Maximum sum combination from the given array

Given an array arr[] of N integers and three integers X, Y and Z. The task is to find the maximum value of (arr[i] * X) + (arr[j] * Y) + (arr[k] * Z) where 0 ≤ i ≤ j ≤ k ≤ N – 1.

Examples:

Input: arr[] = {1, 5, -3, 4, -2}, X = 2, Y = 1, Z = -1
Output: 18
(2 * 5) + (1 * 5) + (-1 * -3) = 18
is the maximum possible sum.

Input: arr[] = {2, 4, -9, -64, 7, 3}, X = -1, Y = 1, Z = 1
Output: 78

Approach: Find the maximum and the minimum negative and positive values from the array. Also, check whether 0 is present in the array or not. Now, for the given values of X, Y and Z. Choose the values found previously from the array which maximizes the overall sum.



Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the maximum possible
// value of the given equation
int maxSum(int arr[], int n, int x, int y, int z)
{
  
    // To store the minimum and the maximum negative
    // and positive values from the array
    int minNeg = INT_MAX, maxNeg = INT_MAX;
    int minPos = INT_MIN, maxPos = INT_MIN;
  
    // To store whether 0 is present in the array
    bool isZeroPresent = false;
  
    // Update the values of the
    // above defined variables
    for (int i = 0; i < n; i++) {
        if (arr[i] == 0) {
            isZeroPresent = true;
        }
        else if (arr[i] < 0) {
            minNeg = min(minNeg, arr[i]);
            maxNeg = max(maxNeg, arr[i]);
        }
        else {
            minPos = min(minPos, arr[i]);
            maxPos = max(maxPos, arr[i]);
        }
    }
  
    // To store the resultant sum
    int sum = 0;
  
    // x will not contibute to the
    // sum if it is equal to 0
    if (x != 0) {
  
        // If x is negative
        if (x < 0) {
  
            // Either multiply it with the minimum
            // negative number from the array
            if (minNeg != INT_MAX)
                sum += (x * minNeg);
  
            // Or multiply it with the minimum
            // positive element if zero is
            // not present in the array
            else if (!isZeroPresent)
                sum += (x * minPos);
        }
  
        // If x is positive
        else {
  
            // Multiply it with the maximum
            // positive value from the array
            if (maxPos != INT_MIN)
                sum += (x * maxPos);
  
            // Or multiply it with the maximum
            // negative element if zero is
            // not present in the array
            else if (!isZeroPresent)
                sum += (x * maxPos);
        }
    }
  
    // Same as x
    if (y != 0) {
        if (y < 0) {
            if (minNeg != INT_MAX)
                sum += (y * minNeg);
            else if (!isZeroPresent)
                sum += (y * minPos);
        }
        else {
            if (maxPos != INT_MIN)
                sum += (y * maxPos);
            else if (!isZeroPresent)
                sum += (y * maxPos);
        }
    }
  
    // Same as x
    if (z != 0) {
        if (z < 0) {
            if (minNeg != INT_MAX)
                sum += (z * minNeg);
            else if (!isZeroPresent)
                sum += (z * minPos);
        }
        else {
            if (maxPos != INT_MIN)
                sum += (z * maxPos);
            else if (!isZeroPresent)
                sum += (z * maxPos);
        }
    }
  
    return sum;
}
  
// Driver code
int main()
{
    int arr[] = { 2, 4, -9, -64, 7, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = -1, y = 1, z = 1;
  
    cout << maxSum(arr, n, x, y, z);
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG
{
  
// Function to return the maximum possible
// value of the given equation
static int maxSum(int arr[], int n, int x, int y, int z)
{
  
    // To store the minimum and the maximum negative
    // and positive values from the array
    int minNeg = Integer.MAX_VALUE, 
        maxNeg = Integer.MAX_VALUE;
    int minPos = Integer.MIN_VALUE, 
        maxPos = Integer.MIN_VALUE;
  
    // To store whether 0 is present in the array
    boolean isZeroPresent = false;
  
