## Given an array, this function will find the sum of maximum subsequence of the given array, that is the integers in the subsequence are in sorted order.

A subsequence is a part of an array which is a sequence that is derived from another sequence by deleting some elements without changing the order. This can be explained in below example

### Example

**INPUT:**

arr[] = {18, 5, 17, 23}

**OUTPUT:**

45

In the above example, 45 is the maximum sum. In the above example, there are two increasing subsequences ie, {18, 17} and {5, 17, 23}. But the second subsequence has the maximum sum

**Time Complexity: O( )**

In this method, we will be using recursion

## Algorithm

**1.** Create a new array and initialize the array elements ie, msis[] = arr[]

**2.** Simply run two loops

**3.** In the outer loop pick each element in the array ie, i=0 to size(n)

**4.** In the inner loop, select each element from 0th to i th index ie, j= 0 to i

**5.** If arr[j] < arr[i] and msis[i] < msis[j] + arr[i], then msis[i] = msis[j] + arr[i]

**6.** find the maximum in msis[] array and print the value.

## C++ Program

#include <bits/stdc++.h> using namespace std; void maxSumIncSubSeq(int arr[],int n) { int msis[n]; for (int i = 0; i < n; ++i) //Initializing the values of msis[] { msis[i] = arr[i]; } for (int i = 0; i < n; ++i) //recursion, storing the inc subsequnce sums in msis[] array { for (int j = 0; j < i; ++j) { if(arr[j]<arr[i] && msis[i]<msis[j]+arr[i]) { cout<<msis[i]<<" "<<msis[j]+arr[i]<<endl; msis[i]=msis[j]+arr[i]; } } } int max=msis[0]; for (int i = 0; i < n; ++i) //finding the maximum value { if(max<msis[i]) { max=msis[i]; } } cout<<"Value of Maximum sum increasing subsequence is: "<<max; } int main() { int arr[]={18, 5, 17, 23}; int n=sizeof(arr)/sizeof(arr[0]); maxSumIncSubSeq(arr,n); return 0; }