Maximum Number of Operations With the Same Score I

Maximum Number of Operations With the Same Score I

What is this problem about?

The Maximum Number of Operations With the Same Score I coding problem gives you an array of integers nums. You are allowed to perform an operation where you select two adjacent elements, remove them, and record their sum. You want to find the maximum number of operations you can perform such that all recorded sums are equal to the sum of the first two elements.

Why is this asked in interviews?

Microsoft and Google use this problem to check a candidate's grasp of basic simulation and array manipulation. It's an easy-level problem designed to verify fundamental programming skills, including careful indexing and loop control. The constraints are simple enough that a straightforward simulation approach works well.

Algorithmic pattern used

Simulation / Iterative Check: The problem specifies that all subsequent sums must be equal to the sum of the first two elements. This sets a fixed target sum. The strategy is to calculate this target sum from nums[0] + nums[1]. Then, iterate through the rest of the array, taking two adjacent elements at a time. If their sum matches the target, increment a counter. If at any point their sum does not match, then no further valid operations can be performed.

def max_operations(nums):
    if len(nums) < 2:
        return 0

    target_sum = nums[0] + nums[1]
    operations = 1 # Initial operation for nums[0] and nums[1]
    
    # Start checking from index 2, taking pairs (i, i+1)
    i = 2
    while i + 1 < len(nums):
        current_sum = nums[i] + nums[i+1]
        if current_sum == target_sum:
            operations += 1
            i += 2 # Move to the next un-removed pair
        else:
            # Cannot form any more operations with the same score
            break
    return operations

Example explanation

nums = [3, 2, 6, 1, 4, 3]

1. First two elements are 3 and 2. Their sum is 3 + 2 = 5. This is our target_sum. operations = 1.
2. Next adjacent pair: 6 and 1. Their sum is 6 + 1 = 7. This is not equal to target_sum (5).
3. We stop here. The maximum number of operations is 1.

nums = [1, 1, 1, 1, 1, 1]

1. First two elements are 1 and 1. Their sum is 1 + 1 = 2. This is our target_sum. operations = 1.
2. Next adjacent pair: 1 and 1. Their sum is 1 + 1 = 2. Matches target_sum. operations = 2.
3. Next adjacent pair: 1 and 1. Their sum is 1 + 1 = 2. Matches target_sum. operations = 3.
4. No more elements. The maximum number of operations is 3.

Common mistakes candidates make

• Incorrectly calculating the target sum: The target sum is fixed by the first operation.
• Off-by-one errors in loop boundaries: Ensure the loop correctly processes adjacent pairs and handles arrays with odd lengths.
• Not handling edge cases: Empty array or array with only one element.

Interview preparation tip

For the Array Simulation interview pattern, focus on careful indexing, clear variable names, and thinking through edge cases. Easy problems often test attention to detail and fundamental loop/conditional logic more than complex algorithms.