Maximum Sum Increasing Subsequence

Author: Ankitr19

Competitive Coding/Dynamic Programming/Maximum Sum Increasing Subsequence/Maximum_sum_increasing_subsequence.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int MaxSumIncrsSubseq(int arr[],int n)
+{
+	int i,j,mx=0;
+	int MSIS[n];   //An array of initial size as that of the original array to store the maximum sum of the increasing subsequence till that point.
+	for(i=0;i<n;i++)
+	{
+		MSIS[i]=arr[i];
+	}
+	/* The main condition to check if the next element of the array should be considered in the maximum sum subsequence array or not , 
+	   by checking the given two conditions:-
+	   1.) arr[i]>arr[j]
+	   2.)MSIS[i]<MSIS[j] + arr[i]
+	*/
+	for(i=1;i<n;i++)
+	{
+		for(j=0;j<i;j++)
+		{
+			if(arr[i]>arr[j] && MSIS[i]<MSIS[j]+arr[i])
+				MSIS[i]=MSIS[j]+arr[i];
+		}
+	}
+	for(i=0;i<n;i++)
+		if(mx<MSIS[i])
+			mx=MSIS[i];
+
+	return mx;       // The maximum sum of the increasing subsequence.
+}
+
+int main()
+{
+	int arr[] = {2,3,100,5,6,101,1};
+	int n = sizeof(arr)/sizeof(arr[0]);
+	int ans = MaxSumIncrsSubseq(arr,n);
+	cout<<ans<<"\n";
+	return 0;
+}

Competitive Coding/Dynamic Programming/Maximum Sum Increasing Subsequence/Maximum_sum_increasing_subsequence.md

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+Maximum Sum in an increasing subsequence - Dynamic Programming
+
+-This algorithm is a slight variation in the Longest Increasing Subsequence.
+-In this algorithm we insert a case to check whether the sum of the new increasing subsequence is greater than the previous one or not.
+
+Example:-
+
+arr[] = {2,3,100,5,6,101,1}
+
+Now, here the maximum sum increasing subsequence will be = 206.