Maximum sum from three arrays such that picking elements consecutively from same is not allowed in C++

In this problem, we are given three arrays arr1[], arr2[], and arr3[] all of size N. Our task is to create a program to find the Maximum sum from three arrays such that picking elements consecutively from same is not allowed in C++.

Problem Description

We will find the maximum sum by choosing N elements. i=th element can be chosen of the sum from the i-th element of the array i.e. ith sum is from arr1[i]/ arr2[i]/ arr3[i]. Also, keep in mind that we cannot choose two consecutive elements that can be chosen from the same array.

Let’s take an example to understand the problem,

Inout

arr1[] = {5, 8, 9, 20},
arr2[] = {7, 12, 1, 10},
arr3[] = {8, 9, 10, 11}
N = 4

Output

50

Explanation

For i = 1, we will consider 8 for sum from arr3. For i = 2, we will consider 12 for sum from arr2. For i = 3, we will consider 10 for sum from arr3. For i = 4, we will consider 20 for sum from arr1. Sum = 8 + 12 + 10 + 20 = 50

Solution Approach

To solve the problem, we will be using the dynamic programming approach, we also need memorization of sums till the index to avoid extra calculations. We will create a 2-D matrix, DP[][]. The element at index i,j will be the sum of elements till i-th index and using j-th array. We will recursively find elements for the current and then call the sum of the next elements from the other two arrays.

Example

Program to illustrate the working of our solution,

 Live Demo

#include <bits/stdc++.h>
using namespace std;
const int N = 3;
int findMaxVal(int a, int b){
   if(a > b)
      return a;
      return b;
}
int FindMaximumSum(int index, int arrNo, int arr1[], int arr2[], int arr3[], int n, int DP[][N]){
   if (index == n)
      return 0;
   if (DP[index][arrNo] != -1)
      return DP[index][arrNo];
      int maxVal = -1;
   if (arrNo == 0){
      maxVal = findMaxVal(maxVal, arr2[index] + FindMaximumSum(index + 1, 1, arr1, arr2, arr3, n, DP));
      maxVal = findMaxVal(maxVal, arr3[index] + FindMaximumSum(index + 1, 2, arr1, arr2, arr3, n, DP));
   }
   else if (arrNo == 1){
      maxVal = findMaxVal(maxVal, arr1[index] + FindMaximumSum(index + 1, 0, arr1, arr2, arr3, n, DP));
      maxVal = findMaxVal(maxVal, arr3[index] + FindMaximumSum(index + 1, 2, arr1, arr2, arr3, n, DP));
   }
   else if (arrNo == 2){
      maxVal = findMaxVal(maxVal, arr1[index] + FindMaximumSum(index + 1, 1, arr1, arr2, arr3, n, DP));
      maxVal = findMaxVal(maxVal, arr2[index] + FindMaximumSum(index + 1, 0, arr1, arr2, arr3, n, DP));
   }
   return DP[index][arrNo] = maxVal;
}
int main(){
   int arr1[] = { 5, 8, 9, 20 };
   int arr2[] = { 7, 12, 1, 10 };
   int arr3[] = { 8, 9, 10, 11 };
   int n = sizeof(arr1) / sizeof(arr1[0]);
   int DP[n][N];
   memset(DP, -1, sizeof DP);
   int val1 = FindMaximumSum(0, 0, arr1, arr2, arr3, n, DP);
   int val2 = FindMaximumSum(0, 1, arr1, arr2, arr3, n, DP);
   int val3 = FindMaximumSum(0, 2, arr1, arr2, arr3, n, DP);
   cout<<"The maximum sum from three arrays such that picking elements consecutively from same is not allowed is "<<findMaxVal(val1, findMaxVal(val2, val3));
   return 0;
}

Output

The maximum sum from three arrays such that picking elements consecutively from same is not allowed is 50