Hackerland is a one-dimensional city with houses aligned at integral locations along a road. The Mayor wants to install radio transmitters on the roofs of the city's houses. Each transmitter has a fixed range meaning it can transmit a signal to all houses within that number of units distance away.
Given a map of Hackerland and the transmission range, determine the minimum number of transmitters so that every house is within range of at least one transmitter. Each transmitter must be installed on top of an existing house.
For example, assume houses are located at and the transmission range . antennae at houses and and would provide complete coverage. There is no house at location to cover both and . Ranges of coverage, are , , and .
Function Description
Complete the hackerlandRadioTransmitters function in the editor below. It must return an integer that denotes the minimum number of transmitters to install.
hackerlandRadioTransmitters has the following parameter(s):
- x: integer array that denotes the locations of houses
- k: an integer that denotes the effective range of a transmitter
Input Format
The first line contains two space-separated integers and , the number of houses in Hackerland and the range of each transmitter.
The second line contains space-separated integers describing the respective locations of each house .
Constraints
- There may be more than one house at the same location.
Subtasks
- for of the maximum score.
Output Format
Print a single integer denoting the minimum number of transmitters needed to cover all of the houses.
Sample Input 0
5 1
1 2 3 4 5
Sample Output 0
2
Explanation 0
The diagram below depicts our map of Hackerland:
We can cover the entire city by installing transmitters on houses at locations and .
Sample Input 1
8 2
7 2 4 6 5 9 12 11
Sample Output 1
3
Explanation 1
The diagram below depicts our map of Hackerland:
We can cover the entire city by installing transmitters on houses at locations , , and .