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:

Niobium 2019

PAST CHALLENGES

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

ambitious

Compute a winning move in a game in which you remove slices with even sums of elements.

Programming language:
Spoken language:

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

You play this game against your opponent and you want to know if you can win, assuming both you and your opponent play optimally. You move first.

Write a function:

char * solution(int A[], int N);

that, given an array A consisting of N integers, returns a string of format "`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

the function should return "`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

Note that removing slice "`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

You play this game against your opponent and you want to know if you can win, assuming both you and your opponent play optimally. You move first.

Write a function:

string solution(vector<int> &A);

that, given an array A consisting of N integers, returns a string of format "`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

the function should return "`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

Note that removing slice "`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

You play this game against your opponent and you want to know if you can win, assuming both you and your opponent play optimally. You move first.

Write a function:

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

that, given an array A consisting of N integers, returns a string of format "`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

the function should return "`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

Note that removing slice "`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

func Solution(A []int) string

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

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

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

function solution(A);

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

fun solution(A: IntArray): String

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

function solution(A)

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

NSString * solution(NSMutableArray *A);

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

function solution(A: array of longint; N: longint): PChar;

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

function solution($A);

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

sub solution { my (@A)=@_; ... }

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

def solution(A)

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

def solution(a)

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

object Solution { def solution(a: Array[Int]): String }

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

public func solution(_ A : inout [Int]) -> String

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

*Even sums* is a game for two players. Players are given a sequence of N positive integers and take turns alternately. In each turn, a player chooses a non-empty slice (a subsequence of consecutive elements) such that the sum of values in this slice is even, then removes the slice and concatenates the remaining parts of the sequence. The first player who is unable to make a legal move loses the game.

Write a function:

Private Function solution(A As Integer()) As String

`X,Y`" where X and Y are, respectively, the first and last positions (inclusive) of the slice that you should remove on your first move in order to win, assuming you have a winning strategy. If there is more than one such winning slice, the function should return the one with the smallest value of X. If there is more than one slice with the smallest value of X, the function should return the shortest. If you do not have a winning strategy, the function should return "`NO SOLUTION`".

For example, given the following array:

`1,2`". After removing a slice from positions 1 to 2 (with an even sum of 5 + 3 = 8), the remaining array is [4, 7, 2]. Then the opponent will be able to remove the first element (of even sum 4) or the last element (of even sum 2). Afterwards you can make a move that leaves the array containing just [7], so your opponent will not have a legal move and will lose. One of possible games is shown on the following picture:

`2,3`" (with an even sum of 3 + 7 = 10) is also a winning move, but slice "`1,2`" has a smaller value of X.

For the following array:

the function should return "`NO SOLUTION`", since there is no strategy that guarantees you a win.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [1..1,000,000,000].

Information about upcoming challenges, solutions and lessons directly in your inbox.

© 2009–2019 Codility Ltd., registered in England and Wales (No. 7048726). VAT ID GB981191408. Registered office: 107 Cheapside, London EC2V 6DN