Largest Sum of Non-Adjacent Numbers - Amazon Top Interview Questions


Problem Statement :


Given a list of integers nums, write a function that returns the largest sum of non-adjacent numbers. Numbers can be 0 or negative.

Constraints

n ≤ 100,000 where n is the length of nums.

Example 1

Input

nums = [2, 4, 6, 2, 5]

Output

13

Explanation

We can take 2, 6, and 5 to get 13.

Example 2

Input

nums = [5, 1, 1, 5]

Output

10

Explanation

We can take 5 + 5 since they are not adjacent.

Example 3

Input

nums = [-10, -22, -18, -3, -100]

Output

0

Explanation

We don't pick any negative numbers.



Solution :



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                        Solution in C++ :

int solve(vector<int>& nums) {
    if (nums.size() == 0) return 0;
    int incl = max(0, nums[0]), excl = 0;
    for (int i = 1; i < nums.size(); i++) {
        int temp = incl;
        incl = max(excl + nums[i], incl);
        excl = temp;
    }
    return incl;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        if (nums.length <= 1) {
            return nums[0];
        }
        // dp[i] = dp[i - 2] + nums[i] or dp[i - 1]
        // corner case
        int len = nums.length;
        int[] dp = new int[len];
        dp[0] = Math.max(0, nums[0]);
        dp[1] = Math.max(0, Math.max(nums[0], nums[1]));

        for (int i = 2; i < len; i++) {
            if (nums[i] > 0) {
                dp[i] = Math.max(dp[i - 2] + nums[i], dp[i - 1]);
            } else {
                dp[i] = dp[i - 1];
            }
        }
        return dp[len - 1];
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, nums):
        previous, largest = 0, 0
        for n in nums:
            previous, largest = largest, max(largest, previous + n)
        return largest
                    


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