CF 102697058 - Switch Case

CF 102697058 - Switch Case

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Solve time: 42s
Verified: yes

Solution

Problem Understanding

The task is to transform one string by changing the case of every alphabetic character. An uppercase letter must become its lowercase counterpart, while a lowercase letter must become uppercase. The characters themselves stay in the same positions, and the statement guarantees that the string contains only English letters, with no spaces or other symbols. The official problem specifies a 1 second time limit and 256 MB memory limit.

For example, the input HeLlO becomes hElLo. Each position is handled independently, so there is no interaction between characters and no need for data structures such as arrays, maps, or graphs.

The statement does not expose a useful explicit upper bound on the string length beyond saying that the input is one string. Regardless of the hidden length limit, an algorithm must at least read every character, so Ω(n) time is unavoidable for a string of length n. A quadratic solution would repeatedly process already-seen characters and would become unsuitable as n grows. A linear scan is the natural target because it performs only a constant amount of work per character.

The main edge cases are simple but easy to mishandle. A one-character string such as A should produce a, because the only character still has to be switched. A string containing only lowercase letters, such as abc, should produce ABC; an implementation that only converts uppercase characters would incorrectly leave the input unchanged. Similarly, ABC must become abc. Finally, a mixed string such as aBcD must become AbCd, so the implementation must decide independently for every position rather than applying one conversion to the whole string.

Approaches

A direct brute-force interpretation is to process each character and search through a collection containing all possible uppercase and lowercase letters until the current character is found. Once its counterpart is located, we append that counterpart to the answer. This is correct because every input character belongs to exactly one of the 52 English alphabet characters.

If the search checks the 52 possible letters in the worst case for every input character, a string of length n can require up to 52n character comparisons. Since 52 is a constant, this is technically O(n), so unlike many brute-force approaches, it does not become asymptotically too slow. Its weakness is that it performs unnecessary comparisons when the case can be determined directly from the character value.

The key observation is that uppercase and lowercase English letters occupy contiguous ranges in the character encoding used by Python. More conveniently, Python already exposes the required transformation through str.swapcase(). If we want to understand the underlying algorithm rather than rely on a library operation, we can inspect whether a character lies in a through z or A through Z and move it by the fixed ASCII distance between the two cases.

The brute-force method works because every character can be mapped to its opposite case. The observation that the mapping is a fixed transformation lets us replace a search through possible letters with one constant-time operation per character. The resulting algorithm is still O(n), but it has the minimum possible asymptotic complexity and very little work per character.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force	O(52n) = O(n)	O(n)	Accepted, but unnecessary work
Optimal	O(n)	O(n) for the output	Accepted

Algorithm Walkthrough

1. Read the entire string and remove only the trailing newline. The input contains no spaces, so strip() is sufficient here, although removing only \n would also work.
2. Create an empty result string. We will append exactly one character for every input character, so the output length remains identical to the input length.
3. Scan the input from left to right. For each character, determine whether it is lowercase or uppercase.
4. If the character is lowercase, convert it to uppercase. If it is uppercase, convert it to lowercase. Python's swapcase() performs exactly this transformation for each character, and because the input is guaranteed to contain alphabetic characters, there are no other character categories to handle.
5. Print the transformed string. The relative order of all characters is unchanged because each character is transformed independently.

Why it works

The invariant during the scan is that after processing the first k characters, the result contains exactly the case-switched versions of those same k characters in their original order. When the next character is processed, swapcase() changes uppercase to lowercase and lowercase to uppercase, so the invariant remains true for k + 1 characters. After the final character is processed, the invariant covers the entire string, which means the produced string is exactly the required output.

Python Solution

import sys
input = sys.stdin.readline

def solve():
    s = input().strip()
    print(s.swapcase())

if __name__ == "__main__":
    solve()

The input line is read once, matching the fact that the problem contains a single string. strip() removes the newline added by standard input. Since the statement guarantees that there are no spaces inside the string, it cannot accidentally remove meaningful whitespace.

