# Maximum value after merging all elements in the array

Given an array a of size N. The task is to merge all elements in the array and find the maximum possible value. One can merge two elements in the array as explained below.

If i and j are two indexes of the array(i j). Merging jth element into ith element makes a[i] as a[i] – a[j] and remove a[j] from the array.

Examples:

Input : a[] = {2 1 2 1} (n == 4)
Output : 4
Merge 3rd element into 2nd element then the array becomes {2, -1, 1}
Merge 3rd element into 2nd element then the array becomes {2, -2}
Merge 2rd element into 1nd element then the array becomes {4}

Input: a[] = {1, 3, 5, -2, -6}
Output: 17
Merge 4th element into 3rd element then the array becomes {1, 3, -7, -6}
Merge 2rd element into 3rd element then the array becomes {1, -10, -6}
Merge 2nd element into 1st element then the array becomes {11, -6}
Merge 2rd element into 1st element then the array becomes {17}

Approach:

• If the array contains both positive and negative elements, then add absolute value all elements of the array
• If the array contains the only positive elements. Then subtract the least element from the summation of all other elements
• If the array contains the only negative elements. First, replace all elements with their absolute values. Then subtract the least element from the summation of all other elements

Below is the implementation of the above approach:

## C++

 `// CPP program to maximum value after  ` `// merging all elements in the array ` `#include ` `using` `namespace` `std; ` ` `  `// Function to maximum value after  ` `// merging all elements in the array ` `int` `Max_sum(``int` `a[], ``int` `n) ` `{ ` `    ``// To check if positive and negative  ` `    ``// elements present or not ` `    ``int` `pos = 0, neg = 0; ` `     `  `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``// Check for positive integer ` `        ``if``(a[i] > 0) ` `            ``pos = 1; ` `             `  `        ``// Check for negative integer ` `        ``else` `if``(a[i] < 0) ` `            ``neg = 1; ` `             `  `        ``// If both positive and negative ` `        ``// elements are present ` `        ``if``(pos == 1 and neg == 1) ` `            ``break``; ` `    ``} ` `     `  `    ``// To store maximum value possible ` `    ``int` `sum = 0; ` `     `  `    ``if``(pos==1 and neg==1) ` `    ``{ ` `        ``for``(``int` `i=0; i < n ; i++) ` `            ``sum += ``abs``(a[i]); ` `    ``} ` `     `  `    ``else` `if``(pos == 1) ` `    ``{ ` `        ``// To find minimum value ` `        ``int` `mini = a; ` `        ``sum = a; ` `        ``for``(``int` `i=1; i < n; i++) ` `        ``{ ` `            ``mini = min(mini, a[i]); ` `            ``sum += a[i]; ` `        ``}     ` `         `  `        ``// Remove minimum element ` `        ``sum -= 2*mini; ` `    ``}     ` `     `  `    ``else` `if``(neg == 1) ` `    ``{ ` `        ``// Replace with absolute values ` `        ``for``(``int` `i = 0; i < n; i++) ` `            ``a[i] = ``abs``(a[i]); ` `             `  `        ``// To find minimum value ` `        ``int` `mini = a; ` `        ``sum = a; ` `        ``for``(``int` `i=1; i < n; i++) ` `        ``{ ` `            ``mini = min(mini, a[i]); ` `            ``sum += a[i]; ` `        ``}     ` `         `  `        ``// Remove minimum element ` `        ``sum -= 2*mini; ` `         `  `    ``} ` `     `  `    ``// Return the required sum ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[] = {1, 3, 5, -2, -6}; ` `     `  `    ``int` `n = ``sizeof``(a) / ``sizeof``(a); ` `     `  `    ``// Function call ` `    ``cout << Max_sum(a, n); ` `     `  `    ``return` `0; ` `} `