    // Update the values of the
    // above defined variables
    for (int i = 0; i < n; i++)
    {
        if (arr[i] == 0
        {
            isZeroPresent = true;
        }
        else if (arr[i] < 0)
        {
            minNeg = Math.min(minNeg, arr[i]);
            maxNeg = Math.max(maxNeg, arr[i]);
        }
        else 
        {
            minPos = Math.min(minPos, arr[i]);
            maxPos = Math.max(maxPos, arr[i]);
        }
    }
  
    // To store the resultant sum
    int sum = 0;
  
    // x will not contibute to the
    // sum if it is equal to 0
    if (x != 0
    {
  
        // If x is negative
        if (x < 0)
        {
  
            // Either multiply it with the minimum
            // negative number from the array
            if (minNeg != Integer.MAX_VALUE)
                sum += (x * minNeg);
  
            // Or multiply it with the minimum
            // positive element if zero is
            // not present in the array
            else if (!isZeroPresent)
                sum += (x * minPos);
        }
  
        // If x is positive
        else
        {
  
            // Multiply it with the maximum
            // positive value from the array
            if (maxPos != Integer.MIN_VALUE)
                sum += (x * maxPos);
  
            // Or multiply it with the maximum
            // negative element if zero is
            // not present in the array
            else if (!isZeroPresent)
                sum += (x * maxPos);
        }
    }
  
    // Same as x
    if (y != 0
    {
        if (y < 0
        {
            if (minNeg != Integer.MAX_VALUE)
                sum += (y * minNeg);
            else if (!isZeroPresent)
                sum += (y * minPos);
        }
        else 
        {
            if (maxPos != Integer.MIN_VALUE)
                sum += (y * maxPos);
            else if (!isZeroPresent)
                sum += (y * maxPos);
        }
    }
  
    // Same as x
    if (z != 0
    {
        if (z < 0)
        {
            if (minNeg != Integer.MAX_VALUE)
                sum += (z * minNeg);
            else if (!isZeroPresent)
                sum += (z * minPos);
        }
        else
        {
            if (maxPos != Integer.MIN_VALUE)
                sum += (z * maxPos);
            else if (!isZeroPresent)
                sum += (z * maxPos);
        }
    }
    return sum;
}
  
// Driver code
public static void main(String[] args)
{
    int arr[] = { 2, 4, -9, -64, 7, 3 };
    int n = arr.length;
    int x = -1, y = 1, z = 1;
  
    System.out.print(maxSum(arr, n, x, y, z));
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 implementation of the approach
  
# Function to return the maximum possible
# value of the given equation
def maxSum(arr, n, x, y, z):
  
    # To store the minimum and the maximum negative
    # and positive values from the array
    minNeg = 10**9
    maxNeg = 10**9
    minPos = -10**9
    maxPos = -10**9
  
    # To store whether 0 is present in the array
    isZeroPresent = False
  
    # Update the values of the
    # above defined variables
    for i in range(n):
        if (arr[i] == 0):
            isZeroPresent = True
        elif (arr[i] < 0):
            minNeg = min(minNeg, arr[i])
            maxNeg = max(maxNeg, arr[i])
        else:
            minPos = min(minPos, arr[i])
            maxPos = max(maxPos, arr[i])
  
    # To store the resultant summ
    summ = 0
  
    # x will not contibute to the
    # summ if it is equal to 0
    if (x != 0):
  
        # If x is negative
        if (x < 0):
  
            # Either multiply it with the minimum
            # negative number from the array
            if (minNeg != 10**9):
                summ += (x * minNeg)
  
            # Or multiply it with the minimum
            # positive element if zero is
            # not present in the array
        elif (isZeroPresent == False):
                summ += (x * minPos)
  
        # If x is positive
        else:
  
            # Multiply it with the maximum
            # positive value from the array
            if (maxPos != -10**9):
                summ += (x * maxPos)
  
            # Or multiply it with the maximum
            # negative element if zero is
            # not present in the array
            elif (isZeroPresent == False):
                summ += (x * maxPos)
                  
