How to Count the Maximum Number of Elements in an Array that Sum to an Even Number

How can I count the maximum number of elements in an array such that their sum is even?

To solve the problem of counting the maximum number of elements in an array that sum to an even number, one must understand the properties of even and odd numbers. An even sum results from adding even numbers together or an even number of odd numbers. Therefore, the approach involves evaluating the elements in the given array based on these properties.

def max_even_sum_elements(arr):
    evens = sum(1 for x in arr if x % 2 == 0)
    odds = sum(1 for x in arr if x % 2 != 0)
    if odds % 2 == 0:
        return evens + odds  # all elements can be included
    else:
        return evens + odds - 1  # exclude one odd number to make sum even

Causes

• Understanding even and odd numbers: A sum is even if it contains an even count of odd numbers.
• The presence of even numbers does not affect the overall evenness unless paired with odd numbers.

Solutions

• Count the total number of odd and even integers in the array.
• If there are no odd numbers, return the count of even numbers.
• If there are odd numbers, check if their count is odd or even: If the count is odd, subtract one from it to make it even.

Mistake: Overlooking the need to exclude one odd number when the total count of odds is odd.

Solution: Always check the count of odd numbers; if odd, subtract one from the total.

Mistake: Assuming that only even numbers can contribute to an even sum.

Solution: Remember that an even sum can result from pairs of odd numbers or through only even numbers.