## Java

 `// Java program to maximum value after  ` `// merging all elements in the array ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function to maximum value after  ` `// merging all elements in the array ` `static` `int` `Max_sum(``int` `a[], ``int` `n) ` `{ ` `    ``// To check if positive and negative  ` `    ``// elements present or not ` `    ``int` `pos = ``0``, neg = ``0``; ` `     `  `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `        ``// Check for positive integer ` `        ``if``(a[i] > ``0``) ` `            ``pos = ``1``; ` `             `  `        ``// Check for negative integer ` `        ``else` `if``(a[i] < ``0``) ` `            ``neg = ``1``; ` `             `  `        ``// If both positive and negative ` `        ``// elements are present ` `        ``if``((pos == ``1``) && (neg == ``1``)) ` `            ``break``; ` `    ``} ` `     `  `    ``// To store maximum value possible ` `    ``int` `sum = ``0``; ` `     `  `    ``if``((pos == ``1``) && (neg == ``1``)) ` `    ``{ ` `        ``for``(``int` `i = ``0``; i < n ; i++) ` `            ``sum += Math.abs(a[i]); ` `    ``} ` `     `  `    ``else` `if``(pos == ``1``) ` `    ``{ ` `        ``// To find minimum value ` `        ``int` `mini = a[``0``]; ` `        ``sum = a[``0``]; ` `        ``for``(``int` `i = ``1``; i < n; i++) ` `        ``{ ` `            ``mini = Math.min(mini, a[i]); ` `            ``sum += a[i]; ` `        ``}  ` `         `  `        ``// Remove minimum element ` `        ``sum -= ``2``*mini; ` `    ``}  ` `     `  `    ``else` `if``(neg == ``1``) ` `    ``{ ` `        ``// Replace with absolute values ` `        ``for``(``int` `i = ``0``; i < n; i++) ` `            ``a[i] = Math.abs(a[i]); ` `             `  `        ``// To find minimum value ` `        ``int` `mini = a[``0``]; ` `        ``sum = a[``0``]; ` `        ``for``(``int` `i = ``1``; i < n; i++) ` `        ``{ ` `            ``mini = Math.min(mini, a[i]); ` `            ``sum += a[i]; ` `        ``}  ` `         `  `        ``// Remove minimum element ` `        ``sum -= ``2``*mini; ` `         `  `    ``} ` `     `  `    ``// Return the required sum ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args) ` `{ ` ` `  `    ``int` `[]a = {``1``, ``3``, ``5``, -``2``, -``6``}; ` `    ``int` `n = a.length; ` `    ``// Function call ` `    ``System.out.println (Max_sum(a, n)); ` `} ` `} ` ` `  `// This code is contributed by ajit. `

