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Which data structure is often used to store the resulting polynomial after multiplication?

Question

Which data structure is often used to store the resulting polynomial after multiplication?

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Solution

The data structure commonly used to store the resulting polynomial after multiplication is a linked list or a sparse array.

  1. Linked List: This structure allows for efficient insertion and deletion of terms, making it ideal for representing polynomials that can have varying numbers of non-zero coefficients. Each node in the linked list typically includes a coefficient and an exponent, effectively allowing the representation of each term in the polynomial.

  2. Sparse Array: When a polynomial contains a lot of zero coefficients, a sparse array can be a more space-efficient way to store it. In this case, only non-zero terms are stored, often in the form of pairs of coefficients and exponents.

  3. Dictionary/Map: In programming, another convenient way to represent a polynomial is to use a dictionary or hash map, where each key represents the exponent, and the value represents the coefficient. This approach allows for quick access and manipulation of polynomial terms.

Choosing the right data structure depends on the specific use case, such as ease of manipulation, memory efficiency, and the operations required on the polynomial.

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