#1138

Medium

LeetCode Problem Workspace

Alphabet Board Path

Find the path to type a target string on an alphabet board using directional moves and the 'hash table plus string' pattern.

hash table string

Problem Statement

Given a 5x5 alphabet board, we begin at the position (0, 0), which corresponds to the letter 'a'. The board is structured as follows: ['abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy', 'z']. Our goal is to find the shortest path to type a given target string, consisting only of lowercase English letters. At each step, we move to the target letter's position on the board by moving right (R), left (L), up (U), or down (D), with '!' to indicate a key press.

For example, if the target is 'leet', we must calculate the sequence of moves to reach each letter, starting from 'a'. The movement should be efficient, minimizing unnecessary steps and adhering to the grid's constraints. This problem emphasizes using a hash table for fast lookups of the positions of letters on the board, combined with string processing to produce the correct sequence of moves.

Examples

Example 1

Input: target = "leet"

Output: "DDR!UURRR!!DDD!"

Example details omitted.

Example 2

Input: target = "code"

Output: "RR!DDRR!UUL!R!"

Example details omitted.

Constraints

1 <= target.length <= 100
target consists only of English lowercase letters.

Solution Approach

Hash Table Mapping

Create a hash map to store the positions of each letter on the board. This allows for O(1) lookups to find the coordinates of each letter in the target string, reducing time complexity significantly compared to brute force approaches.

Path Calculation

For each letter in the target string, compute the necessary moves to go from the current position to the letter's position on the board. The moves are calculated based on the difference in row and column indices, producing a string of directional moves (L, R, U, D) followed by '!' to represent the key press.

String Concatenation

As each movement is calculated for each target letter, append the directional moves and '!' to a result string. Once all letters are processed, the final string represents the entire sequence of moves needed to type the target string.

Complexity Analysis

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

Time complexity is O(n) where n is the length of the target string, as each letter's position lookup and move calculation is done in constant time. Space complexity is O(1) due to the fixed size of the board and hash table, since the hash table only stores the positions of 26 letters.

What Interviewers Usually Probe

The candidate should demonstrate understanding of the hash table for efficient letter position lookup.
Look for the ability to optimize movement calculations and reduce unnecessary steps.
Check if the candidate can maintain efficient space and time complexity while handling string manipulation.

Common Pitfalls or Variants

Common pitfalls

Overcomplicating the move calculation process, leading to inefficient or incorrect paths.
Forgetting to account for the exact movement required between rows and columns.
Not leveraging the hash table properly, leading to repeated scans of the board.

Follow-up variants

Consider an extended board where rows and columns are dynamically added.
What if the board is provided as a list of strings where each row can vary in length?
How would this approach change if the board contains more than one key per position?

FAQ

How do I efficiently find the position of each letter on the alphabet board?

By using a hash table to store the row and column positions of each letter, you can instantly access the position of any letter in constant time.

What are the possible moves on the alphabet board?

The moves are right (R), left (L), up (U), and down (D), with each move followed by '!' to represent pressing the key.

Can I optimize the path calculation further?

Ensure you're calculating the minimal horizontal and vertical distance to reduce unnecessary movements. Avoid backtracking or extra steps.

What is the time complexity of this problem?

The time complexity is O(n), where n is the length of the target string, since each letter lookup and move calculation takes constant time.

How does the board look for this problem?

The board is a 5x5 grid with the letters 'a' to 'z', arranged as ['abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy', 'z'].

terminal

Solution

Solution 1: Simulation

Starting from the origin point $(0, 0)$, simulate each step of the movement, appending the result of each step to the answer. Note that the direction of movement follows the order "left, up, right, down".

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class Solution:
    def alphabetBoardPath(self, target: str) -> str:
        i = j = 0
        ans = []
        for c in target:
            v = ord(c) - ord("a")
            x, y = v // 5, v % 5
            while j > y:
                j -= 1
                ans.append("L")
            while i > x:
                i -= 1
                ans.append("U")
            while j < y:
                j += 1
                ans.append("R")
            while i < x:
                i += 1
                ans.append("D")
            ans.append("!")
        return "".join(ans)

Continue Practicing

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