Software Developer

Print the following pattern for the given N number of rows.

Pattern for N = 4

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Note : There are no spaces between the stars (*).

You are given an integer ‘N’, your task is to return the number of structurally unique BST's (binary search trees) which have exactly 'N' nodes of unique values from 1 to 'N'.

For example:

Given  ‘N’ = 2, The total number of BST’s is 2.

Note:

1. A binary search tree is a rooted binary tree whose internal nodes each store a key greater than all the keys in the node's left subtree and less than those in its right subtree.

2. A structurally unique binary search tree is a tree that has at least 1 node at a different position or with a different value compared to another binary search tree.

You are given an array ‘ARR’ of size ‘N’ containing each number between 1 and ‘N’ - 1 at least once. There is a single integer value that is present in the array twice. Your task is to find the duplicate integer value present in the array.

For example:

Consider ARR = [1, 2, 3, 4, 4], the duplicate integer value present in the array is 4. Hence, the answer is 4 in this case.

Note :

A duplicate number is always present in the given array.

You are given an array of integers. You need to sort the array in ascending order using quick sort.

Quick sort is a divide and conquer algorithm in which we choose a pivot point and partition the array into two parts i.e, left and right. The left part contains the numbers smaller than the pivot element and the right part contains the numbers larger than the pivot element. Then we recursively sort the left and right parts of the array.

Example:

Let the array = [ 4, 2, 1, 5, 3 ]
Let pivot to be the rightmost number.

After the 1st level partitioning the array will be { 2, 1, 3, 4, 5 } as 3 was the pivot. After 2nd level partitioning the array will be { 1, 2, 3, 4, 5 } as 1 was the pivot for the left part and 5 was the pivot for the right part. Now our array is sorted and there is no need to divide it again.

Print the following pattern for the given number of rows.

Pattern for N = 4

The dots represent spaces.

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