lcb-0070

1.000

2/2 tests· algorithms

Proposed solution

I'll solve this step by step.

## Problem Understanding

1. We need a length-N string with characters '-' and '='
2. The string must be a palindrome
3. It must contain exactly 1 or exactly 2 '=' characters
4. If there are 2 '=', they must be adjacent
5. The solution is unique

## Analysis

Let me think about the structure:

- Since it's a palindrome, if we have N positions, the first half determines the second half
- For exactly 1 '=':
  - It can be in the middle (if N is odd) or paired symmetrically (if N is even)
- For exactly 2 '=' that are adjacent:
  - They must form a pair like "=="
  - This pair must be symmetrically placed

## Case Analysis

**Case 1: Exactly one '='**
- If N is odd: place '=' in the center position
- If N is even: we can't have exactly one '=' while maintaining palindrome property (since it would need to be at the center, but that's impossible for even N)

Wait, let me reconsider. For a palindrome of even length, if there's exactly one '=', it must be at the center... but that's impossible since even length has no true center.

Actually, let me re-read: "If it contains two =s, they are adjacent."

So:
- If we have 1 '=', it must be in the middle (for odd N)
- If we have 2 '=', they must be adjacent and symmetric

Let me trace through examples:

**Example 1: N=4**
Output: "-==-" 
This has 2 '='s that are adjacent and symmetric.

**Example 2: N=7**  
Output: "---=---"
This has 1 '=' in the middle.

## Strategy

1. If N is odd: place one '=' in the center
2. If N is even: we must have exactly 2 '='s that are adjacent - they should be placed symmetrically

Let me think more carefully about even case:
- For even N, to have 2 adjacent '='s that form a palindrome, they need to be at positions (N/2-1, N/2) or similar symmetric positions.

Actually, let me reconsider the constraint. The two '='s must be adjacent AND symmetrically placed.

For even N with 2 adjacent '='s:
- If we place them at positions i and i+1, for palindrome they need to be symmetric
- This means positions (N/2-1, N/2) or similar

But wait - let me think of it differently. 
If we have exactly two '=' that are adjacent, they form a "==" pair.
In a palindrome, if this pair is at position k and k+1, then for symmetry:
- Position k should match position N-1-k  
- Position k+1 should match position N-1-(k+1) = N-2-k

So we need: k = N-1-k and k+1 = N-2-k
This gives us: 2k = N-1 and 2k = N-3, which is impossible.

Let me re-read... 

Actually, let me look at the examples:
N=4: "-==-" - positions 1,2 are '=' (0-indexed)
N=7: "---=---" - position 3 is '='

So for even N, we can't have exactly 2 adjacent '=' that form a palindrome unless they're in the center positions.

Wait, I think I misunderstood. Let me re-read...

Actually, let's think of it this way:
- For N=4: "-==-" 
  - Positions 1,2 are '='
  - This is symmetric because position 0 (which is '-') matches position 3 ('-'))
  - So we have a palindrome with 2 adjacent '='s

So for even N, if we want exactly 2 adjacent '='s:
- We place them in the middle: positions N/2-1 and N/2
- This works because they are symmetrically placed (positions N/2-1 and N/2)

Let me verify with examples:

N=4: positions 1,2 are '==', positions 0,3 are '--' - palindrome ✓
N=7: position 3 is '=', positions 0,1,2 are '---', positions 4,5,6 are '---' - palindrome ✓

## Solution Approach

1. If N is odd: place one '=' in the middle (position N//2)
2. If N is even: place two '='s at positions N//2-1 and N//2 (these are adjacent)

Wait, let me double-check this logic with examples:

N=4 (even): 
- Positions 1,2 should be '='
- This means we put '==' at the middle
- Result: "-==-" ✓

N=7 (odd):
- Position 3 should be '='  
- Result: "---=---" ✓

This looks correct.

## Implementation

```python
N = int(input())

# Create a list of '-' characters
result = ['-' for _ in range(N)]

if N % 2 == 1:
    # Odd length: place one '=' in the center
    result[N // 2] = '='
else:
    # Even length: place two '='s in the middle positions
    result[N // 2 - 1] = '='
    result[N // 2] = '='

print(''.join(result))
```

Test output (stdout)

..                                                                       [100%]
2 passed in 0.03s

System prompt

You are an expert programmer. Solve the task exactly as specified. Output your solution as fenced code blocks using the required file name(s) and the exact function/type signatures requested. Prefer correctness; do not include prose outside code unless asked.