate binary search tree.

• Step 4 − This function recursively searches for the appropriate position to insert the new node based on the binary search tree property.

• Step 5 − Now, define a function called ceil(). It takes a node root and a value val as input and returns the smallest value in the tree that is greater than or equal to val.

• Step 6 − Then, define the floor() function that takes a node root and a value val as input and returns the largest value in the tree that is less than or equal to val.

• Step 7 − Start the main() function. Inside the main() function, insert several nodes into the Binary Search tree.

• Step 8 − Now, calls the ceil() and floor() function and pass the integer value as argument to the function.

• Step 9 − Further, the ceil and floor value of binary search tree is printed on the screen by using the fmt.Println() function.

## Example1

In this example, we will define a ceil() and floor() function iteratively that is used to find the ceil and floor in a binary search tree.

package main

import (
"fmt"
)

type Node struct {
val   int
left  *Node
right *Node
}

func insert(root *Node, val int) *Node {
if root == nil {
root = &Node{val, nil, nil}
return root
}

if val < root.val {
root.left = insert(root.left, val)
} else {
root.right = insert(root.right, val)
}

return root
}

func ceil(root *Node, val int) int {
if root == nil {
return -1
}

if root.val == val {
return root.val
}

if val > root.val {
return ceil(root.right, val)
}

leftCeil := ceil(root.left, val)
if leftCeil >= val {
return leftCeil
}

return root.val
}

func floor(root *Node, val int) int {
if root == nil {
return -1
}

if root.val == val {
return root.val
}

if val < root.val {
return floor(root.left, val)
}

rightFloor := floor(root.right, val)
if rightFloor <= val {
return rightFloor
}

return root.val
}

func main() {
var root *Node

root = insert(root, 10)
insert(root, 5)
insert(root, 15)
insert(root, 1)
insert(root, 8)
insert(root, 12)
insert(root, 18)

fmt.Println("Floor of 9:", floor(root, 9))
fmt.Println("Ceil of 9:", ceil(root, 9))
fmt.Println("Floor of 11:", floor(root, 11))
fmt.Println("Ceil of 11:", ceil(root, 11))
}


## Output

Floor of 9: -1
Ceil of 9: 10
Floor of 11: -1
Ceil of 11: 12


## Example 2

In this example, we will define a floorCeil() function recursively that is used to find the ceil and floor in a binary search tree.

package main

import (
"fmt"
)

type Node struct {
val   int
left  *Node
right *Node
}

func newnode(val int) *Node {
node := &Node{}
node.val = val
node.left = nil
node.right = nil
return node
}

func floorCeil(root *Node, key int) (int, int) {
floor := -1
ceil := -1

if root == nil {
return floor, ceil
}

if root.val == key {
return root.val, root.val
}

if root.val > key {
ceil = root.val
f, c := floorCeil(root.left, key)
if f != -1 {
floor = f
}
if c != -1 && c < ceil {
ceil = c
}
} else {
floor = root.val
f, c := floorCeil(root.right, key)
if f != -1 && f > floor {
floor = f
}
if c != -1 {
ceil = c
}
}

return floor, ceil
}

func main() {
root := newnode(8)
root.left = newnode(4)
root.right = newnode(12)
root.left.left = newnode(2)
root.left.right = newnode(6)
root.right.left = newnode(10)
root.right.right = newnode(14)

key := 14
floor, ceil := floorCeil(root, key)
fmt.Printf("Floor of %d is %d\n", key, floor)
fmt.Printf("Ceil of %d is %d\n", key, ceil)

key = 11
floor, ceil = floorCeil(root, key)
fmt.Printf("Floor of %d is %d\n", key, floor)
fmt.Printf("Ceil of %d is %d\n", key, ceil)

key = 5
floor, ceil = floorCeil(root, key)
fmt.Printf("Floor of %d is %d\n", key, floor)
fmt.Printf("Ceil of %d is %d\n", key, ceil)
}


## Output

Floor of 14 is 14
Ceil of 14 is 14
Floor of 11 is 10
Ceil of 11 is 12
Floor of 5 is 4
Ceil of 5 is 6


## Conclusion

We have successfully compiled and executed a go language program to find floor and ceil in binary search tree using recursion and iterative methodalong with two examples. In the first example, we have used the iterative method and in the second example, we have used the recursive method.

Updated on: 10-May-2023

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