Max double slice sum

Question

Recently, I tried to solve the Max Double Slice Sum problem in codility which is a variant of max slice problem. My Solution was to look for a slice that has maximum value w

Answer 1

The most clear Python solution among others:

def solution(A):
    mid = 1
    total = 0
    max_slice = 0

    for idx, end in enumerate(A[2:-1], start=2):

        if total < 0:
            mid = idx
            total = 0

        elif total == 0 and A[idx - 1] > A[mid]:
            mid = idx - 1
            total = end

        else:
            if A[mid] > end:
                total += A[mid]
                mid = idx
            else:
                total += end

        max_slice = max(max_slice, total)

    return max_slice

Answer 2

Hello this implementacion has 100 score

int i,n ;

n = A.size();

if (3==n) return 0;

vector<int>  max_sum_end(n,0);
vector<int>  max_sum_start(n,0);

for (i=1; i< (n-1); i++) // i=0 and i=n-1 are not used because x=0,z=n-1
{
  max_sum_end[i]   = max ( 0 , max_sum_end[i-1] + A[i]  ); 
}

for (i=n-2; i > 0; i--) // i=0 and i=n-1 are not used because x=0,z=n-1
{
   max_sum_start[i]   = max ( 0 , max_sum_start[i+1] + A[i]  ); 
}  

int maxvalue,temp;
maxvalue = 0;

for (i=1; i< (n-1); i++)
{
 temp = max_sum_end[i-1]  + max_sum_start[i+1];
 if ( temp >  maxvalue) maxvalue=temp;
}

return maxvalue ;

Answer 3

C# solution 100/100

public int solution(int[] A) {
        int[] forw = new int[A.Length];
        int[] rewi = new int[A.Length];

        bool isAllNeg = true;
        for (int i = 1; i < A.Length; i++)
        {
            forw[i] = Math.Max(0, forw[i - 1] + A[i]);
            if (A[i] > 0 && isAllNeg) isAllNeg = false;

        }

        if (isAllNeg)
            return 0;

        for (int i = A.Length - 2; i >= 0; i--)
        {
            rewi[i] = Math.Max(0, rewi[i + 1] + A[i]);
        }

        int maxsum = 0;
        for (int i = 1; i < A.Length - 1; i++)
        {
            maxsum = Math.Max(maxsum, forw[i - 1] + rewi[i + 1]);
        }

        return maxsum;
}

Answer 4

Vb.net version of the above solution is as below:

Private Function solution(A As Integer()) As Integer
    ' write your code in VB.NET 4.0
    Dim Slice1() As Integer = Ending(A)
        Dim slice2() As Integer = Starting(A)
        Dim maxSUM As Integer = 0
        For i As Integer = 1 To A.Length - 2
            maxSUM = Math.Max(maxSUM, Slice1(i - 1) + slice2(i + 1))
        Next
        Return maxSUM
End Function
    Public Shared Function Ending(input() As Integer) As Integer()
        Dim result As Integer() = New Integer(input.Length - 1) {}
        result(0) = InlineAssignHelper(result(input.Length - 1), 0)
        For i As Integer = 1 To input.Length - 2
            result(i) = Math.Max(0, result(i - 1) + input(i))
        Next
        Return result
    End Function
    Public Shared Function Starting(input() As Integer) As Integer()
        Dim result As Integer() = New Integer(input.Length - 1) {}
        result(0) = InlineAssignHelper(result(input.Length - 1), 0)
        For i As Integer = input.Length - 2 To 1 Step -1
            result(i) = Math.Max(0, result(i + 1) + input(i))
        Next
        Return result
    End Function
        Private Shared Function InlineAssignHelper(Of T)(ByRef target As T, value As T) As T
            target = value
            Return value
        End Function

View result on codility

Answer 5

Javascript implementation based on Abhishek Bansal's solution.100/100 on Codility.

function solution(A) {

  let maxsum=0;
  let max_end_at=Array(A.length);
  let max_start_at=Array(A.length);
  max_end_at[0]=max_start_at[A.length-1]=max_end_at[A.length-1]=max_start_at[0]=0;
  let {max}=Math;
  for(let i=1;i<A.length-1;i++){

  max_end_at[i]=max(0,max_end_at[i-1]+A[i]);
   }

  for(let n=A.length-2;n>0;n--){

  max_start_at[n]=max(0,max_start_at[n+1]+A[n]);
   }

  for(let m=1;m<A.length-1;m++){

    maxsum=max(maxsum,max_end_at[m-1]+max_start_at[m+1]);

    }
return maxsum;
}

Answer 6

Using the idea from http://en.wikipedia.org/wiki/Maximum_subarray_problem and Abhishek Bansal's answer above. 100% test pass:

public class Solution {

public int solution(int[] A) {
    int[] maxEndingHere = maxEndingHere(A);
    int[] maxStartingHere = maxStartingHere(A);
    int maxSlice = 0;
    for (int i = 1; i < A.length-1;i++) {
      maxSlice = Math.max(maxSlice, maxEndingHere[i-1]+maxStartingHere[i+1]);
    }
    return maxSlice;
}


/**
 * Precalculate ending subarrays. Take into account that first and last element are always 0
 * @param input
 * @return
 */
public static int[] maxEndingHere(int[] input) {
    int[] result = new int[input.length];
    result[0] = result[input.length-1] = 0;
    for (int i = 1; i < input.length-1; i++) {
        result[i] = Math.max(0, result[i-1] + input[i]);
    }
    return result;
}

/**
 * Precalculate starting subarrays. Take into account that first and last element are always 0
 * @param input
 * @return
 */
public static int[] maxStartingHere(int[] input) {
    int[] result = new int[input.length];
    result[0] = result[input.length-1] = 0;
    for (int i = input.length-2; i >= 1; i--) {
        result[i] = Math.max(0, result[i+1] + input[i]);
    }
    return result;
}

}