Check if each recipe is a contiguous subsequence

You are given:

• An ordered ingredient list ingredients[0..n-1] .
• A list of m recipes. Each recipe recipes[j] is itself a list of ingredients and is intended to represent a sequence of consecutive ingredients.

Task

For each recipe, determine whether it can be formed by taking a contiguous subarray of ingredients (i.e., there exists an index s such that ingredients[s .. s + len(recipe)-1] equals the recipe exactly, element by element).

Return an array ans[0..m-1] of booleans.

Input

• Array ingredients (length n )
• List of arrays recipes (total m recipes)

Output

• Boolean array ans , where ans[j] = true if recipes[j] appears contiguously in ingredients , else false .

Follow-ups

1. How would you solve it if you are allowed only O(1) extra space (beyond the input/output)?
2. How would you solve it if ingredients arrives as a data stream and is too large to store fully?

Constraints (typical)

• 1 <= n <= 2e5
• 1 <= m <= 2e5
• Total length of all recipes <= 2e5
• Ingredients can be treated as strings or integers.