Maximum Number of Operations With the Same Score I

Maximum Number of Operations With the Same Score I - Problem

Array Simulation Easy

You are given an array of integers nums. Your goal is to perform a series of operations where each operation involves:

Deleting the first two elements from the array
Calculating the score as the sum of these two deleted elements

The key constraint is that all operations must have the same score. You need to find the maximum number of operations you can perform while maintaining this constraint.

Example: If nums = [3, 2, 1, 4, 5], the first operation removes 3 and 2 (score = 5). For subsequent operations to be valid, they must also have a score of 5.

Input & Output

example_1.py — Basic Case

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

› Output: 2

💡 Note: First operation: remove 3 and 2 (score = 5). Second operation: remove 1 and 4 (score = 5). Cannot continue as only one element remains.

example_2.py — No Valid Operations

$ Input: nums = [3, 2, 6, 1, 4]

› Output: 1

💡 Note: First operation: remove 3 and 2 (score = 5). Next pair would be 6 and 1 (score = 7), which doesn't match, so we stop.

example_3.py — Edge Case

$ Input: nums = [1]

› Output: 0

💡 Note: Cannot perform any operation since we need at least 2 elements for each operation.

Constraints

1 ≤ nums.length ≤ 1000
1 ≤ nums[i] ≤ 1000
All operations must have the same score
Each operation removes exactly 2 elements from the front

Visualization

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Understanding the Visualization

Set Target Score

The sum of the first two elements becomes our target score

Process Pairs

Check each consecutive pair to see if it matches our target

Count Operations

Increment counter for each valid pair and advance position

Stop on Mismatch

Break immediately when we encounter a pair that doesn't match

Key Takeaway

🎯 Key Insight: Since we must remove elements sequentially from the front, only the sum of the first two elements can serve as a valid target score. This reduces the problem to a simple simulation.

Asked in

G Google 15 a Amazon 12 f Meta 8 ⊞ Microsoft 6

The optimal approach uses the sum of the first two elements as the target score and simulates operations in a single pass. Since elements must be removed sequentially from the front, we only need to check consecutive pairs against this target. Time complexity: O(n), Space complexity: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force Simulation	O(n²)	O(1)	Try all possible target scores and simulate each scenario
Single Pass Simulation (Optimal)	O(n)	O(1)	Use first pair's sum as target and simulate operations in one pass

Brute Force Simulation — Algorithm Steps

Generate all possible sums from consecutive pairs in the array
For each possible target score, simulate the operation sequence
In each simulation, repeatedly remove first two elements if their sum equals target
Count operations until we can't proceed
Return the maximum count across all simulations

Visualization

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Step-by-Step Walkthrough

Generate Targets

Consider all consecutive pair sums as potential targets

Simulate Each

For each target, simulate the operation sequence from start to finish

Count Operations

Track how many valid operations we can perform with each target

Find Maximum

Return the highest count among all simulations

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int max(int a, int b) {
    return a > b ? a : b;
}

int maxOperations(int* nums, int numsSize) {
    if (numsSize < 2) return 0;
    
    int maxOps = 0;
    
    // Try all possible target scores
    for (int i = 0; i < numsSize - 1; i++) {
        int target = nums[i] + nums[i + 1];
        
        // Simulate operations with this target
        int operations = 0;
        int start = 0;
        
        while (start + 1 < numsSize) {
            if (nums[start] + nums[start + 1] == target) {
                start += 2;
                operations++;
            } else {
                break;
            }
        }
        
        maxOps = max(maxOps, operations);
    }
    
    return maxOps;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

We potentially try O(n) different target scores, and for each one we simulate O(n) operations

⚠ Quadratic Growth

Space Complexity

O(1)

Only using a few variables to track current state during simulation

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force Simulation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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