SDE - Intern

You are given a number N. You need to return the position of the rightmost set bit.

For example:

If the given number is 10 with the binary representation: 1010
The rightmost set bit would be 2 (counted from right). 

Ninja is assigned a task to reach the last stone by his master. These stones are numbered with some value and in the form of an array. He is allowed to jump either odd-numbered jumps or even-numbered jumps and has to reach the last stone.

So your task is to find the number of starting index from which he may start jumping so he reaches the last stones. You are provided with the given array and you have to find the number of starting index of the array from which Ninja can reach the end of the array by jumping some number of times.

For jumping you have to follow below instructions:

You may jump forward from index ‘i’ to index ‘j’ (with i < j) in the following way:

During odd-numbered jumps (i.e., jumps 1, 3, 5, ...), you jump to the index ‘j’ such that ‘arr[i] <= arr[j]’ and ‘arr[j]’ is the smallest possible value. If there are multiple such indices ‘j’, you can only jump to the smallest such index j.

During even-numbered jumps (i.e., jumps 2, 4, 6, ...), you jump to the index ‘j’ such that ‘arr[i] >= arr[j]’ and ‘arr[j]’ is the largest possible value. If there are multiple such indices ‘j’, you can only jump to the smallest such index ‘j’.

It may be the case that for some index ‘i’, there are no legal jumps.

You have been given a number of stairs. Initially, you are at the 0th stair, and you need to reach the Nth stair.

Each time, you can climb either one step or two steps.

You are supposed to return the number of distinct ways you can climb from the 0th step to the Nth step.

Note:

Note: Since the number of ways can be very large, return the answer modulo 1000000007.

Example :

N=3

We can climb one step at a time i.e. {(0, 1) ,(1, 2),(2,3)} or we can climb the first two-step and then one step i.e. {(0,2),(1, 3)} or we can climb first one step and then two step i.e. {(0,1), (1,3)}.

camel and banana puzzle
A person has 3000 bananas and a camel. The person wants to transport the maximum number of bananas to a destination which is 1000 KMs away, using only the camel as a mode of transportation. The camel cannot carry more than 1000 bananas at a time and eats a banana every km it travels. What is the maximum number of bananas that can be transferred to the destination using only camel (no other mode of transportation is allowed).

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