• Graph Theory ## Problem solving

There are N problems numbered 1..N which you need to complete. You've arranged the problems in increasing difficulty order, and the i th problem has estimated difficulty level i . You have also assigned a rating vi to each problem. Problems with similar vi values are similar in nature. On each day, you will choose a subset of the problems and solve them. You've decided that each subsequent problem solved on the day should be tougher than the previous problem you solved on that day. Also, to make it less boring, consecutive problems you solve should differ in their vi rating by at least K. What is the least number of days in which you can solve all problems?

Input Format

The first line contains the number of test cases T. T test cases follow. Each case contains an integer N and K on the first line, followed by integers v1,...,vn on the second line.

Constraints

1 <= T <= 100 1 <= N <= 300 1 <= vi <= 1000 1 <= K <= 1000

Output Format

Output T lines, one for each test case, containing the minimum number of days in which all problems can be solved.

Sample Input

Sample Output

Explanation

For the first example, you can solve the problems with rating 5 and 7 on the first day and the problem with rating 4 on the next day. Note that the problems with rating 5 and 4 cannot be completed consecutively because the ratings should differ by at least K (which is 2). Also, the problems cannot be completed in order 5,7,4 in one day because the problems solved on a day should be in increasing difficulty level.

For the second example, all problems can be solved on the same day.

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## hackerrank-solutions HackerRank is a tech company that focuses on competitive programming challenges for both consumers and businesses, where developers compete by trying to program according to provided specifications. HackerRank's programming challenges can be solved in a variety of programming languages (including Java, C++, PHP, Python, SQL, JavaScript) and span multiple computer science domains. When a programmer submits a solution to a programming challenge, their submission is scored on the accuracy of their output. Programmers are then ranked globally on the HackerRank leaderboard and earn badges based on their accomplishments to drive competition among users.

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## Our Effort to provide you the best solutions requires some appreciation

Complete the function solveMeFirst to compute the sum of two integers. Function prototype: int solveMeFirst(int a, int b); where, a is the first integer input. b is the second integer input Return values sum of the above two integers

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Given an array of integers, find the sum of its elements. For example, if the array ar = [1,2,3], 1+2+3 = 6 , so return 6 . Function Description Complete the simpleArraySum function in the editor below. It must return the sum of the array elements as an integer. simpleArraySum has the following parameter(s): ar: an array of integers Input Format The first line contains an integer, n, denoting the size of the array. The second line contains n space-separated integers re

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Alice and Bob each created one problem for HackerRank. A reviewer rates the two challenges, awarding points on a scale from 1 to 100 for three categories: problem clarity, originality, and difficulty. The rating for Alice's challenge is the triplet a = (a, a, a), and the rating for Bob's challenge is the triplet b = (b, b, b). The task is to find their comparison points by comparing a with b, a with b, and a with b. If a[i] > b[i], then Alice is a

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In this challenge, you are required to calculate and print the sum of the elements in an array, keeping in mind that some of those integers may be quite large. Function Description Complete the aVeryBigSum function in the editor below. It must return the sum of all array elements. aVeryBigSum has the following parameter(s): int ar[n]: an array of integers . Return long: the sum of all array elements Input Format The first line of the input consists of an integer n

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