Maximize the sum of array by multiplying prefix of array with -1

Given an array of elements ‘arr’, the task is to maximise the sum of the elements of this array after performing the following operation:
You can take any prefix of ‘arr’ and multiply each element of the prefix with ‘-1’.
In the first line, print the maximised sum then in the next line, print the index upto which the sequence of prefixes were chosen.

Examples:

Input: arr = {1, -2, -3, 4}
Output: 10
2 1 3 2
Flip the prefix till 2nd element then the sequence is -1  2 -3  4
Flip the prefix till 1st element then the sequence is  1  2 -3  4
Flip the prefix till 3rd element then the sequence is -1 -2  3  4
Flip the prefix till 2nd element then the sequence is  1  2  3  4
And, the final maximised sum is 10

Input: arr = {1, 2, 3, 4}
Output: 10
As, all the elements are already positive.


Approach: The max sum will always be \small \sum \left | A_i \right | as all the numbers of the array can be changed from negative to positive with the given operation.

  • Traverse the array from left to right, if the element at index ‘i’ is negative then choose ‘i’ as the ending index of the prefix array and multiply each element by ‘-1’.
  • Due to the operation in the previous step, all the elements in the array before index ‘i’ must be negative. So, take the prefix array ending at index ‘i-1’ and apply the same operation again to change all the elements to positive.
  • Repeat the above steps until the complete array has been traversed and print the sum of all the elements along with all the ending indices of the chosen prefix arrays in the end.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include
using namespace std;

void maxSum(int *a, int n)
{

vector l;

// To store sum
int s = 0;

// To store ending indices
// of the chosen prefix array vect
for (int i = 0; i < n; i++) { // Adding the absolute // value of a[i] s += abs(a[i]); if (a[i] >= 0)
continue;

// If i == 0 then there is no index
// to be flipped in (i-1) position
if (i == 0)
l.push_back(i + 1);
else
{
l.push_back(i + 1);
l.push_back(i);
}

}

// print the maximised sum
cout << s << endl; // print the ending indices // of the chosen prefix arrays for (int i = 0; i < l.size(); i++) cout << l[i] << " "; } // Driver Code int main() { int n = 4; int a[] = {1, -2, -3, 4}; maxSum(a, n); } // This code is contributed by // Surendra_Gangwar [tabby title="Python3"]

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# Python implementation of the approach
def maxSum(arr, n):
    # To store sum
    s = 0
  
    # To store ending indices 
    # of the chosen prefix arrays
    l = []
    for i in range(len(a)):
  
        # Adding the absolute 
        # value of a[i]
        s += abs(a[i])
        if (a[i] >= 0):
            continue
  
        # If i == 0 then there is 
        # no index to be flipped 
        # in (i-1) position
        if (i == 0):
            l.append(i + 1)
        else:
            l.append(i + 1)
            l.append(i)
  
    # print the 
    # maximised sum
    print(s)
  
    # print the ending indices 
    # of the chosen prefix arrays
    print(*l)
      
n = 4
a = [1, -2, -3, 4]
maxSum(a, n)

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PHP

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<?php
// PHP implementation of the approach
function maxSum($a, $n)
{
    // To store sum
    $s = 0;
  
    // To store ending indices 
    // of the chosen prefix arrays
    $l = array();
    for ($i = 0; $i < count($a); $i++)
    {
  
        // Adding the absolute 
        // value of a[i]
        $s += abs($a[$i]);
        if ($a[$i] >= 0)
            continue;
  
        // If i == 0 then there is 
        // no index to be flipped 
        // in (i-1) position
        if ($i == 0)
            array_push($l, $i + 1);
        else
        {
            array_push($l, $i + 1);
            array_push($l, $i);
        }
    }
  
    // print the 
    // maximised sum
    echo $s . "\n";
  
    // print the ending indices 
    // of the chosen prefix arrays
    for($i = 0; $i < count($l); $i++)
    echo $l[$i] . " ";
}
  
// Driver Code
$n = 4;
$a = array(1, -2, -3, 4);
maxSum($a, $n);
  
// This code is contributed by mits
?>

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Output:

10
2 1 3 2


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