# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// C++ implementation of the approach ` `#include ` `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); ` `    ``int` `x = -1, y = 1, z = 1; ` ` `  `    ``cout << maxSum(arr, n, x, y, z); ` ` `  `    ``return` `0; ` `} `

## Java

 `// 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 `

## Python3

 `# 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 `

## C#

 `// 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 `

Output:

```78
```

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