Rotate String
This problem can be solved by checking if goal
is a substring of s
concatenated with s
. This is because any number of rotations of s
will always be a substring of s+s
.
Here is the Python code:


This function first checks if s
and goal
have the same length. If they don’t, it immediately returns False
because it’s impossible to rotate s
to match goal
if their lengths are different. If they do have the same length, it checks whether goal
is a substring of s
concatenated with itself. If it is, it returns True
, indicating that s
can be rotated to match goal
. If it’s not, it returns False
.
The key insight to solving this problem lies in understanding that any rotation of a string s
is a substring of s + s
.
When you rotate a string, you’re essentially just moving its characters around. Therefore, if you take two copies of the string and put them together, you create a situation where every possible rotation of the string exists as a substring in this concatenated string.
This observation allows us to solve the problem by simply checking if goal
is a substring of s + s
, after verifying they are of the same length. If it is, then s
can be rotated to become goal
. If it isn’t, then no rotation of s
will result in goal
.
This approach leverages the power of substring checking to solve the problem of string rotation.
Generating key insights often involves understanding the problem’s constraints and finding patterns or relationships within those constraints. Here’s how one could arrive at the key insight for this problem:
Understanding the problem and the constraints: The problem involves rotations, i.e., moving the leftmost character to the rightmost position. It’s also mentioned that the two strings
s
andgoal
are of the same length.Observing examples: If we manually perform the rotations and observe the results, we may notice a pattern. For example, for
s = "abcde"
, the rotations would be:"bcdea"
,"cdeab"
,"deabc"
,"eabcd"
, and back to"abcde"
.Noticing patterns and forming insights: From the examples, we might notice that all the rotated strings are substrings of
s + s = "abcdeabcde"
. Thus, we can check ifgoal
is a substring ofs + s
to see ifs
can be rotated to formgoal
.Verifying the insight: We can confirm this insight by trying various examples and corner cases, and seeing if this pattern holds true in every case.
This process involves some creativity and lateral thinking, and it may not always be straightforward. It often comes with practice, so don’t be discouraged if you don’t see these insights immediately!
Generating key insights often involves understanding the problem’s constraints and finding patterns or relationships within those constraints. Here’s how one could arrive at the key insight for this problem:
Understanding the problem and the constraints: The problem involves rotations, i.e., moving the leftmost character to the rightmost position. It’s also mentioned that the two strings
s
andgoal
are of the same length.Observing examples: If we manually perform the rotations and observe the results, we may notice a pattern. For example, for
s = "abcde"
, the rotations would be:"bcdea"
,"cdeab"
,"deabc"
,"eabcd"
, and back to"abcde"
.Noticing patterns and forming insights: From the examples, we might notice that all the rotated strings are substrings of
s + s = "abcdeabcde"
. Thus, we can check ifgoal
is a substring ofs + s
to see ifs
can be rotated to formgoal
.Verifying the insight: We can confirm this insight by trying various examples and corner cases, and seeing if this pattern holds true in every case.
This process involves some creativity and lateral thinking, and it may not always be straightforward. It often comes with practice, so don’t be discouraged if you don’t see these insights immediately!
The key takeaway from solving this problem is that we analyze the given cases and see if we can find any relationships between the given inputs. If there is a relationship we can express it in code.
Indeed, that’s an accurate summary. Recognizing patterns and relationships within the problem constraints is an essential skill in problemsolving, especially in coding challenges. It’s also important to understand the properties and behaviors of the data structures or elements involved. In this case, understanding the nature of rotations in a string, and how they form a part of a concatenated string, was key.
Being able to spot these relationships and translate them into efficient, concise code is a valuable skill that often comes with practice and experience. So, always take time to analyze and understand the problem thoroughly, experiment with examples, look for patterns, and verify your findings. This kind of analysis can lead to key insights that make the solution more straightforward.
The brute force solution for this problem would involve rotating the string s
in all possible ways and comparing each rotation to the string goal
. If any rotation matches goal
, then we return True
. If none of the rotations match goal
, then we return False
.
Here’s how this can be implemented in Python:


This function works by trying all possible rotations of s
. For each rotation, it slices the string s
from index i
to the end and appends the beginning of the string up to index i
. It then compares this rotated string to goal
.
While this solution works, it’s not very efficient. It has a time complexity of O(n^2), as slicing a string is an O(n) operation and we are doing this n times in the worst case. The optimized solution we discussed earlier, which checks if goal
is a substring of s + s
, has a much better time complexity of O(n).