    # Same as x
    if (y != 0):
        if (y < 0):
            if (minNeg != 10**9):
                summ += (y * minNeg)
            elif (isZeroPresent == False):
                summ += (y * minPos)
  
        else:
            if (maxPos != -10**9):
                summ += (y * maxPos)
            elif (isZeroPresent == False):
                summ += (y * maxPos)
                  
    # Same as x
    if (z != 0):
        if (z < 0):
            if (minNeg != 10**9):
                summ += (z * minNeg)
            elif (isZeroPresent == False):
                summ += (z * minPos)
  
        else:
            if (maxPos != -10**9):
                summ += (z * maxPos)
            elif (isZeroPresent == False):
                summ += (z * maxPos)
  
    return summ
  
# Driver code
arr = [2, 4, -9, -64, 7, 3]
n = len(arr)
x = -1
y = 1
z = 1
  
print(maxSum(arr, n, x, y, z))
  
# This code is contributed by Mohit Kumar

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
  
    // Function to return the maximum possible 
    // value of the given equation 
    static int maxSum(int []arr, int n, 
                      int x, int y, int z) 
    
          
        int INT_MAX = int.MaxValue;
        int INT_MIN = int.MinValue;
          
        // To store the minimum and the maximum negative 
        // and positive values from the array 
        int minNeg = INT_MAX, maxNeg = INT_MAX; 
        int minPos = INT_MIN, maxPos = INT_MIN; 
      
        // To store whether 0 is present in the array 
        bool isZeroPresent = false
      
        // Update the values of the 
        // above defined variables 
        for (int i = 0; i < n; i++)
        
            if (arr[i] == 0) 
            
                isZeroPresent = true
            
            else if (arr[i] < 0) 
            
                minNeg = Math.Min(minNeg, arr[i]); 
                maxNeg = Math.Max(maxNeg, arr[i]); 
            
            else
            
                minPos = Math.Min(minPos, arr[i]); 
                maxPos = Math.Max(maxPos, arr[i]); 
            
        
      
        // To store the resultant sum 
        int sum = 0; 
      
        // x will not contibute to the 
        // sum if it is equal to 0 
        if (x != 0) 
        
      
            // If x is negative 
            if (x < 0)
            
      
                // Either multiply it with the minimum 
                // negative number from the array 
                if (minNeg != INT_MAX) 
                    sum += (x * minNeg); 
      
                // Or multiply it with the minimum 
                // positive element if zero is 
                // not present in the array 
                else if (!isZeroPresent) 
                    sum += (x * minPos); 
            
      
            // If x is positive 
            else 
            
      
                // Multiply it with the maximum 
                // positive value from the array 
                if (maxPos != INT_MIN) 
                    sum += (x * maxPos); 
      
                // Or multiply it with the maximum 
                // negative element if zero is 
                // not present in the array 
                else if (!isZeroPresent) 
                    sum += (x * maxPos); 
            
        
      
        // Same as x 
        if (y != 0) 
        
            if (y < 0)
            
                if (minNeg != INT_MAX) 
                    sum += (y * minNeg); 
                else if (!isZeroPresent) 
                    sum += (y * minPos); 
            
            else 
            
                if (maxPos != INT_MIN) 
                    sum += (y * maxPos); 
                else if (!isZeroPresent) 
                    sum += (y * maxPos); 
            
        
      
        // Same as x 
        if (z != 0) 
        
            if (z < 0) 
            
                if (minNeg != INT_MAX) 
                    sum += (z * minNeg); 
                else if (!isZeroPresent) 
                    sum += (z * minPos); 
            
            else 
            
                if (maxPos != INT_MIN) 
                    sum += (z * maxPos); 
                else if (!isZeroPresent) 
                    sum += (z * maxPos); 
            
        
        return sum; 
    
      
    // Driver code 
    static public void Main ()
    
        int []arr = { 2, 4, -9, -64, 7, 3 }; 
        int n = arr.Length; 
        int x = -1, y = 1, z = 1; 
      
        Console.Write(maxSum(arr, n, x, y, z)); 
    
}
  
// This code is contributed by AnkitRai01

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Output:

78

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