Given a array of n positive and negative integers, find the subsequence with the maximum even sum and display that even sum.
Examples:
Input: arr[] = {-2, 2, -3, 1, 3}
Output: 6
Explanation: The longest subsequence
with even sum is 2, 1 and 3.
Input: arr[] = {-2, 2, -3, 4, 5}
Output: 8
Explanation: The longest subsequence
with even sum is 2,-3,4 and 5The approach to the problem can be shorted down to points:
- Sum up all positive numbers
- If the sum is even then that will be the max sum possible
- If the sum is not even then either subtract a positive odd number from it, or add a negative odd.
- Find maximum max odd of negative odd numbers, hence sum+a[I] (as a[I] is itself negative)
- Find minimum min odd of positive odd numbers, hence sun-a[I].
- The maximum of the both the results will be the answer.
Below is the implementation of the above approach
// CPP program to find longest even sum
// subsequence.
#include <bits/stdc++.h>
using namespace std;
// Returns sum of maximum even sum subsequence
int maxEvenSum(int arr[], int n)
{
// Find sum of positive numbers
int pos_sum = 0;
for (int i = 0; i < n; ++i)
if (arr[i] > 0)
pos_sum += arr[i];
// If sum is even, it is our
// answer
if (pos_sum % 2 == 0)
return pos_sum;
// Traverse the array to find the
// maximum sum by adding a positive
// odd or subtracting a negative odd
int ans = INT_MIN;
for (int i = 0; i < n; ++i) {
if (arr[i] % 2 != 0) {
if (arr[i] > 0)
ans = max(ans, pos_sum - arr[i]);
else
ans = max(ans, pos_sum + arr[i]);
}
}
return ans;
}
// driver program
int main()
{
int a[] = { -2, 2, -3, 1 };
int n = sizeof(a) / sizeof(a[0]);
cout << maxEvenSum(a, n);
return 0;
}
// Java program to find longest
// even sum subsequence.
class MaxevenSum
{
// Returns sum of maximum even sum
// subsequence
static int maxEvenSum(int arr[], int n)
{
// Find sum of positive numbers
int pos_sum = 0;
for (int i = 0; i < n; ++i)
if (arr[i] > 0)
pos_sum += arr[i];
// If sum is even, it is our
// answer
if (pos_sum % 2 == 0)
return pos_sum;
// Traverse the array to find the
// maximum sum by adding a
// positive odd or subtracting a
// negative odd
int ans = Integer.MIN_VALUE;
for (int i = 0; i < n; ++i) {
if (arr[i] % 2 != 0) {
if (arr[i] > 0)
ans = ans>(pos_sum - arr[i]) ?
ans:(pos_sum - arr[i]);
else
ans = ans>(pos_sum + arr[i]) ?
ans:(pos_sum + arr[i]);
}
}
return ans;
}
// driver program
public static void main(String s[])
{
int a[] = {-2, 2, -3, 1};
System.out.println(maxEvenSum(a, a.length));
}
}
// This code is contributed by Prerna Saini
# Python 3 program to find longest
# even sum subsequence.
INT_MIN = -100000000
# Returns sum of maximum even
# sum subsequence
def maxEvenSum(arr, n):
# Find sum of positive numbers
pos_sum = 0
for i in range(n):
if (arr[i] > 0):
pos_sum += arr[i]
# If sum is even, it is our answer
if (pos_sum % 2 == 0):
return pos_sum
# Traverse the array to find the
# maximum sum by adding a positive
# odd or subtracting a negative odd
ans = INT_MIN;
for i in range(n):
if (arr[i] % 2 != 0):
if (arr[i] > 0):
ans = max(ans, pos_sum - arr[i])
else:
ans = max(ans, pos_sum + arr[i])
return ans
# Driver Code
a = [-2, 2, -3, 1]
n = len(a)
print(maxEvenSum(a, n))
# This code is contributed by sahilshelangia
// C# program to find longest
// even sum subsequence.
using System;
class GFG {
// Returns sum of maximum even sum
// subsequence
static int maxEvenSum(int []arr, int n)
{
// Find sum of positive numbers
int pos_sum = 0;
for (int i = 0; i < n; ++i)
if (arr[i] > 0)
pos_sum += arr[i];
// If sum is even, it is our
// answer
if (pos_sum % 2 == 0)
return pos_sum;
// Traverse the array to find the
// maximum sum by adding a
// positive odd or subtracting a
// negative odd
int ans = int.MinValue;
for (int i = 0; i < n; ++i)
{
if (arr[i] % 2 != 0)
{
if (arr[i] > 0)
ans = (ans > (pos_sum - arr[i]))
? ans : (pos_sum - arr[i]);
else
ans = (ans > (pos_sum + arr[i]))
? ans : (pos_sum + arr[i]);
}
}
return ans;
}
// driver program
public static void Main()
{
int []a = {-2, 2, -3, 1};
Console.WriteLine(maxEvenSum(a, a.Length));
}
}
// This code is contributed by vt_m.
<?php
// PHP program to find longest
// even sum subsequence.
// Returns sum of maximum even
// sum subsequence
function maxEvenSum( $arr, $n)
{
// Find sum of positive numbers
$pos_sum = 0;
for ( $i = 0; $i < $n; ++$i)
if ($arr[$i] > 0)
$pos_sum += $arr[$i];
// If sum is even, it is our
// answer
if ($pos_sum % 2 == 0)
return $pos_sum;
// Traverse the array to find
// the maximum sum by adding
// a positive odd or
// subtracting a negative odd
$ans = PHP_INT_MIN;
for ( $i = 0; $i < $n; ++$i) {
if ($arr[$i] % 2 != 0) {
if ($arr[$i] > 0)
$ans = max($ans,
$pos_sum - $arr[$i]);
else
$ans = max($ans,
$pos_sum + $arr[$i]);
}
}
return $ans;
}
// driver program
$a = array( -2, 2, -3, 1 );
$n = count($a);
echo maxEvenSum($a, $n);
// This code is contributed by anuj_67.
?>
<script>
// javascript program to find longest
// even sum subsequence.
// Returns sum of maximum even sum
// subsequence
function maxEvenSum(arr , n)
{
// Find sum of positive numbers
var pos_sum = 0;
for (i = 0; i < n; ++i)
if (arr[i] > 0)
pos_sum += arr[i];
// If sum is even, it is our
// answer
if (pos_sum % 2 == 0)
return pos_sum;
// Traverse the array to find the
// maximum sum by adding a
// positive odd or subtracting a
// negative odd
var ans = Number.MIN_VALUE;
for (i = 0; i < n; ++i) {
if (arr[i] % 2 != 0) {
if (arr[i] > 0)
ans = ans > (pos_sum - arr[i]) ? ans : (pos_sum - arr[i]);
else
ans = ans > (pos_sum + arr[i]) ? ans : (pos_sum + arr[i]);
}
}
return ans;
}
// driver program
var a = [ -2, 2, -3, 1 ];
document.write(maxEvenSum(a, a.length));
// This code is contributed by Rajput-Ji
</script>
Output
2
Time complexity : O(n)
Auxiliary Space : O(1)