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,

#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