S1Q2 · Check String Rotation¶

⚡ Quick Reference

Function: is_rotation(str1: str, str2: str) -> bool

Core idea: if str2 is a rotation of str1, it will always appear as a substring of str1 + str1.

def is_rotation(str1: str, str2: str) -> bool:
    if len(str1) != len(str2):
        return False
    return str2 in str1 + str1

Key rules: - Both strings must have the same length - else not a rotation - str2 in (str1 + str1) checks if str2 is any rotation of str1 - Same string (str1 == str2) counts as a rotation (shift by 0)

Problem Statement¶

Problem

Write a function is_rotation(str1, str2) that returns True if str2 is a rotation of str1.

Examples:

Input

str1="abcde", str2="cdeab"

Output

True

Input

str1="hello", str2="ehllo"

Output

False

Input

str1="hello", str2="helol"

Output

False

Understanding the trick¶

Concatenating str1 with itself contains every possible rotation of str1 as a contiguous substring:

str1 = "apple"
str1 + str1 = "appleapple"

Rotations visible inside "appleapple":
  a[pplea]pple  → "pplea"
  ap[pleap]ple  → "pleap"
  app[leapp]le  → "leapp"
  appl[eappl]e  → "eappl"
  apple[apple]  → "apple"

So checking str2 in str1 + str1 checks all 5 rotations in one step.

Why the length check matters

Without it, "ab" in "abcabc" would return True even though "ab" is not a rotation of "abc" - it's a different-length string that just happens to appear as a substring. Always check len(str1) == len(str2) first.

Tracing all examples¶

`str1`	`str2`	Lengths equal?	`str1+str1`	`str2 in ...`	Result
`"abcde"`	`"cdeab"`	✅ (5=5)	`"abcdeabcde"`	✅	`True`
`"hello"`	`"ehllo"`	✅ (5=5)	`"hellohello"`	❌	`False`
`"hello"`	`"helol"`	✅ (5=5)	`"hellohello"`	❌	`False`

Solution approaches¶

Pythonic (the classic trick)ExplanatoryBrute force (all rotations)Using lambda

def is_rotation(str1: str, str2: str) -> bool:
    if len(str1) != len(str2):
        return False
    return str2 in str1 + str1

def is_rotation(str1: str, str2: str) -> bool:
    # Different lengths can't be rotations of each other
    if len(str1) != len(str2):
        return False
    # Every rotation of str1 appears as a substring of str1+str1
    doubled = str1 + str1
    return str2 in doubled

def is_rotation(str1: str, str2: str) -> bool:
    if len(str1) != len(str2):
        return False
    n = len(str1)
    for i in range(n):
        rotation = str1[i:] + str1[:i]
        if rotation == str2:
            return True
    return False

Generates each rotation explicitly and compares. O(n²) vs O(n) for the in approach, but shows clearly what a rotation is.

is_rotation = lambda s1, s2: len(s1) == len(s2) and s2 in s1 + s1

Key takeaways¶

01

str2 in str1+str1 - elegant O(n) trick

Concatenating a string with itself contains every rotation as a contiguous substring. Python's in operator runs an efficient substring search - one line replaces an entire loop over rotations.

02

Length check is mandatory

Two strings of different lengths can never be rotations of each other. Without the length check, shorter strings would incorrectly match as substrings of the doubled string.

03

Anagram ≠ Rotation

"ehllo" is an anagram of "hello" (same letters) but not a rotation (order matters). Rotations preserve the original sequence - only the starting point shifts.