SDE - 1

You are given an infinite supply of coins of each of denominations D = {D0, D1, D2, D3, ...... Dn-1}. You need to figure out the total number of ways W, in which you can make a change for value V using coins of denominations from D. Print 0, if a change isn't possible.

Aahad and Harshit always have fun by solving problems. Harshit took a sorted array consisting of distinct integers and rotated it clockwise by an unknown amount. For example, he took a sorted array = [1, 2, 3, 4, 5] and if he rotates it by 2, then the array becomes: [4, 5, 1, 2, 3].

After rotating a sorted array, Aahad needs to answer Q queries asked by Harshit, each of them is described by one integer Q[i]. which Harshit wanted him to search in the array. For each query, if he found it, he had to shout the index of the number, otherwise, he had to shout -1.

For each query, you have to complete the given method where 'key' denotes Q[i]. If the key exists in the array, return the index of the 'key', otherwise, return -1.

Note:

Can you solve each query in O(logN) ?

You are given the root node of a binary tree with N nodes, whose nodes have integer values. Your task is to find the maximum depth of the given Binary tree.

Depth of a binary tree is the same as its height. In simpler terms, you have to find the total number of nodes encountered while moving from the root node to the farthest leaf node, along the longest path of the binary tree.

Example:-

If we are given the above binary tree as input then moving from root node(5) to the farthest leaf node(50), the path formed will be [ 5->10->25->35->40->45->50 ]. The total number of nodes encountered is 7, therefore the maximum depth of the binary tree is 7.

You have been given an array 'ARR' of ‘N’ integers. You have to return the minimum number of jumps needed to reach the last index of the array i.e ‘N - 1’.

From index ‘i’, we can jump to an index ‘i + k’ such that 1<= ‘k’ <= ARR[i] .

'ARR[i]' represents the maximum distance you can jump from the current index.

If it is not possible to reach the last index, return -1.

Note:

Consider 0-based indexing.

Example:

Consider the array 1, 2, 3, 4, 5, 6 
We can Jump from index 0 to index 1
Then we jump from index 1 to index 2
Then finally make a jump of 3 to reach index N-1

There is also another path where
We can Jump from index 0 to index 1
Then we jump from index 1 to index 3
Then finally make a jump of 2 to reach index N-1

So multiple paths may exist but we need to return the minimum number of jumps in a path to end which here is 3.