The call to swapcase() applies the required transformation independently to every character. It also avoids writing separate branches for uppercase and lowercase letters. The resulting string is printed directly, so there is no indexing or boundary condition that could introduce an off-by-one error.

An alternative implementation could use ord() and chr() to manually add or subtract the ASCII case difference, but that would make the solution longer without improving its asymptotic complexity.

Worked Examples

The official sample is HeLlO, which produces hElLo.

Position	Input character	Transformed character	Result so far
0	H	h	h
1	e	E	hE
2	L	l	hEl
3	l	L	hElL
4	O	o	hElLo

This example exercises both directions of the conversion in the same string. The invariant holds after every character because each processed prefix already has exactly the required case switches.

For a second example, consider aBcD.

Position	Input character	Transformed character	Result so far
0	a	A	A
1	B	b	Ab
2	c	C	AbC
3	D	d	AbCd

The final output is AbCd. This example demonstrates why the case decision must be made independently at every position. There is no single case for the entire string.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(n)	Every character is processed once.
Space	O(n)	The transformed string has n characters.

The linear time bound is optimal because the input itself contains n characters and every character has to be considered. The algorithm uses no auxiliary data structure proportional to anything other than the output string, so it also fits comfortably within the 256 MB memory limit for any practical input size allowed by the problem.

Test Cases

# helper: run solution on input string, return output string
import sys
import io

def solve():
    s = input().strip()
    print(s.swapcase())

def run(inp: str) -> str:
    global input
    old_stdin = sys.stdin
    sys.stdin = io.StringIO(inp)
    input = sys.stdin.readline

    out = io.StringIO()
    old_stdout = sys.stdout
    sys.stdout = out

    try:
        solve()
    finally:
        sys.stdin = old_stdin
        sys.stdout = old_stdout

    return out.getvalue()

# Provided sample
assert run("HeLlO\n") == "hElLo\n", "sample 1"

# Minimum-size input
assert run("A\n") == "a\n", "single uppercase character"

# All lowercase
assert run("abcdef\n") == "ABCDEF\n", "all lowercase characters"

# All uppercase
assert run("ABCDEF\n") == "abcdef\n", "all uppercase characters"

# Mixed boundary characters
assert run("aAzZ\n") == "AaZz\n", "first and last letters of both cases"

# Large input
large = "a" * 100000
assert run(large + "\n") == ("A" * 100000) + "\n", "large input"

Test input	Expected output	What it validates
A	a	Minimum-size input and uppercase conversion
abcdef	ABCDEF	Every character requires lowercase-to-uppercase conversion
ABCDEF	abcdef	Every character requires uppercase-to-lowercase conversion
aAzZ	AaZz	Alphabet boundaries and mixed cases
100000 copies of a	100000 copies of A	Linear processing on a large input

Edge Cases

For the one-character input A, the algorithm reads one character, calls swapcase(), and obtains a. The output is therefore a. There is no special handling for the first or last position because every position follows exactly the same rule.

For the all-lowercase input abc, every character is switched independently. The intermediate states are A, then AB, then ABC, giving the final output ABC. This catches an implementation that accidentally handles only uppercase letters.

For the all-uppercase input ABC, the same process produces abc. This catches the opposite mistake, where an implementation converts lowercase characters but leaves uppercase characters unchanged.

For the mixed input aBcD, the characters become A, b, C, and d, producing AbCd. This confirms that the algorithm does not assume that all characters have the same original case.

For the boundary input aAzZ, the first lowercase letter becomes A, the first uppercase letter becomes a, the last lowercase letter becomes Z, and the last uppercase letter becomes z. The exact output is AaZz. Testing both ends of the alphabet is useful because manual ASCII-based implementations often introduce an incorrect offset or boundary condition.

For a large input consisting of 100000 copies of a, every character is processed once and the result contains 100000 copies of A. This confirms that the implementation performs linear work rather than repeatedly rescanning the string.