1. Terms on leetcode

---

⭐ String / Array Rearrangement Terms

Term	Meaning	Example
Permutation	Rearrangement of same elements	abc → bac
Combination	Choose elements, order doesn’t matter	{1,2} same as {2,1}
Anagram	String permutation (same chars, diff order)	listen → silent
Substring	Continuous part of string	bcd from abcde
Subarray	Continuous part of array	[2,3] from [1,2,3,4]
Subset	Any selected elements	{1,3} from {1,2,3}
Subsequence	Keep order	{1,3} from {1,2,3}

---

Relationship

For an array:

arr = [1, 2, 3]

The subsets are: [], [1],, [2], [3], [1,2], [1,3], [2,3], [1,2,3]

Term	Order Preserved?	Contiguous?
Subset	✅ No mathematical order, but when represented from an array we preserve original order	❌ No
Subsequence	✅ Yes	❌ No
Subarray	✅ Yes	✅ Yes

---

⭐ Permutation vs Combination

1️⃣ Permutation = Arrange

When order matters.

Example: From {A,B,C}, pick 2:

• AB, BA, AC, CA, BC, CB
• AB ≠ BA (different order = different answer)

Formula: $P(n,r)=\frac{n!}{(n-r)!}$

Example: $P(3,2)=6$

2️⃣ Combination = Choose

When order does NOT matter.

Example: From {A,B,C}, choose 2:

• {A,B}, {A,C}, {B,C}
• {A,B} = {B,A} (same group = same answer)

Formula: $C(n,r)=\frac{n!}{r!(n-r)!}$

Example: $C(3,2)=3$

---

Quick Check 🔍

From {1,2,3}, pick 2:

Permutation (order matters):

• 12, 21
• 13, 31
• 23, 32

Combination (order doesn’t matter):

• {1,2}
• {1,3}
• {2,3}

---