[Coding Made Simple] Maximum Sum Subsequence Non-adjacent

Given an array of positive number, find maximum sum subsequence such that elements in this subsequence are not adjacent to each other.

Recursive formula: f(n) = Math.max{f(n - 1), f(n - 2) + arr[n - 1]}.

Dynamic programming is used to get rid of the overlapping subproblems.

State: T[i]: the max sum of non-adjacent subsequence from arr[0.... n - 1];

Function: T[i] = Math.max(T[i - 1], T[i - 2] + arr[i - 1]);

Init: T[0] = 0, T[1] = arr[0];

Answer: T[arr.length].

import java.util.ArrayList;

public class MaxSumSubsequence {
    private ArrayList<Integer> subseq;
    public int getMaxSumSubseqNonAdj(int[] arr) {
        if(arr == null || arr.length == 0) {
            return 0;
        }
        int[] T = new int[arr.length + 1];
        T[0] = 0; T[1] = arr[0];
        for(int i = 2; i < T.length; i++) {
            T[i] = Math.max(T[i - 1], T[i - 2] + arr[i - 1]);
        }
        subseq = new ArrayList<Integer>();
        int currSum = T[arr.length];
        int idx = arr.length;
        while(currSum != 0) {
            if(idx >= 2) {
                if(T[idx - 1] <= T[idx - 2] + arr[idx - 1]) {
                    subseq.add(arr[idx - 1]);
                    currSum -= arr[idx - 1];
                    idx -= 2;
                }
                else {
                    idx--;
                }
            }
            else {
                subseq.add(arr[idx - 1]);
                currSum -= arr[idx - 1];
                idx--;
            }
        }
        return T[arr.length];
    }
}