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