Recall the binary search algorithm.1. Using the algorithm/algorithmic environment, give pseudocode using a for loop. AnswerMy algorithm for binary search using a for loop is given in Algorithm 1.Algorithm 1BinarySearchFor(A)[[XXX TODO:pseudocode here]]2. Using the algorithm/algorithmic environment, give pseudocode using a while loop. Answer[[XXX TODO:your answer here]]3. Using the algorithm/algorithmic environment, give pseudocode using recursion. Answer[[XXX TODO:your answer here]]4. What is the loop invariant of your second algorithm

Following are the Pseudo Code to the given question:

Explanation:

Following are the pseudo-code by using the For loop:

Defines the A function (node, element)

The node is larger than 0.

if another value of the node equals its element

Loop Break

That element if node. value becomes lower than that

Node is node equivalent.

right

Using other nodes is node equivalent.

 left

Node Return

If the node is vacant

print the Tree is empty

Following are the pseudo-code by using the while loop:

Defines the function A(node,element)

While this node is not zero.

if the value of the node equals the element

Loop Break

The element if node. value is lower than

Node is node equivalent.

right

Using other nodes is equivalent to an a.left node

Node Return

If the node is vacant

print Tree is empty

following are the Pseudo-code for recursion:

Set the function A (node, key)

If no root is the same as the root or no root.

return the root.

If the root value is lower than that of the quest for key return (root. right, key)

Return your lookup (root.left,key)