MaxDoubleSliceSum.go

package max_slice

import (
	"math"
)


/*
A non-empty zero-indexed array A consisting of N integers is given.

A triplet (X, Y, Z), such that 0 ≤ X < Y < Z < N, is called a double slice.

The sum of double slice (X, Y, Z) is the total of
A[X + 1] + A[X + 2] + ... + A[Y − 1] + A[Y + 1] + A[Y + 2] + ... + A[Z − 1].

For example, array A such that:

    A[0] = 3
    A[1] = 2
    A[2] = 6
    A[3] = -1
    A[4] = 4
    A[5] = 5
    A[6] = -1
    A[7] = 2
contains the following example double slices:

double slice (0, 3, 6), sum is 2 + 6 + 4 + 5 = 17,
double slice (0, 3, 7), sum is 2 + 6 + 4 + 5 − 1 = 16,
double slice (3, 4, 5), sum is 0.
The goal is to find the maximal sum of any double slice.

Write a function:

func Solution(A []int) int
that, given a non-empty zero-indexed array A consisting of N integers,
returns the maximal sum of any double slice.

For example, given:

    A[0] = 3
    A[1] = 2
    A[2] = 6
    A[3] = -1
    A[4] = 4
    A[5] = 5
    A[6] = -1
    A[7] = 2
the function should return 17, because no double slice of array A has a sum
of greater than 17.

Assume that:

N is an integer within the range [3..100,000];
each element of array A is an integer within the range [−10,000..10,000].
Complexity:

expected worst-case time complexity is O(N);
expected worst-case space complexity is O(N), beyond input storage
(not counting the storage required for input arguments).
 */

// Due to the fact that the first and the last element are not counted just compute
// The maxSliceSum for 2...n-1 and then remove the smallest element

func MaxDoubleSliceSum(A []int) int {
	maxSliceSum := 1 - (1 << 32 - 1)
	N := len(A) - 2

	if len(A) < 4 {
		return 0;
	}

	leftSum := make([]int, N)
	rightSum := make([]int, N)

	for i := 0; i < N - 1; i += 1 {
		leftValue := A[i + 1]
		rightValue := A[N - i]

		leftSum[i + 1] = int(math.Max(0, float64(leftValue) + float64(leftSum[i])))
		rightSum[N - i - 2] = int(math.Max(0, float64(rightValue) + float64(rightSum[N - i - 1])))
	}

	for i := 0; i < N; i += 1 {
		maxSliceSum = int(math.Max(float64(maxSliceSum), float64(rightSum[i]) + float64(leftSum[i])))
	}

	return maxSliceSum
}