SDE - 1

You are given two water jugs with capacities X and Y litres respectively. Both the jugs are initially empty. There is an infinite amount of water supply available. The jugs do not have markings to measure smaller quantities.

The following operations are allowed:

• Fill any of the jugs entirely with water.
• Empty any of the jugs.
• Pour water from one jug into another till the other jug is full, or the first jug itself is empty.

You are required to tell whether it is possible to measure exactly ‘Z’ litres using both of the jugs.

If Z litres of water is measurable, you must have Z litres of water contained within one or both buckets by the end.

For example:

In order to measure 2 litres from jugs of 4 and 6 litres we can follow the following steps-

• Fill 6-litres jugs to its maximum capacity.
• Pour water from 6-litres jug to the jug with 4-litres capacity.
• Pour water from 6-litres jug to the jug with 4-litres capacity.

Smit has been given a string ‘STR’ of length ‘N’, which only consists of ‘0’ and ‘1’ and an operation to be performed ‘K’ times on the string.

The operation description is as follows:

For every ‘i’ from ‘0’ <= ‘i’ < ‘N’, if there exist indices ‘(i-1)’ and ‘(i+1)’ such that ‘STR[i-1] = STR[i+1]’ then set the value of ‘STR[i]’ to ‘1’. If ‘(i-1)’ or ‘(i+1)’ is out of the index range or ‘STR[i-1]’ != ‘STR[i+1]’ then set ‘STR[i]’ to ‘0’.

For e.g. if ‘STR’ = “0000”, then after the operation the string ‘STR’ will be transformed to “0110” because for ‘i’ = ‘1’ and ‘i’ = ‘2’ the condition mentioned above is satisfied.

Note: When transforming we take into account the values of the old string given in the problem or we received after the application of the last operation not the newly transformed string in the current operation.

He has got an answer but is not completely sure if it is correct. So being, his friend he asked you to help him verify if his answer is correct or not. Can you help Smit to determine the correct string ‘STR’ after ‘K’ above-mentioned operations?.

EXAMPLE :

Input: ‘N’ = 5, ‘K’ = 1, ‘STR’ = “10101”

Output: 01110
In this case, the indices satisfying the condition of ‘STR[i-1] = STR[i+1]’ are ‘1’, ‘2’, and ‘3’. Hence the string ‘STR’ after applying the given operation for ‘K(=1)’ times will be “01110”.

Ninja is the manager of a restaurant. There were ‘N’ customers who visit the restaurant. Ninja is interested in calculating what was the maximum number of customers in the restaurant at a time. He finds this problem is tough for him, so he wants your help.

You are given the arrival and leaving time of ‘N’ customers in the form of arrays named ‘ARRIVAL’ and ‘LEAVING’. Your task is to find the maximum number of customers at any point in time.

Note :

All arrival and leaving times are distinct.

Hybrid Search: Consider a sorted list: 12 43 65 78 98 101 187. If a "Hsearch" technique compares the middle element first and then searches linearly in the appropriate half, how many comparisons are made to find the number 187?

You are given a string denoting a valid Prefix expression containing ‘+’, ’-’, ’*’, ‘/’ and lowercase letters.

Convert the given Prefix expression into an Infix expression.

Note:

Infix notation is a method of writing mathematical expressions in which operators are placed between operands. For example, "a + b" represents the addition of a and b.

Prefix notation is a method of writing mathematical expressions in which operators are placed before the operands. For example, "+ a b" represents the addition of a and b.

Expression contains lowercase English letters, ‘+’, ‘-’, ‘*’, and  ‘/’. 

Example:

Input: /-ab+-cde

Output: ((a-b)/((c-d)+e))

Explanation:
In this test case, there are four operators ‘/’, ‘-’, ‘+’, ‘-’.
Prefix expression:  /-ab+-cde. 
The operator between  ‘a’ and ‘b’ is ‘-’. Resulting expression: /(a-b)+-cde.
The operator between  ‘c’ and ‘d’ is ‘-’. Resulting expression: /(a-b)+(c-d)e.
The operator between ‘c-d’ and ‘e’ is +. Resulting expression: /(a-b)((c-d)+e).
The operator between ‘a-b’ and ‘((c-d)+e)’ is ‘/’. Resulting expression: ((a-b)/((c-d)+e)).

Geometry & Patterns: Some balls are arranged in rows to form an equilateral triangle (the 1st row has 1 ball, the 2nd has 2, and so on). If 472 balls are added, they can form a square in which each side has 7 balls fewer than the side of the original triangle. Find the initial number of balls.

Probability: Rajesh and Ramesh each have a 5, 10, and 20 paise coin. They randomly select one. If the sum is odd, Rajesh wins; if even, Ramesh wins. Find the probability that Rajesh wins exactly one odd and one even coin in the first two games.

You are given a string 'S'. Your task is to partition 'S' such that every substring of the partition is a palindrome. You need to return all possible palindrome partitioning of 'S'.

Note: A substring is a contiguous segment of a string.

For Example:

For a given string “BaaB”
3 possible palindrome partitioning of the given string are:
{“B”, “a”, “a”, “B”}
{“B”, “aa”, “B”}
{“BaaB”}
Every substring of all the above partitions of “BaaB” is a palindrome.

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