LeetCode #3847 — MEDIUM

Find the Score Difference in a Game

Move from brute-force thinking to an efficient approach using core interview patterns strategy.

Solve on LeetCode

The Problem

Problem Statement

You are given an integer array nums, where nums[i] represents the points scored in the i^th game.

There are exactly two players. Initially, the first player is active and the second player is inactive.

The following rules apply sequentially for each game i:

If nums[i] is odd, the active and inactive players swap roles.
In every 6th game (that is, game indices 5, 11, 17, ...), the active and inactive players swap roles.
The active player plays the i^th game and gains nums[i] points.

Return the score difference, defined as the first player's total score minus the second player's total score.

Example 1:

Input: nums = [1,2,3]

Output: 0

Explanation:

Game 0: Since the points are odd, the second player becomes active and gains nums[0] = 1 point.
Game 1: No swap occurs. The second player gains nums[1] = 2 points.
Game 2: Since the points are odd, the first player becomes active and gains nums[2] = 3 points.
The score difference is 3 - 3 = 0.

Example 2:

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

Output: 4

Explanation:

Games 0 to 2: The first player gains 2 + 4 + 2 = 8 points.
Game 3: Since the points are odd, the second player is now active and gains nums[3] = 1 point.
Game 4: The second player gains nums[4] = 2 points.
Game 5: Since the points are odd, the players swap roles. Then, because this is the 6th game, the players swap again. The second player gains nums[5] = 1 point.
The score difference is 8 - 4 = 4.

Example 3:

Input: nums = [1]

Output: -1

Explanation:

Game 0: Since the points are odd, the second player is now active and gains nums[0] = 1 point.
The score difference is 0 - 1 = -1.

Constraints:

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

Step 01

Brute Force Baseline

Problem summary: You are given an integer array nums, where nums[i] represents the points scored in the ith game. There are exactly two players. Initially, the first player is active and the second player is inactive. The following rules apply sequentially for each game i: If nums[i] is odd, the active and inactive players swap roles. In every 6th game (that is, game indices 5, 11, 17, ...), the active and inactive players swap roles. The active player plays the ith game and gains nums[i] points. Return the score difference, defined as the first player's total score minus the second player's total score.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: General problem-solving

Example 1

[1,2,3]

Example 2

[2,4,2,1,2,1]

Example 3

[1]

Step 02

Core Insight

What unlocks the optimal approach

Simulate as described

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #3847: Find the Score Difference in a Game
class Solution {
    public int scoreDifference(int[] nums) {
        int ans = 0;
        int k = 1;
        for (int i = 0; i < nums.length; ++i) {
            int x = nums[i];
            if ((x & 1) == 1) {
                k = -k;
            }
            if (i % 6 == 5) {
                k = -k;
            }
            ans += k * x;
        }
        return ans;
    }
}

// Accepted solution for LeetCode #3847: Find the Score Difference in a Game
func scoreDifference(nums []int) int {
	ans := 0
	k := 1
	for i, x := range nums {
		if x%2 != 0 {
			k = -k
		}
		if i%6 == 5 {
			k = -k
		}
		ans += k * x
	}
	return ans
}

# Accepted solution for LeetCode #3847: Find the Score Difference in a Game
class Solution:
    def scoreDifference(self, nums: List[int]) -> int:
        ans, k = 0, 1
        for i, x in enumerate(nums):
            if x % 2:
                k *= -1
            if i % 6 == 5:
                k *= -1
            ans += k * x
        return ans

// Accepted solution for LeetCode #3847: Find the Score Difference in a Game
// Rust example auto-generated from java reference.
// Replace the signature and local types with the exact LeetCode harness for this problem.
impl Solution {
    pub fn rust_example() {
        // Port the logic from the reference block below.
    }
}

// Reference (java):
// // Accepted solution for LeetCode #3847: Find the Score Difference in a Game
// class Solution {
//     public int scoreDifference(int[] nums) {
//         int ans = 0;
//         int k = 1;
//         for (int i = 0; i < nums.length; ++i) {
//             int x = nums[i];
//             if ((x & 1) == 1) {
//                 k = -k;
//             }
//             if (i % 6 == 5) {
//                 k = -k;
//             }
//             ans += k * x;
//         }
//         return ans;
//     }
// }

// Accepted solution for LeetCode #3847: Find the Score Difference in a Game
function scoreDifference(nums: number[]): number {
    let ans = 0;
    let k = 1;

    nums.forEach((x, i) => {
        if (x % 2 !== 0) {
            k = -k;
        }
        if (i % 6 === 5) {
            k = -k;
        }
        ans += k * x;
    });

    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.