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

Given an array of elements ‘arr’, the task is to maximize 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 maximized sum than 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 as all the numbers of the array can be changed from negative to positive with the given operation. 
 


Below is the implementation of the above approach:
 

// C++ implementation of the approach
#include<bits/stdc++.h>
using namespace std;
 
void maxSum(int *a, int n)
{
     
    vector<int> 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 maximized 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

                    
// Java implementation of the approach
import java.util.*;
 
class GFG
{
     
static void maxSum(int []a, int n)
{
    Vector<Integer> l = new Vector<Integer>();
     
    // 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 += Math.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.add(i + 1);
        else
        {
            l.add(i + 1);
            l.add(i);
        }
    }
 
    // print the maximised sum
    System.out.println(s);
 
    // print the ending indices
    // of the chosen prefix arrays
    for (int i = 0; i < l.size(); i++)
    System.out.print(l.get(i) + " ");
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 4;
    int a[] = {1, -2, -3, 4};
    maxSum(a, n);
}
}
 
// This code is contributed by 29AjayKumar

                    
# 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)

                    
// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG
{
     
static void maxSum(int []a, int n)
{
    List<int> l = new List<int>();
     
    // 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 += Math.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.Add(i + 1);
        else
        {
            l.Add(i + 1);
            l.Add(i);
        }
    }
 
    // print the maximised sum
    Console.WriteLine(s);
 
    // print the ending indices
    // of the chosen prefix arrays
    for (int i = 0; i < l.Count; i++)
    Console.Write(l[i] + " ");
}
 
// Driver Code
public static void Main(String[] args)
{
    int n = 4;
    int []a = {1, -2, -3, 4};
    maxSum(a, n);
}
}
 
// This code is contributed by PrinciRaj1992

                    
<?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
?>

                    
<script>
 
// Javascript implementation of the above approach
 
    function maxSum(a, n)
{
    let l = [];
       
    // To store sum
    let s = 0;
   
    // To store ending indices
    // of the chosen prefix array vect
    for (let i = 0; i < n; i++)
    {
   
        // Adding the absolute
        // value of a[i]
        s += Math.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(i + 1);
        else
        {
            l.push(i + 1);
            l.push(i);
        }
    }
   
    // print the maximised sum
    document.write(s + "<br/>");
   
    // print the ending indices
    // of the chosen prefix arrays
    for (let i = 0; i < l.length; i++)
    document.write(l[i] + " ");
}
 
// driver code
 
    let n = 4;
    let a = [1, -2, -3, 4];
    maxSum(a, n);
   
</script>

                    

Output: 
10
2 1 3 2

 

Time Complexity: O(n)

Auxiliary Space: O(n)


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