SDE - Intern

You are given a sorted array A consisting of N integers. Your task is to find the magic index in the given array.

Note :

1. A magic index in an array A[0 ... N - 1] is defined to be an index i such that A[i] = i.
2. The elements in the array can be negative.
3. The elements in the array can be repeated multiple times.
4. There can be more than one magic index in an array.

Wong is hungry and wants to eat tuna melt. He checks his pocket and finds that he has only a buck left. He asked Dr. Strange to lend him some money, for which Strange agrees but to get the money, Wong has to beat Strange in a game of coins. The game will be played by two players. Being kind enough Strange allows Wong to play first. Now, Strange arranges N coins in a row. Each coin is associated with a value. In his turn, every player can remove only one coin from either end. Once a player removes a coin, it can not be placed back into the row. At the end when all coins are removed, the player with the maximum value of coins wins. Wong will only get money if he wins the game. Wong knows that he can not beat sorcerer supreme, so he asked for your help.

You are given an array of integers, say, ‘ARR’ of size ‘N’ containing the values associated with ‘N’ coins. Your task is to determine the maximum value of coins you can obtain by following two rules:

a) Both players play in alternate turns and they can remove only one coin in their turn.
b) Any player can remove coins only from either of the two ends of ‘ARR’.

Note:

There can be more than one set of coins with maximum value.

For example:

a) Consider 3 coins are placed with values [10, 20, 30]: Wong removes 30, then Strange removes 20, then Wong removes 10. Now all coins are taken, and Wong has coins with value 40 and he wins.

b) Consider 1 coin is placed with value [100]: Wong removes the coin and no other coin is left. So, Wong wins with value 100.

Note:

a) The game only ends when NO MORE COIN IS LEFT to play with.

b) If a game ends in a draw, Wong is declared the winner. 

The gardener wants to water the garden by opening the minimum number of taps. The garden is one-dimensional along the x-axis of length N i.e. the garden starts from point 0 and ends at point N. There are N + 1 tap located at points [0, 1, 2, …, N] in the garden.

You are given an integer N, and an array named “ranges” of size N + 1(0-indexed). The ith tap, if opened, can water the gardener from point (i - ranges[i]) to (i + ranges[i]) including both. The task is to find the minimum number of taps that should be open to water the whole garden, return -1 if the garden can not be watered.

Example :

Follow Up:

Can you solve the problem in O(N) time?

You are given ‘n’ carrots numbered from 1 to ‘n’. There are k rabbits. Rabbits can jump to carrots only with the multiples of Aj(Aj,2Aj,3Aj…) for all rabbits from 1 to k.

Whenever Rabbit reaches a carrot it eats a little carrot. All rabbits start from the same beginning point. You have to determine the remaining carrots(i.e., carrots which are not eaten by any rabbit) after all rabbits reach the end.