#2075

Medium

LeetCode Problem Workspace

Decode the Slanted Ciphertext

Decode the Slanted Ciphertext problem requires decoding a slanted cipher using string manipulation and simulation based on matrix-like structure.

string simulation

Problem Statement

The string originalText is encoded using a slanted transposition cipher. In this encoding, the originalText fills up a matrix with a fixed number of rows, and the characters are placed starting from the top-left corner and moving diagonally. The matrix cells are filled in a sequence of blue, red, yellow, and so on, filling each diagonal row-by-row. After encoding, the characters are read in a column-major order to form the encodedText.

To decode the encodedText, we need to reverse the encoding process. The problem asks to reconstruct the originalText from the given encodedText by simulating how it was placed into a matrix with a specific number of rows. This involves determining the correct dimensions of the matrix and filling it in the reverse order from how the encodedText was arranged.

Examples

Example 1

Input: encodedText = "ch ie pr", rows = 3

Output: "cipher"

This is the same example described in the problem description.

Example 2

Input: encodedText = "iveo eed l te olc", rows = 4

Output: "i love leetcode"

The figure above denotes the matrix that was used to encode originalText. The blue arrows show how we can find originalText from encodedText.

Example 3

Input: encodedText = "coding", rows = 1

Output: "coding"

Since there is only 1 row, both originalText and encodedText are the same.

Constraints

0 <= encodedText.length <= 106
encodedText consists of lowercase English letters and ' ' only.
encodedText is a valid encoding of some originalText that does not have trailing spaces.
1 <= rows <= 1000
The testcases are generated such that there is only one possible originalText.

Solution Approach

Determine Matrix Dimensions

First, calculate the number of columns by dividing the length of encodedText by the number of rows, and rounding up if necessary. This gives us the number of columns needed to construct the matrix.

Fill Matrix and Simulate Transposition

Next, simulate how the encodedText was placed into the matrix, filling each diagonal in the correct order, as described in the problem statement. Once the matrix is correctly filled, reconstruct the originalText by reading the characters row by row.

Reconstruct the Original Text

Finally, iterate through the matrix column by column, retrieving the characters in their correct sequence and concatenating them to form the originalText. This can be done efficiently using a nested loop structure.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity of this solution is O(n), where n is the length of the encodedText, as we are performing linear scans of the matrix to reconstruct the originalText. The space complexity is O(n) as well, since we store the entire encodedText and the matrix to reconstruct the originalText.

What Interviewers Usually Probe

Can the candidate determine the number of columns for the matrix based on the given rows?
Does the candidate correctly simulate the diagonal filling of the matrix?
Can the candidate optimize the matrix manipulation process without unnecessary computations?

Common Pitfalls or Variants

Common pitfalls

Not correctly calculating the number of columns when given the rows.
Misunderstanding the matrix filling order and transposition logic.
Not accounting for the spaces in the encodedText and their correct placement in the matrix.

Follow-up variants

Varying the number of rows in the matrix.
Changing the encodedText length while keeping rows constant.
Encoding a larger text and requiring the candidate to handle edge cases in matrix filling.

FAQ

What is the main approach for solving the "Decode the Slanted Ciphertext" problem?

The solution involves simulating the transposition cipher's encoding process by determining the matrix dimensions, filling it based on the given rows, and then reconstructing the originalText.

How do I find the number of columns for the matrix in the "Decode the Slanted Ciphertext" problem?

You can calculate the number of columns by dividing the length of encodedText by the number of rows and rounding up if needed.

What are common pitfalls when solving "Decode the Slanted Ciphertext"?

Common issues include incorrect calculation of columns, misunderstanding the matrix filling order, and not properly placing spaces within the encodedText.

How do spaces in the encodedText affect the solution?

Spaces are treated as characters in the encodedText and must be correctly placed in the matrix during both encoding and decoding.

What are the time and space complexities of solving "Decode the Slanted Ciphertext"?

Both time and space complexity are O(n), where n is the length of the encodedText, as the solution involves processing each character and constructing the matrix.

terminal

Solution

Solution 1: Simulation

First, we calculate the number of columns in the matrix $cols = \textit{len}(encodedText) / rows$. Then, following the rules described in the problem, we start traversing the matrix from the top left corner, adding characters to the answer.

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class Solution:
    def decodeCiphertext(self, encodedText: str, rows: int) -> str:
        ans = []
        cols = len(encodedText) // rows
        for j in range(cols):
            x, y = 0, j
            while x < rows and y < cols:
                ans.append(encodedText[x * cols + y])
                x, y = x + 1, y + 1
        return ''.join(ans).rstrip()

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