Introduction

In this blog post, we will explore how to solve the LeetCode problem "514" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

In the video game Fallout 4, the quest "Road to Freedom" requires players to reach a metal dial called the "Freedom Trail Ring" and use the dial to spell a specific keyword to open the door. Given a string ring that represents the code engraved on the outer ring and another string key that represents the keyword that needs to be spelled, return the minimum number of steps to spell all the characters in the keyword. Initially, the first character of the ring is aligned at the "12:00" direction. You should spell all the characters in key one by one by rotating ring clockwise or anticlockwise to make each character of the string key aligned at the "12:00" direction and then by pressing the center button. At the stage of rotating the ring to spell the key character key[i]: You can rotate the ring clockwise or anticlockwise by one place, which counts as one step. The final purpose of the rotation is to align one of ring's characters at the "12:00" direction, where this character must equal key[i]. If the character key[i] has been aligned at the "12:00" direction, press the center button to spell, which also counts as one step. After the pressing, you could begin to spell the next character in the key (next stage). Otherwise, you have finished all the spelling. Example 1: Input: ring = "godding", key = "gd" Output: 4 Explanation: For the first key character 'g', since it is already in place, we just need 1 step to spell this character. For the second key character 'd', we need to rotate the ring "godding" anticlockwise by two steps to make it become "ddinggo". Also, we need 1 more step for spelling. So the final output is 4. Example 2: Input: ring = "godding", key = "godding" Output: 13 Constraints: 1 <= ring.length, key.length <= 100 ring and key consist of only lower case English letters. It is guaranteed that key could always be spelled by rotating ring.

Explanation

Here's the solution to the problem, along with explanations:

High-Level Approach:

• Dynamic Programming: Use dynamic programming to store the minimum steps required to spell the first i characters of the key string, ending with a specific character of the ring at the 12:00 position.
• Calculate Distances: For each character in the key, find all occurrences of that character in the ring. Calculate the clockwise and anti-clockwise distances from the current position on the ring to each of those occurrences.
• Minimize Steps: Update the DP table by considering the minimum steps to reach each possible next position, including the cost of rotating the ring and pressing the button.

Complexity:

• Runtime Complexity: O(m n n), where m is the length of key and n is the length of ring.
• Storage Complexity: O(m * n)

Code

    def road_to_freedom(ring: str, key: str) -> int:
    """
    Calculates the minimum number of steps to spell the key using the ring.
    """

    n = len(ring)
    m = len(key)

    # dp[i][j] stores the minimum steps to spell key[:i+1] with ring[j] at 12:00
    dp = [[float('inf')] * n for _ in range(m)]

    # Find indices of each character in the ring
    char_indices = {}
    for i in range(n):
        if ring[i] not in char_indices:
            char_indices[ring[i]] = []
        char_indices[ring[i]].append(i)

    # Initialize the first row of dp
    for j in char_indices.get(key[0], []):
        dp[0][j] = min(j, n - j) + 1  # Distance to rotate + 1 for pressing the button

    # Iterate through the key
    for i in range(1, m):
        # Iterate through possible ending positions in the ring for the previous key character
        for j in range(n):
            # If dp[i-1][j] is reachable (not infinity)
            if dp[i - 1][j] != float('inf'):
                # Iterate through possible ending positions for the current key character
                for k in char_indices.get(key[i], []):
                    # Calculate the distance to rotate from ring[j] to ring[k]
                    diff = abs(j - k)
                    distance = min(diff, n - diff)

                    # Update the dp table
                    dp[i][k] = min(dp[i][k], dp[i - 1][j] + distance + 1)

    # Find the minimum steps to spell the entire key
    min_steps = min(dp[m - 1])

    return min_steps