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:

Fast & Curious

PAST CHALLENGES

The Fellowship of the Code

May the 4th Challenge

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

For each node in a tree find the sum of distances to all other nodes.

A computer network consisting of N routers and N−1 links connecting them is given. Routers are labeled with distinct integers within the range [0..(N−1)]. Links connect routers in such a way that each distinct pair of routers is connected either by a direct link or through a path consisting of direct links. There is exactly one way to reach any router from another and the number of direct links that must be traversed is called the *distance* between these two routers. For example, consider the following network consisting of ten routers and nine links:

Routers 2 and 4 are connected directly, so the distance between them is 1. Routers 4 and 7 are connected through a path consisting of direct links 4−0, 0−9 and 9−7; hence the distance between them is 3.

The location of a router in the network determines how quickly a packet dispatched by that router can reach other routers. The *peripherality* of a router is the average distance to all other routers on the network. For example, the peripherality of router 4 in the network shown above is 2.11, because:

distance to 0: 1 distance to 1: 3 distance to 2: 1 distance to 3: 3 distance to 5: 1 distance to 6: 3 distance to 7: 3 distance to 8: 2 distance to 9: 2 average: 19/9 = 2.11

The peripherality of router 0 is 1.66 and no other router has lower peripherality.

Write a function

class Solution { public int solution(int[] T); }

that, given a non-empty array T consisting of N integers describing a network of N routers and N−1 links, returns the label of the router that has minimum peripherality. If there is more than one router that has minimum peripherality, the function should return the lowest label.

Array T describes a network of routers as follows:

- if T[P] = Q and P ≠ Q, then there is a direct link between routers P and Q.

For example, given the following array T consisting of ten elements:

the function should return 0, because this array describes the network shown above and router 0 has minimum peripherality.

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

- N is an integer within the range [1..100,000];
- each element of array T is an integer within the range [0..(N−1);
- there is exactly one (possibly indirect) connection between any two distinct routers.