Adjacent Constraint
相邻约束
Arrangement / 排列组合What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Must sit together
- 2Must stay next to each other
- 3Adjacent condition given
What It Really Tests
The core mathematical idea behind this structure:
Required neighbors can be bound into one block, then arrange blocks.
必须相邻的元素可以捆绑成一个块, 再排列各块。
Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Arranging all items first and filtering later (too slow)
- ⚠Forgetting internal order inside the block
- ⚠Miscounting mirrored situations
Your First Step
How to begin thinking about problems with this structure:
Bind the required adjacent items into a single block first.
先把必须相邻的元素看成一个整体。
Try a Problem
Four books — A, B, C, and D — are placed on a shelf. How many different orders are possible if A and B must be next to each other?
💡 Show Solution & Key Insight
Answer
C
Explanation
Treat A and B as one block [AB]. Then arrange 3 objects: [AB], C, D in 3! = 6 ways. Inside the block, A and B can be AB or BA, multiply by 2. Total = 6 × 2 = 12.
Key Insight
Bind required neighbors into a single block, then count arrangements of blocks.
Common Wrong Path
Listing all 24 permutations and filtering, which is slow and error-prone.
Related Structures
These structures share similar patterns or thinking approaches: