#3038

Easy

LeetCode Problem Workspace

Maximum Number of Operations With the Same Score I

Determine the maximum number of operations in an integer array where each operation must produce the same score.

Problem Statement

Given an array of integers nums, you can perform operations that remove any two elements whose sum equals a chosen score. Each operation reduces the array size, and all operations must achieve the same score.

Return the maximum number of operations you can perform on the array where every operation produces the identical sum, following the Array plus Simulation pattern.

Examples

Example 1

Input: nums = [3,2,1,4,5]

Output: 2

Example 2

Input: nums = [1,5,3,3,4,1,3,2,2,3]

Output: 2

Example 3

Input: nums = [5,3]

Output: 1

Example details omitted.

Constraints

2 <= nums.length <= 100
1 <= nums[i] <= 1000

Solution Approach

Frequency Map Approach

Count occurrences of each number in nums. Iterate through all potential sums and for each, calculate how many pairs can be formed without exceeding counts. Track the maximum number of operations.

Two-Pointer Approach on Sorted Array

Sort nums and use two pointers at the start and end. Move pointers inward when a pair sum is too low or high. Increment operation count when pair matches the chosen score, simulating the operations efficiently.

Simulation and Tracking

Simulate removing pairs for each candidate score, ensuring the same sum is used in all operations. Keep track of used numbers to avoid double-counting, maximizing the total operation count while respecting constraints.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(n^2) for checking all pair sums or O(n log n) with sorting and two-pointer scanning. Space complexity is O(n) for frequency map or O(1) with two-pointer simulation.

What Interviewers Usually Probe

The interviewer may ask if all pairs must use the same sum or if sums can vary.
Expect clarification questions on array constraints and operation limits.
They might probe for edge cases like repeated numbers or minimal array length.

Common Pitfalls or Variants

Common pitfalls

Assuming pairs can have different sums and miscounting operations.
Not updating counts or pointers correctly, leading to double-counting elements.
Forgetting to consider that array size reduces after each operation, affecting subsequent pairs.

Follow-up variants

Maximum operations with varying sums allowed for each operation.
Operations restricted to consecutive elements only, still matching the sum.
Finding minimum operations to reach a target score using Array plus Simulation.

FAQ

What is the Maximum Number of Operations With the Same Score I problem about?

It asks for the maximum number of operations where each removes two numbers summing to the same value in an array.

Can pairs have different sums in this problem?

No, all pairs selected for operations must achieve the same sum throughout the array.

What is the best way to simulate operations efficiently?

Use either a frequency map to count numbers or a two-pointer method on a sorted array to track valid pairs without double-counting.

Are there edge cases to watch for?

Yes, repeated numbers, minimal array lengths, and sums at the extreme of possible values require careful handling.

Which pattern does this problem exemplify?

It follows the Array plus Simulation pattern, combining array manipulation with stepwise operation tracking.

terminal

Solution

Solution 1: Traversal

First, we calculate the sum of the first two elements, denoted as $s$. Then we traverse the array, taking two elements at a time. If their sum is not equal to $s$, we stop the traversal. Finally, we return the number of operations performed.

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class Solution:
    def maxOperations(self, nums: List[int]) -> int:
        s = nums[0] + nums[1]
        ans, n = 0, len(nums)
        for i in range(0, n, 2):
            if i + 1 == n or nums[i] + nums[i + 1] != s:
                break
            ans += 1
        return ans

Continue Practicing

#3028 ant on the boundary #3066 minimum operations to exceed threshold value ii #3069 distribute elements into two arrays i