Find Smallest Letter Greater Than Target

The task is to find the smallest character in a sorted array of characters (letters) that is lexicographically greater than a given character (target). If such a character does not exist, return the first character in letters.

Since letters is sorted in non-decreasing order, we can take advantage of this property and use binary search to find the desired character efficiently.

Here’s a step-by-step guide to solving the problem:

We’ll perform binary search to find the position of the smallest character greater than target.

2. Handling Edge Cases

If the character at the position found in step 1 is not greater than target or if the target is greater than all elements, return the first character in letters.

3. Return the Result

Return the character found at the position obtained from step 1.

Code

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class Solution:
    def nextGreatestLetter(self, letters: List[str], target: str) -> str:
        left, right = 0, len(letters) - 1

        while left <= right:
            mid = left + (right - left) // 2
            if letters[mid] <= target:
                left = mid + 1
            else:
                right = mid - 1

        # If target is greater than all elements or character at position left is not greater than target
        if left == len(letters) or letters[left] <= target:
            return letters[0]

        return letters[left]

Insights

  • Binary Search: By using binary search, the time complexity is reduced to (O(\log n)), where (n) is the length of the letters array.
  • Space Complexity: The space complexity of the code is (O(1)), as we are using only a constant amount of extra space.
  • Edge Cases: The code handles the case where the target is greater than all characters in letters.

This solution efficiently finds the smallest character in letters that is lexicographically greater than target by leveraging the sorted property of letters.

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class Solution(object):
    def nextGreatestLetter(self, letters, target):
        """
        :type letters: List[str]
        :type target: str
        :rtype: str
        """

        if target >= letters[-1] or target < letters[0]:
            return letters[0]

        low = 0
        high = len(letters)-1
        while low <= high:
            mid = (high+low)//2

            if  target >= letters[mid]: 
                low = mid+1

            if target < letters[mid]:
                high = mid-1

        return letters[low]

Problem Classification

This problem is under the arrays and binary search.

What:

  1. Array of Characters (letters): The problem provides a sorted array of characters.

  2. Character (target): A specific character is given, which we use to find the smallest lexicographically greater character in the array.

  3. Return Character: The function needs to return the smallest character that is lexicographically greater than the target. If no such character exists, it should return the first character in the array.

The problem can be further classified as a Binary Search problem. The binary search algorithm is typically used to efficiently find a specific element in a sorted array. In this case, it can be used to find the smallest lexicographically greater character in a sorted array of characters.

This problem involves knowledge of arrays, character comparisons, binary search algorithms, and understanding of lexicographic ordering. A correct solution will require an understanding of how to perform binary searches on the array and character comparison operations in the given programming language.

Language Agnostic Coding Drills

  1. Dissecting the Code into Distinct Concepts:

  • Data Types and Variables: The code begins by declaring the parameters of the function and their types, such as lists and strings.

  • Conditional Statements (if): The solution uses ‘if’ statements to check conditions. Here, it’s used to determine if the target character is larger or smaller than the characters in the list, and guide the search process.

  • Working with Lists: The solution makes extensive use of Python lists. It accesses list elements by index, uses list slicing, and determines the length of the list.

  • Loops (while): The ‘while’ loop is used to iterate through the list until a certain condition is met.

  • Binary Search Algorithm: The core of the solution is implementing a binary search algorithm to efficiently find the smallest lexicographically greater character.

  1. Order of Increasing Difficulty and Description:

  • Data Types and Variables: This is a fundamental concept in all programming languages. Here, the understanding of Python variables and specific types like lists and strings is necessary.

  • Working with Lists: Interacting with lists is a bit more complex than just understanding data types and variables, hence its position here. It requires understanding of list indices, slicing, and built-in functions like len().

  • Conditional Statements (if): Conditional statements control the flow of the program and allow the code to react differently to different conditions. It is a concept that is slightly more difficult because it requires logical thinking to construct the right conditions.

  • Loops (while): While loops require a good understanding of control flow and conditions, making it a bit more challenging. This concept is used here to iterate over the array until the desired character is found.

  • Binary Search Algorithm: This is the most complex concept as it involves a combination of loops, conditionals, and array manipulation to work. It’s a classic algorithm that requires understanding of the problem, the data, and the algorithm itself.

  1. Problem-Solving Approach:

The problem-solving approach here begins with checking if the target character is already larger than the largest character or smaller than the smallest character in the array. If it is, the solution returns the first character of the array as it’s the smallest and meets the lexicographically greater condition.

If the target is within the range of characters in the list, the solution applies the binary search algorithm. It starts from the middle of the list and checks if the target is larger or smaller. If it’s larger, the search moves to the right half of the list, if it’s smaller, it moves to the left.

This process continues iteratively until the smallest lexicographically greater character is found. Each coding drill or concept identified here contributes directly to this solution. The knowledge of loops and conditions aids in implementing the binary search, while understanding of lists helps in accessing and manipulating the data.

The steps to solve the problem would involve performing these drills in the given order, starting with understanding the data and variables, working with lists and conditions, implementing the loop, and finally using all these to implement the binary search algorithm.

Targeted Drills in Python

  1. Data Types and Variables

This is a simple drill to understand how to declare and use variables and data types in Python.

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letters = ['a', 'b', 'c', 'd', 'e', 'f']
target = 'c'
  1. Working with Lists

This drill will focus on accessing elements of a list and getting its length.

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letters = ['a', 'b', 'c', 'd', 'e', 'f']
first_letter = letters[0]
last_letter = letters[-1]
list_length = len(letters)
  1. Conditional Statements (if)

This drill will demonstrate how to use if statements in Python.

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target = 'c'
if target > 'f':
    print("Target is greater than 'f'")
elif target < 'a':
    print("Target is less than 'a'")
else:
    print("Target is within the range 'a' to 'f'")
  1. Loops (while)

This drill focuses on creating a while loop.

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i = 0
while i < 5:
    print(i)
    i += 1
  1. Binary Search Algorithm

This drill demonstrates how to implement a binary search in Python.

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def binary_search(letters, target):
    low = 0
    high = len(letters) - 1
    while low <= high:
        mid = (low + high) // 2
        if letters[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return low  # return index of the smallest letter that is larger than target

letters = ['a', 'b', 'c', 'd', 'e', 'f']
target = 'c'
index = binary_search(letters, target)
print(f"The smallest letter that is larger than {target} is {letters[index]}")

In the given problem, the problem-specific concept is the lexicographical comparison of characters, which is essentially a string comparison and is a built-in operation in Python. This operation is essential for our problem as we need to find the lexicographically next letter to the target.

After all the drills, we can combine these concepts together to solve the initial problem. We start by understanding the data types and declaring the variables. Then we perform conditional checks and traverse through the list with a while loop, implementing a binary search algorithm inside the loop to find the smallest character that is lexicographically greater than the target. If the target is larger than the last character or smaller than the first character, we return the first character in the list. The combination of these drills leads to the final solution.