Massive Algorithms: Codility 7.1 Max Double Slice Sum

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:

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

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.

Elements of input arrays can be modified.

这道题其实和leetcode 的Best Time to Buy and Sell Stock III是一道题。

    public int solution(int[] A) {

        int[] fromLeft = new int[A.length];

        int[] fromRight = new int[A.length];

        int max = 0;

        for (int i = 2; i < A.length; i++) {

            fromLeft[i] = Math.max(0, fromLeft[i-1] + A[i-1]);

}

        for (int i = A.length - 3; i >= 0; i--) {

            fromRight[i] = Math.max(0, fromRight[i+1] + A[i+1]);

}

        for (int i = 1; i < A.length - 1; i++) {

            max = Math.max(max, fromLeft[i] + fromRight[i]);

}

        return max;

}

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