Algorithms Set 3

Given a String S, Find all possible Palindromic partitions of the given String.

Example 1:

Your Task:
You don't need to read input or print anything. Your task is to complete the function allPalindromicPerms() which takes a String S as input parameter and returns a list of lists denoting all the possible palindromic partitions.

Expected Time Complexity: O(N*2^N)
Expected Auxiliary Space: O(N²), where N is the length of the String

Constraints:
1 <= |S| <= 20

A number n can be broken into three parts n/2, n/3 and n/4 (consider only integer part). Each number obtained in this process can be divided further recursively. Find the maximum sum that can be obtained by summing up the divided parts together.
Note: The maximum sum may be obtained without dividing n also.

Example 1:

Example 2:

Your Task:
You don't need to read input or print anything. Your task is to complete the function maxSum() which accepts an integer n and returns the maximum sum.

Expected Time Complexity: O(n)
Expected Auxiliary Space: O(n)

Constraints:
1 <= n <= 10⁶

Suppose you have N eggs and you want to determine from which floor in a K-floor building you can drop an egg such that it doesn't break. You have to determine the minimum number of attempts you need in order find the critical floor in the worst case while using the best strategy.There are few rules given below. 

• An egg that survives a fall can be used again.
• A broken egg must be discarded.
• The effect of a fall is the same for all eggs.
• If the egg doesn't break at a certain floor, it will not break at any floor below.
• If the eggs breaks at a certain floor, it will break at any floor above.

For more description on this problem see wiki page

Example 1:

Example 2:

Your Task:
Complete the function eggDrop() which takes two positive integer N and K as input parameters and returns the minimum number of attempts you need in order to find the critical floor.

Expected Time Complexity : O(N*K)
Expected Auxiliary Space: O(N*K)

Constraints:
1<=N<=200
1<=K<=200

You need to sort elements of an array where the array can be of following data-types:

• Integer
• String
• floating number

Your task is to complete the given two functions: sortArray() and printArray().

The input line contains 2 lines. The first line contains n(size of array) and q(type of array) separated by space. Below is the description about q.

• q = 1, means elements of the array are of integer type
• q = 2, means elements of the array are of string type
• q = 3, means elements of array are of floating digit type  

The second line contains n elements of the array separated by space.

We have to print the elements in sorted form of given type of array separated by space.

Example 1:

Example 2:

Constraints:
1 <= T <= 50
1 <= n <= 100
1 <= q <= 3

Given a sorted array arr[] of distinct integers. Sort the array into a wave-like array and return it. In other words, arrange the elements into a sequence such that a1 >= a2 <= a3 >= a4 <= a5..... (considering the increasing lexicographical order).

Example 1:

Example 2:

Your Task:
The task is to complete the function convertToWave() which converts the given array to wave array.

Expected Time Complexity: O(n).
Expected Auxiliary Space: O(1).

Constraints:
1 ≤ n ≤ 10⁶
0 ≤ A[i] ≤10⁷