## Python3

 `# Python 3 program to maximum value after  ` `# merging all elements in the array ` ` `  `# Function to maximum value after  ` `# merging all elements in the array ` `def` `Max_sum(a, n): ` `    ``# To check if positive and negative  ` `    ``# elements present or not ` `    ``pos ``=` `0` `    ``neg ``=` `0` `     `  `    ``for` `i ``in` `range``(n): ` `        ``# Check for positive integer ` `        ``if``(a[i] > ``0``): ` `            ``pos ``=` `1` `             `  `        ``# Check for negative integer ` `        ``elif``(a[i] < ``0``): ` `            ``neg ``=` `1` `             `  `        ``# If both positive and negative ` `        ``# elements are present ` `        ``if``(pos ``=``=` `1` `and` `neg ``=``=` `1``): ` `            ``break` `     `  `    ``# To store maximum value possible ` `    ``sum` `=` `0` `     `  `    ``if``(pos``=``=``1` `and` `neg``=``=``1``): ` `        ``for` `i ``in` `range``(n): ` `            ``sum` `+``=` `abs``(a[i]) ` `     `  `    ``elif``(pos ``=``=` `1``): ` `        ``# To find minimum value ` `        ``mini ``=` `a[``0``] ` `        ``sum` `=` `a[``0``] ` `        ``for` `i ``in` `range``(``1``,n,``1``): ` `            ``mini ``=` `min``(mini, a[i]) ` `            ``sum` `+``=` `a[i]  ` `         `  `        ``# Remove minimum element ` `        ``sum` `-``=` `2``*``mini ` `     `  `    ``elif``(neg ``=``=` `1``): ` `        ``# Replace with absolute values ` `        ``for` `i ``in` `range``(n): ` `            ``a[i] ``=` `abs``(a[i]) ` `             `  `        ``# To find minimum value ` `        ``mini ``=` `a[``0``] ` `        ``sum` `=` `a[``0``] ` `        ``for` `i ``in` `range``(``1``,n): ` `            ``mini ``=` `min``(mini, a[i]) ` `            ``sum` `+``=` `a[i]  ` `         `  `        ``# Remove minimum element ` `        ``sum` `-``=` `2``*``mini ` `            `  `    ``# Return the required sum ` `    ``return` `sum` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``a ``=` `[``1``, ``3``, ``5``, ``-``2``, ``-``6``] ` `     `  `    ``n ``=` `len``(a) ` `     `  `    ``# Function call ` `    ``print``(Max_sum(a, n)) ` ` `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# program to maximum value after  ` `// merging all elements in the array  ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Function to maximum value after  ` `    ``// merging all elements in the array  ` `    ``static` `int` `Max_sum(``int``[] a, ``int` `n) ` `    ``{ ` `        ``// To check if positive and negative  ` `        ``// elements present or not  ` `        ``int` `pos = 0, neg = 0; ` ` `  `        ``for` `(``int` `i = 0; i < n; i++) ` `        ``{ ` `            ``// Check for positive integer  ` `            ``if` `(a[i] > 0) ` `                ``pos = 1; ` ` `  `            ``// Check for negative integer  ` `            ``else` `if` `(a[i] < 0) ` `                ``neg = 1; ` ` `  `            ``// If both positive and negative  ` `            ``// elements are present  ` `            ``if` `((pos == 1) && (neg == 1)) ` `                ``break``; ` `        ``} ` ` `  `        ``// To store maximum value possible  ` `        ``int` `sum = 0; ` ` `  `        ``if` `((pos == 1) && (neg == 1)) ` `        ``{ ` `            ``for` `(``int` `i = 0; i < n; i++) ` `                ``sum += Math.Abs(a[i]); ` `        ``} ` ` `  `        ``else` `if` `(pos == 1) ` `        ``{ ` `            ``// To find minimum value  ` `            ``int` `mini = a; ` `            ``sum = a; ` `            ``for` `(``int` `i = 1; i < n; i++) ` `            ``{ ` `                ``mini = Math.Min(mini, a[i]); ` `                ``sum += a[i]; ` `            ``} ` ` `  `            ``// Remove minimum element  ` `            ``sum -= 2 * mini; ` `        ``} ` ` `  `        ``else` `if` `(neg == 1) ` `        ``{ ` `            ``// Replace with absolute values  ` `            ``for` `(``int` `i = 0; i < n; i++) ` `                ``a[i] = Math.Abs(a[i]); ` ` `  `            ``// To find minimum value  ` `            ``int` `mini = a; ` `            ``sum = a; ` `            ``for` `(``int` `i = 1; i < n; i++) ` `            ``{ ` `                ``mini = Math.Min(mini, a[i]); ` `                ``sum += a[i]; ` `            ``} ` ` `  `            ``// Remove minimum element  ` `            ``sum -= 2 * mini; ` ` `  `        ``} ` ` `  `        ``// Return the required sum  ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` ` `  `        ``int``[] a = { 1, 3, 5, -2, -6 }; ` `        ``int` `n = a.Length; ` `         `  `        ``// Function call  ` `        ``Console.WriteLine(Max_sum(a, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// sanjeev2552 `

Output:

```17
```

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