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Step-by-Step Explanation for Solving "Count Vowel Strings in Ranges"

This document explains the solution to the "Count Vowel Strings in Ranges" problem in five languages: C++, Java, JavaScript, Python, and Go.

Problem Statement

Given a list of strings and multiple queries, determine how many strings in each range of queries start and end with a vowel.

C++ Code Explanation

  1. Initialize Vowels Set:
    Create a set of vowels (a, e, i, o, u) for quick lookup.

  2. Prepare Prefix Array:
    Use a prefix array to precompute the cumulative count of strings that start and end with vowels.

    • If the current word starts and ends with a vowel, increment the prefix count at the current index.
    • Add the previous prefix value to maintain cumulative counts.

  3. Handle Queries:
    For each query [l, r], calculate the difference between prefix sums:

    • If l > 0: Use prefix[r] - prefix[l-1].
    • Otherwise: Simply use prefix[r].

  4. Return Results:
    Store the results for all queries in a vector and return them.

Java Code Explanation

  1. Initialize Vowels Set:
    Use Java's Set.of() to store the vowels (a, e, i, o, u) for fast lookups.

  2. Build Prefix Array:

    • Create an array prefix to store cumulative counts.
    • Check if each string starts and ends with a vowel.
    • Update the prefix sum:
      • Add 1 if valid, and carry forward the previous sum otherwise.

  3. Process Queries:
    Loop through each query and calculate the result using the prefix array:

    • For l > 0, use the difference between prefix[r] and prefix[l-1].
    • Otherwise, use prefix[r] directly.

  4. Output Results:
    Store the results for all queries in an array and return it.

JavaScript Code Explanation

  1. Define Vowels Set:
    Use a Set in JavaScript for vowels (a, e, i, o, u) to enable fast lookups.

  2. Compute Prefix Array:

    • Initialize an array prefix to store cumulative counts.
    • Iterate through the list of strings:
      • If the string starts and ends with a vowel, increment the count at the current index.
      • Add the value from the previous prefix index to maintain cumulative counts.

  3. Answer Queries:
    Use the prefix array to compute the result for each query:

    • Subtract prefix[l-1] from prefix[r] when l > 0.
    • If l == 0, directly use prefix[r].

  4. Return Results:
    Store and return the results as an array.

Python Code Explanation

  1. Create a Vowel Set:
    Use a set to store the vowels (a, e, i, o, u) for quick membership checks.

  2. Generate Prefix Array:

    • Initialize a prefix list with zeros.
    • For each word:
      • Check if it starts and ends with a vowel.
      • If valid, increment the prefix value at the current index.
      • Add the value from the previous index to maintain cumulative counts.

  3. Process Queries:
    For each query:

    • If l > 0, calculate the difference prefix[r] - prefix[l-1].
    • Otherwise, use prefix[r].

  4. Return the Results:
    Collect the results for all queries in a list and return.

Go Code Explanation

  1. Define Vowel Map:
    Use a map with vowels (a, e, i, o, u) as keys for quick lookups.

  2. Compute Prefix Array:

    • Initialize an array prefix to store cumulative counts.
    • Check if each word starts and ends with a vowel:
      • Increment the count if valid.
      • Add the previous prefix value to maintain cumulative sums.

  3. Answer Queries:
    For each query:

    • Subtract prefix[l-1] from prefix[r] when l > 0.
    • If l == 0, directly use prefix[r].

  4. Output Results:
    Store and return the results for all queries in a slice.

Key Insights

  • Optimization with Prefix Sums:
    Using a prefix sum array reduces the time complexity of handling multiple range queries. Instead of checking strings in each query range repeatedly, we preprocess the counts once.

  • Edge Cases:
    Handle cases where the range starts at the beginning of the list (l == 0) or if there are no valid strings in a query range.

Complexity Analysis

Time Complexity

  • Precomputing the prefix sum: $$O(n)$$
  • Answering queries: $$O(m)$$
  • Total: $$O(n + m)$$, where (n) is the number of strings, and (m) is the number of queries.

Space Complexity

  • Prefix array: $$O(n)$$
  • Additional data structures (constant): $$O(1)$$
  • Total: $$O(n)$$.