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Rahul lives in City A and would like to travel to City B for work. There is a shuttle service for people in these cities which has a fixed schedule. The schedule for City A is a list of boarding times(at City A) and departure times(from City A) for each bus.

Note: No one is allowed to board a shuttle after the boarding time.

He arrives at time t and sometimes has to wait at the station. You are given a list of arrival times for n days.

Question 1.

Mickeymouse loves numbers in the range [m1, m2] (m1 and m2 included). Minnie decides to gift Mickey an array of numbers for his birthday. Mickey wants to find the number of pairs of indices [l, r] for which the sum of all the  elements in the range [l, r] lies between m1 and m2.   

1. Come up with an algorithm with a worst case complexity of O(N2).   (5 marks) 
2. Now improvise this algorithm, assuming all numbers are positive integers.    (7 marks)
3. What if the numbers could be negative as well? Can you think of an O(nlogn) solution in this case? (Hint: use sorting)  (10 marks)

Sample case: 

Array = [-2, 5, -1]

M1 = -2

M2 = 2

Output: 3 

[[0, 0], [2, 2], [0, 2]] are the three pairs of [l, r] that satisfy the condition. So, that is why, the output is 3.  

Notes: Recurrence relation not needed in first two parts. But do explain the reason for the resulting time complexity in words. 

Akshita loves chocolates, numbers and algorithms. Her friends Ina and Mina gave her a and b chocolates respectively.  Given her love for numbers, she likes all the numbers that are divisible by either ‘a’ or ‘b’ or both. She wants to find the nth smallest such number that is divisible by either a or b. Suggest her an algorithm to find the desired number, describe the principle on which the algorithm is based, write the pseudocode and the recurrence relation for the same. Also state which subproblem will give the answer to the original problem.

Expected Complexity → O(log(N∗min(A,B))).  

Assume a and b to be co-prime positive integers.

12. Write a Java program to print the sum of two numbers.

13. Write a Java program that simulates a guessing number game. The program will generate a random value the user needs to guess and keep asking the user for a guess until the user provides the expected value. If a value has already provided, the program will print the message “Value already provided”. If the value is higher than the value to guess, the program will print“Too high”; if it is less, the program will print the message “Too low”. Once the user enters the expected value, the program will print the number of attempts.

12. Show the Java code to declare and allocate an array with 497 elements of type double.

13. Print i as long as i is less than 6.

11.Evaluate the following Java expressions, assuming x and y are both declared as integer variables and x = 17and y = 6:

x/y+3     =                                         

x%y*4     =                                         

x-y/3     =                                       

Mickeymouse loves numbers in the range [m1, m2] (m1 and m2 included). Minnie decides to gift Mickey an array of numbers for his birthday. Mickey wants to find the number of pairs of indices [l, r] for which the sum of all the  elements in the range [l, r] lies between m1 and m2.   

1. Come up with an algorithm with a worst case complexity of O(N2).   (5 marks) 
2. Now improvise this algorithm, assuming all numbers are positive integers.    (7 marks)
3. What if the numbers could be negative as well? Can you think of an O(nlogn) solution in this case? (Hint: use sorting)  (10 marks)

Sample case: 

Array = [-2, 5, -1]

M1 = -2

M2 = 2

Output: 3 

[[0, 0], [2, 2], [0, 2]] are the three pairs of [l, r] that satisfy the condition. So, that is why, the output is 3.

Akshita loves chocolates, numbers and algorithms. Her friends Ina and Mina gave her a and b chocolates respectively.  Given her love for numbers, she likes all the numbers that are divisible by either ‘a’ or ‘b’ or both. She wants to find the nth smallest such number that is divisible by either a or b. Suggest her an algorithm to find the desired number, describe the principle on which the algorithm is based, write the pseudocode and the recurrence relation for the same. Also state which subproblem will give the answer to the original problem.

Expected Complexity → O(log(N∗min(A,B))).  

Assume a and b to be co-prime positive integers.

Rahul lives in City A and would like to travel to City B for work. There is a shuttle service for people in these cities which has a fixed schedule. The schedule for City A is a list of boarding times(at City A) and departure times(from City A) for each bus.

Note: No one is allowed to board a shuttle after the boarding time.

He arrives at time t and sometimes has to wait at the station. You are given a list of arrival times for n days.

1. Devise an algorithm to find him the shuttle with the least waiting time. (waiting time  = boardingj - t ,  where j is the next shuttle. And boardingj  >= t ) for each ti
2. If he also has access to the travel time of each shuttle. Can you help him find the shuttle which will help him reach his destination at the earliest ?

Return an array of shuttle indexes that Rahul took for n days

If there is no such shuttle return -1.

Write your algorithms as pseudo-code and make sure to explain how your algorithm works and the time and space complexity of your algorithm.