Elimination Game - Problem
The Elimination Game Challenge
Imagine you're playing a strategic elimination game with a list of consecutive integers from
🎯 Round 1: Start from the left, eliminate every other number (1st, 3rd, 5th, ...)
🎯 Round 2: From the remaining numbers, start from the right, eliminate every other number
🎯 Round 3: Back to left, eliminate every other number
🎯 Continue alternating directions until only one number survives!
For example, with
• Start: [1,2,3,4,5,6,7,8,9]
• Left→: [2,4,6,8] (removed 1,3,5,7,9)
• ←Right: [2,6] (removed 4,8)
• Left→: [6] (removed 2)
Your mission: Given
Imagine you're playing a strategic elimination game with a list of consecutive integers from
1 to n. The rules are simple but the pattern is fascinating:🎯 Round 1: Start from the left, eliminate every other number (1st, 3rd, 5th, ...)
🎯 Round 2: From the remaining numbers, start from the right, eliminate every other number
🎯 Round 3: Back to left, eliminate every other number
🎯 Continue alternating directions until only one number survives!
For example, with
n = 9:• Start: [1,2,3,4,5,6,7,8,9]
• Left→: [2,4,6,8] (removed 1,3,5,7,9)
• ←Right: [2,6] (removed 4,8)
• Left→: [6] (removed 2)
Your mission: Given
n, find the last survivor without actually simulating the entire elimination process! Input & Output
example_1.py — Small Case
$
Input:
n = 9
›
Output:
6
💡 Note:
Starting with [1,2,3,4,5,6,7,8,9]. Round 1 (left→right): remove 1,3,5,7,9 → [2,4,6,8]. Round 2 (right←left): remove 8,4 → [2,6]. Round 3 (left→right): remove 2 → [6]. The last remaining number is 6.
example_2.py — Even Case
$
Input:
n = 4
›
Output:
2
💡 Note:
Starting with [1,2,3,4]. Round 1 (left→right): remove 1,3 → [2,4]. Round 2 (right←left): remove 4 → [2]. The last remaining number is 2.
example_3.py — Edge Case
$
Input:
n = 1
›
Output:
1
💡 Note:
With only one number [1], no elimination is needed. The last (and only) remaining number is 1.
Constraints
- 1 ≤ n ≤ 109
- Large input values require efficient O(log n) solution
- Integer overflow is not a concern for this problem
Visualization
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Understanding the Visualization
1
Pattern Recognition
Each round eliminates exactly half the remaining elements
2
Position Tracking
We only need to track the first remaining position and spacing
3
Update Rules
Start position changes based on direction and parity
4
Convergence
Continue until only one position remains
Key Takeaway
🎯 Key Insight: Instead of simulating the entire elimination process, track only the mathematical position and spacing pattern, reducing complexity from O(n²) to O(log n)!
💡
Explanation
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