Problem Classification
The ‘What’ Components:
 Two strings, ’s’ and ‘goal’.
 A transformation operation, which is a ‘shift’ defined as moving the leftmost character of a string to its rightmost position.
 A query about whether ’s’ can be transformed into ‘goal’ through some number of these shifts.
This is a pattern recognition problem. The solution needs to identify if there is a pattern or sequence of shift operations that can transform string ’s’ into string ‘goal’. It’s primarily a problem of string manipulation and comparison.
The problem is categorized under the domain of ‘String Manipulation’ as it primarily involves operations on strings  shifting characters and comparing the two strings. The ‘What’ components are the given elements or conditions in the problem, which include the two input strings, the defined shift operation, and the question. The problem is classified as a pattern recognition problem because we need to identify the right sequence of operations (the pattern) that could transform one string into another.
Language Agnostic Coding Drills
Dissecting the code:
a. Basic Programming Concepts: Data types (string), conditional statements (if), loops (while), string manipulation and length checking.
b. Function Definition: Defining a function with input parameters and return type.
c. String Comparison: Comparing two strings for equality.
d. String Slicing and Concatenation: Cutting the string from a certain position and appending characters at the end of the string.
e. Early Return: Returning a value early from a function if a certain condition is met.
Coding Concepts:
a. Data types and Variables: Understanding basic data types like strings and how to declare variables. This is a basic level concept.
b. Conditional Statements: Using ‘if’ to make decisions based on certain conditions. This is slightly more complex, as it requires understanding of conditions and logical operators.
c. Function Definition: Defining a function with specific inputs and return type. This is a midlevel concept, as it involves understanding function structure and how to specify input parameters and return type.
d. Loops: Using a ‘while’ loop to perform repetitive tasks. This is also a midlevel concept, requiring knowledge of how to set up and control loops.
e. String Comparison: Comparing two strings for equality. This is a midlevel concept that involves understanding how strings are compared in Python.
f. String Slicing and Concatenation: Using string slicing to create a substring and concatenation to append characters to a string. This is a slightly advanced concept as it involves understanding string indexing and manipulation.
g. Early Return: Understanding when and why to return a value early from a function. This is an advanced concept, as it involves a deeper understanding of program flow and control.
ProblemSolving Approach:
a. First, we need to handle edge cases, which are done through early returns. If the strings are not of the same length, we can immediately return False. If the two strings are already equal, we return True.
b. Then, we set up a loop to perform the shift operation as many times as the length of the string. This is where the understanding of loops comes in.
c. Inside the loop, we perform the string manipulation (the shift operation), using string slicing and concatenation.
d. After each shift operation, we compare the transformed string with the target string. This requires an understanding of string comparison.
e. If the strings are equal after a shift, we return True immediately, ending the function. This is an application of early return.
f. If we complete the loop without finding a match, we return False, indicating that no sequence of shifts could make the strings equal.
Targeted Drills in Python
Pythonbased coding drills for each identified concept:
a. Data types and Variables:
1
my_string = "Hello, World!"
b. Conditional Statements:
1 2
if my_string == "Hello, World!": print("Strings are equal.")
c. Function Definition:
1 2
def greeting(): return "Hello, World!"
d. Loops:
1 2
for i in range(5): print(i)
e. String Comparison:
1 2 3 4
string1 = "Hello" string2 = "World" if string1 != string2: print("Strings are not equal.")
f. String Slicing and Concatenation:
1 2 3
string = "Hello" string = string[1:] + string[0] print(string) # Output: "elloH"
g. Early Return:
1 2 3 4
def is_even(number): if number % 2 == 0: return True return False
Problemspecific concepts:
a. String Shifting: The problem requires shifting the characters of the string which can be achieved using slicing and concatenation.
1 2
string = "abcde" string = string[1:] + string[0] # Output: "bcdea"
This drill is essential for our problem because the main operation in the problem is to perform shifts on the string, and the concept of shifting characters in a string is achieved using slicing and concatenation.
Integration of these drills:
Once all drills have been coded, these pieces can be integrated together to solve the initial problem.
a. Begin by defining a function with the appropriate inputs and return type (Function Definition drill).
b. Inside the function, start by checking if the lengths of the two strings are equal (Conditional Statements and String length check drills).
c. If they are equal, check if the strings are the same (String Comparison drill). If they are, return True.
d. Then, setup a loop to perform the shift operation (Loops drill).
e. Inside the loop, perform the shift operation using string slicing and concatenation (String Slicing and Concatenation drill).
f. After each shift operation, compare the shifted string with the target string (String Comparison drill).
g. If the strings are equal after a shift, return True (Early Return drill).
h. If no match is found after completing the loop, return False.