[Facebook] Maximum sum such that no two elements are adjacent

Question

link

Given an array of positive numbers, find the maximum sum of a subsequence that no 2 numbers should be adjacent.

Eg. (3, 2, 7, 10) should return 13 (3+10)

Eg. (3, 2, 5, 10, 7) should return 15 (3+5+7).

Solution

It is an modified version of “max sum subsequence”. Answer given on gfg is:

Loop for all elements in arr[] and maintain two sums ‘incl’ and ‘excl’ where:

incl = Max sum including the previous element

excl = Max sum excluding the previous element

Code

written by me

public int solve(int[] A) {
    if (A == null || A.length == 0) {
        return 0;
    } else if (A.length == 1) {
        return A[0];
    } else if (A.length == 2) {
        return Math.max(A[0], A[1]);
    }

    // prePreMax is the max non-adjacency sequence ending 2 position ahead
    // preMax is the max non-adjacency sequence ending 1 position ahead
    int prePreMax = A[0];
    int preMax = A[1];
    int ans = 0;

    for (int i = 2; i < A.length; i++) {
        ans = Math.max(ans, prePreMax + A[i]);
        // set the 2 variables: prePreMax, preMax
        int temp = preMax;
        preMax = Math.max(0, prePreMax + A[i]);
        prePreMax = Math.max(prePreMax, temp);
    }
    return ans;
}