Maximum Number of Operations With the Same Score I

Ah, the classic problem of trying to maximize operations while keeping the score the same! It’s like trying to eat cake while maintaining your diet—sounds impossible, right? But here we are, diving into the world of algorithms where we can pretend that everything is possible, including balancing our love for sweets with our desire to fit into those jeans.

Links to Other Solutions

Problem Description

In this problem, you are given an array of integers, and your task is to find the maximum number of operations you can perform such that the sum of pairs of numbers remains constant. Imagine you’re at a party, and you want to keep the same number of drinks in your hand while swapping them with your friends. The challenge is to keep the party going without spilling any drinks—sounds like a fun night, right?

Code Solution

Here’s the C++ solution that will help you achieve that elusive maximum number of operations:


class Solution {
 public:
  int maxOperations(vector& nums) {
    int ans = 1;
    int sum = nums[0] + nums[1];

    for (int i = 2; i + 1 < nums.size(); i += 2) {
      if (nums[i] + nums[i + 1] == sum)
        ++ans;
      else
        break;
    }

    return ans;
  }
};

Approach

The approach taken in this solution is straightforward yet effective. The code initializes a counter ans to keep track of the number of operations and calculates the initial sum of the first two elements. It then iterates through the array in pairs, checking if the sum of each pair matches the initial sum. If it does, it increments the counter; if not, it breaks out of the loop. Simple, right? Just like trying to keep your balance while walking on a tightrope!

Time and Space Complexity

Time Complexity: O(n), where n is the number of elements in the array. We traverse the array once.
Space Complexity: O(1), as we are using a constant amount of space for variables.

Real-World Example

Imagine you’re at a buffet, and you want to keep your plate looking full while swapping out items with your friends. You start with a plate of pasta and salad, and you want to keep the same amount of food on your plate while trading bites with your friends. The goal is to maximize the number of swaps (operations) without changing the total amount of food on your plate. This is essentially what the problem is asking you to do with numbers!