Your browser (Unknown 0) is no longer supported. Some parts of the website may not work correctly. Please update your browser.

UPCOMING CHALLENGES:

CURRENT CHALLENGES:

Pi Code Challenge

PAST CHALLENGES

Year of the Rabbit

Carol of the Code

Game of Codes

National Coding Week 2022

Jurassic Code

Fury Road

Bug Wars: The Last Hope

Muad'Dib's

Year of the Tiger

Pair a Coder

Code Alone

Gamer's

Spooktober

National Coding Week

The Coder of Rivia

Fast & Curious

The Fellowship of the Code

May the 4th

The Great Code Off 2021

The Doge 2021

The Matrix 2021

The OLX Group challenge

Silver 2020

Palladium 2020

Rhodium 2019

Ruthenium 2019

Technetium 2019

Molybdenum 2019

Niobium 2019

Zirconium 2019

Yttrium 2019

Strontium 2019

Rubidium 2018

Arsenicum 2018

Krypton 2018

Bromum 2018

Future Mobility

Grand Challenge

Digital Gold

Selenium 2018

Germanium 2018

Gallium 2018

Zinc 2018

Cuprum 2018

Cutting Complexity

Nickel 2018

Cobaltum 2018

Ferrum 2018

Manganum 2017

Chromium 2017

Vanadium 2016

Titanium 2016

Scandium 2016

Calcium 2015

Kalium 2015

Argon 2015

Chlorum 2014

Sulphur 2014

Phosphorus 2014

Silicium 2014

Aluminium 2014

Magnesium 2014

Natrium 2014

Neon 2014

Fluorum 2014

Oxygenium 2014

Nitrogenium 2013

Carbo 2013

Boron 2013

Beryllium 2013

Lithium 2013

Helium 2013

Hydrogenium 2013

Omega 2013

Psi 2012

Chi 2012

Phi 2012

Upsilon 2012

Tau 2012

Sigma 2012

Rho 2012

Pi 2012

Omicron 2012

Xi 2012

Nu 2011

Mu 2011

Lambda 2011

Kappa 2011

Iota 2011

Theta 2011

Eta 2011

Zeta 2011

Epsilon 2011

Delta 2011

Gamma 2011

Beta 2010

Alpha 2010

Connect N points with N line segments so as to minimize the largest distance between them.

You are helping the port management to organize boats moored in a port. There is a straight wharf with N mooring bollards and N boats. The wharf (and the dock in front of it) is of length M. Each boat has the same width: 2*X. The bollards are located at the very edge of the wharf. It is possible for more than one bollard to be at the same position.

You have to moor each boat to a separate bollard so that the following rules are satisfied:

- each boat is fixed with a single mooring rope to the bank of the wharf,
- the mooring rope connects the middle of the boat's bow with a bollard,
- the middle of the boat's bow can be set only on integer positions,
- the sides of the boats can touch each other,
- boats cannot overlap,
- boats cannot be placed outside the dock or extend it,
- two boats cannot be tied to the same bollard.

All the boats must have mooring ropes of the same length. The goal is to minimize this length.

More formally, let the *max distance* be the largest distance between the middle of any boat's bow and the bollard to which the boat is moored. The goal is to align the boats so that the max distance is as small as possible.

You are given a non-empty array R of N integers, and two positive integers X and M. Array R contains the positions of the bollards along the wharf. The wharf's ends are at positions 0 and M.

For example, the following array R, and integers X and M:

describe:

- three bollards at positions 1, 3 and 14,
- three boats of width 4,
- a wharf of length 16.

You can set:

- the center of the first boat at position 2,
- the center of the second boat at position 6,
- the center of the third boat at position 14.

Between the first boat and the first bollard the distance is 1; between the second boat and the second bollard it is 3; and between the third boat and the third bollard it is 0; so the max distance is 3.

Write a function:

class Solution { public int solution(int[] R, int X, int M); }

that, given an array R consisting of N integers, given two integers X and M, returns the minimal max distance you can achieve.

If it is not possible to tie all the boats, the function should return −1.

For example, given the following array R, integers X and M:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- X and M are integers within the range [1..1,000,000,000];
- each element of array R is an integer within the range [0..M];
- array R is sorted in non-decreasing order.

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.