# Maximum sum such that no two elements are adjacent Alternate Method in C++ program

In this problem, we are given an array arr[] of size n consisting of positive values. Our task is to create a program to find the maximum subsequence sum in such a way that no two consecutive elements of the array.

Problem Description − We need to find the sum of subarray which has elements of the array but no two adjacent elements of the array can be taken into consideration.

## Example

Let’s take an example to understand the problem,

## Input

arr[] = {5, 2, 1, 9, 6}

## Output

Explanation

Subarray sum are :
{5, 1, 6}, sum = 5 + 1 + 6 = 12
{2, 9}, sum = 2 + 9 = 11

## Solution Approach

Here, we will have an alternate solution to the problem which is using a dynamic programming approach. In this approach, we will find subsequences satisfying the given condition and printing the maximum of it. We will create an array maxSumDP[n] that stores the maximum sub of the subsequence created. The element maxSumDP[i] stores the maximum sum of subsequences created by taking elements from index i to n-1. For this we can either consider the current element of the array arr[i] i.e. maxSumDP[i] = arr[i] + maxSumDP[i+2]. Or do not consider the current element of the array arr[i] i.e. maxSumDP[i] = maxSumDP[i+2].

## Algorithm

Initialize

maxSumDP[]

Step 2

initialize the values of maxSumDP[n−1] and maxSumDP[n−2].
maxSumDP[n−1] = arr[n−1] and maxSumDP[n−2] = max(arr[n−1], arr[n−2]).

Step 2

loop for i −> n−2 to 0

Step 1.2

initialize the value of maxSumDP[i],
maxSumDP[i] = maximum of (arr[i] + maxSumDP[i + 2],
maxSumDP[i + 1])

Step 3

Return maxSumDP which is the maximum sum sequence sum.

## Example

Program to illustrate the working of our solution,

Live Demo

#include <iostream>
using namespace std;
int retMaxVal(int a, int b){
if(a > b)
return a;
return b;
}
int calcMaxSum(int arr[], int n){
int maxSumDP[n];
maxSumDP[n−1] = arr[n−1];
maxSumDP[n−2] = max(arr[n−1], arr[n−2]);
for (int i = n − 2; i >= 0; i−−) {
maxSumDP[i] = retMaxVal(arr[i] + maxSumDP[i + 2],
maxSumDP[i + 1]);
}
return maxSumDP;
}
int main() {
int arr[] = { 5, 2 , 1, 9, 6 };
int n = sizeof(arr) / sizeof(int);
cout<<"The maximum subsequence sum in such a way that no two consecutive elements of the array is "<<calcMaxSum(arr, n);
return 0;
}

## Output

The maximum subsequence sum in such a way that no two consecutive
elements of the array is 14