CF 2168A1 - Encode and Decode (Easy Version)

Rating: -
Tags: communication, constructive algorithms, interactive
Solve time: 1m 52s
Verified: no

Solution

Problem Understanding

We are asked to design a two-phase program that communicates an array of integers through a single string. On the first run, the program receives an array of length n, where each element is at most 26. It must encode this array into a string composed solely of lowercase English letters. On the second run, the program receives only the encoded string and must recover the original array and its length.

The primary challenge is that no persistent memory exists between runs. Any information used for decoding must be encoded into the string itself. The constraints are moderate: n can be up to 10,000, and each element is at most 26, which matches the 26 letters of the alphabet. The output string cannot exceed 100,000 characters, so simple one-to-one encoding of numbers to letters is feasible.

A non-obvious edge case occurs when multiple elements are identical or when n is at its maximum. For instance, if n = 3 and a = [1, 1, 1], a naive encoding that just concatenates letters without a delimiter would yield "aaa". Decoding this without a pre-defined scheme could misinterpret the length or order if not careful. Similarly, we must handle the smallest input, n = 1 with a = [1], ensuring our scheme works for single-element arrays.

Approaches

The brute-force approach encodes each integer a_i as a corresponding lowercase letter, mapping 1 → 'a', 2 → 'b', …, 26 → 'z'. The encoding is simply the concatenation of these letters. This approach works because all integers fit within the alphabet, and the string length is at most 10,000, well below the 100,000-character limit. Decoding involves reversing the mapping: converting each letter back to its numeric value.

This method is correct and fast because it directly maps numbers to letters in O(n) time and space. A naive variant without careful mapping could misalign letters if, for example, multi-character codes were used or numbers exceeded 26. The key insight is that the problem explicitly limits values to 26, allowing a simple bijection between numbers and letters without additional separators.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force (1-letter per number)	O(n)	O(n)	Accepted
Complicated schemes (multi-letter coding)	O(n)	O(n)	Unnecessary for this version

Algorithm Walkthrough

Encoding Phase (First Run)

Read the integer n and the array a. For each element a_i, convert it to a lowercase letter by computing chr(ord('a') + a_i - 1). Concatenate these letters into a string s. Print s and terminate. 2. Decoding Phase (Second Run)

Read the encoded string s. The length of s is n. Convert each character back to its numeric value with ord(c) - ord('a') + 1 to reconstruct the array a. Print n followed by the elements of a.

The correctness relies on a one-to-one mapping between integers 1-26 and letters 'a'-'z'. Because each letter represents exactly one number and the string length equals the array length, there is no ambiguity during decoding.

Python Solution

import sys
input = sys.stdin.readline

mode = input().strip()

if mode == "first":
    n = int(input())
    a = list(map(int, input().split()))
    # Encode: map 1->'a', 2->'b', ..., 26->'z'
    s = ''.join(chr(ord('a') + x - 1) for x in a)
    print(s)

else:  # second run
    s = input().strip()
    n = len(s)
    a = [ord(c) - ord('a') + 1 for c in s]
    print(n, *a)

The first branch converts each integer into a letter. Using ord and chr ensures the mapping is exact. The second branch reverses the process. Using *a in the print statement efficiently expands the array into space-separated values. Boundary checks are implicit because the problem guarantees 1 ≤ a_i ≤ 26.

Worked Examples

Sample 1

Input (first run):

first
5
1 2 3 4 5

Encoding:

a_i	Letter
1	a
2	b
3	c
4	d
5	e

Encoded string: "abcde"

Input (second run):

second
abcde

Decoding:

Letter	a_i
a	1
b	2
c	3
d	4
e	5

Output: 5 1 2 3 4 5

Sample 2

Input (first run):

first
3
26 1 13

Encoding:

a_i	Letter
26	z
1	a
13	m

Encoded string: "zam"

Input (second run):

second
zam

Decoding:

Letter	a_i
z	26
a	1
m	13

Output: 3 26 1 13

These traces confirm the one-to-one mapping preserves the array exactly, even at boundaries.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(n)	Each element is processed once for encoding and once for decoding.
Space	O(n)	The string `s` has length `n`; the array is also of size `n`.

With n ≤ 10^4 and string length limit 10^5, this solution is comfortably within time and memory constraints.

Test Cases

import sys, io

def run(inp: str) -> str:
    sys.stdin = io.StringIO(inp)
    sys.stdout = io.StringIO()
    exec(open("solution.py").read())  # or paste the solution here
    return sys.stdout.getvalue().strip()

# Provided samples
assert run("first\n5\n1 2 3 4 5\n") == "abcde"
assert run("second\nabcde\n") == "5 1 2 3 4 5"

# Custom cases
assert run("first\n1\n1\n") == "a", "minimum-size input"
assert run("second\na\n") == "1 1", "decode single element"
assert run("first\n4\n26 26 26 26\n") == "zzzz", "all maximum values"
assert run("second\nzzzz\n") == "4 26 26 26 26", "decode all max values"
assert run("first\n3\n1 26 13\n") == "amaz", "mixed boundary values"
assert run("second\namaz\n") == "3 1 26 13", "decode mixed values"

Test input	Expected output	What it validates
`1\n1`	`a`	Minimum input size
`a`	`1 1`	Decoding single element
`26 26 26 26`	`zzzz`	Maximum possible value mapping
`zzzz`	`4 26 26 26 26`	Decoding maximum values
`1 26 13`	`amaz`	Mixed boundary values

Edge Cases

For n = 1 and a = [1], encoding produces "a". Decoding reads the single character, computes ord('a') - ord('a') + 1 = 1, and outputs 1 1. For a = [26, 26, 26, 26], encoding yields "zzzz"; decoding reconstructs [26, 26, 26, 26]. The mapping preserves the array even when all elements are identical or at extremes, avoiding ambiguity.

This editorial demonstrates that for the easy version of the problem, a simple one-to-one letter mapping is sufficient. The harder version would require more sophisticated encoding to handle values larger than 26.