```haskell------------------------------------------------------------------------ | `mulByInt i n` returns the result of multiplying-- the int `i` with `BigInt` `n`.---- >>> mulByInt 9 [9,9,9,9]-- [8,9,9,9,1]----------------------------------------------------------------------mulByInt :: Int -> BigInt -> BigIntmulByInt i n = error "TBD:mulByInt"```### Explanation:This Haskell code snippet defines the type signature and concept for a function called `mulByInt`.- **Function Purpose**: The function `mulByInt` is designed to multiply an integer `i` by a `BigInt` `n`. A `BigInt` is typically a large integer stored in an array format. - **Example Execution**: The example `mulByInt 9 [9,9,9,9]` demonstrates multiplying the integer `9` by the `BigInt` representation `[9,9,9,9]`, which yields the result `[8,9,9,9,1]`.- **Type Signature**: `mulByInt :: Int -> BigInt -> BigInt`, indicates that `mulByInt` takes an integer and a `BigInt` as input and returns a `BigInt`.- **Implementation Note**: The function currently uses `error "TBD:mulByInt"`, indicating that the actual implementation is yet to be defined (TBD stands for "To Be Done"). ### Introduction to Big Integer Representation with HaskellIn this lesson, we explore how to represent and manipulate large integers using lists in Haskell.#### Big-Integer RepresentationWe use a list `[d1, d2, ..., dn]` where each element `di` is a digit between `0` and `9`, to represent the positive big-integer `d1d2...dn`.```haskelltype BigInt = [Int]```#### ExampleThe list `[9, 9, 9, 9, 9, 9, 9, 9, 9, 8]` represents the big-integer `9999999998`. Your task is to implement the function:```haskellbigAdd :: BigInt -> BigInt -> BigInt```This function should take two integer lists (each integer being between `0` and `9`) and return a list representing the sum of the two big-integers. This involves completing the implementation to provide appropriate values to `f`, `base`, and `args`.#### Desired BehaviorThe function should exhibit the following behavior:```haskellghci> bigAdd [9, 9] [1, 0, 0, 2][1, 1, 0, 1]ghci> bigAdd [9, 9, 9, 9] [9, 9][1, 0, 9, 9, 8]```By mastering the manipulation of these lists, you'll be able to handle computations involving large numbers efficiently in Haskell.

Algorithm:Define a data type BigInt as a list of integers to represent positive big…

Let us use the list [d1, d2, represent the (positive) big-integer d1d2...dn. type BigInt = [Int] dn], where each di is between 0 and 9, to For example, [9, 9, 9, 9, 9, 9, 9, 9, 9, 8] represents the big-integer 9999999998. Fill out the implementation for bigAdd :: BigInt -> BigInt -> BigInt so that it takes two integer lists, where each integer is between 0 and 9 and returns the list corresponding to the addition of the two big-integers. Again, you have to fill in the implementation to supply the appropriate values to f, base, args. You should get the following behavior: ghci> bigAdd [9, 9] [1, 0, 0, 2] [1, 1, 0, 1] ghci> bigAdd [9, 9, 9, 9] [9, 9, 9] [1, 0, 9, 9, 8]

Let us use the list [d1, d2, represent the (positive) big-integer d1d2...dn. type BigInt = [Int] dn], where each di is between 0 and 9, to For example, [9, 9, 9, 9, 9, 9, 9, 9, 9, 8] represents the big-integer 9999999998. Fill out the implementation for bigAdd :: BigInt -> BigInt -> BigInt so that it takes two integer lists, where each integer is between 0 and 9 and returns the list corresponding to the addition of the two big-integers. Again, you have to fill in the implementation to supply the appropriate values to f, base, args. You should get the following behavior: ghci> bigAdd [9, 9] [1, 0, 0, 2] [1, 1, 0, 1] ghci> bigAdd [9, 9, 9, 9] [9, 9, 9] [1, 0, 9, 9, 8]

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Merge sort

Merge Sort recursively sorts a given collection of numbers or elements by using the divide and conquer strategy in less time. It is one of the most used algorithms, with the worst-case time complexity of O (n log n). It was invented by John Von Neumann. The algorithm continuously divides an array into sub-arrays until each sub-array consists of a single element. It then merges those sub-arrays to produce a sorted array.

Question

```haskell
----------------------------------------------------------------------
-- | `mulByInt i n` returns the result of multiplying
-- the int `i` with `BigInt` `n`.
--
-- >>> mulByInt 9 [9,9,9,9]
-- [8,9,9,9,1]
----------------------------------------------------------------------

mulByInt :: Int -> BigInt -> BigInt
mulByInt i n = error "TBD:mulByInt"
```

### Explanation:

This Haskell code snippet defines the type signature and concept for a function called `mulByInt`.

- **Function Purpose**: The function `mulByInt` is designed to multiply an integer `i` by a `BigInt` `n`. A `BigInt` is typically a large integer stored in an array format.

- **Example Execution**: The example `mulByInt 9 [9,9,9,9]` demonstrates multiplying the integer `9` by the `BigInt` representation `[9,9,9,9]`, which yields the result `[8,9,9,9,1]`.

- **Type Signature**: `mulByInt :: Int -> BigInt -> BigInt`, indicates that `mulByInt` takes an integer and a `BigInt` as input and returns a `BigInt`.

- **Implementation Note**: The function currently uses `error "TBD:mulByInt"`, indicating that the actual implementation is yet to be defined (TBD stands for "To Be Done").

### Introduction to Big Integer Representation with Haskell

In this lesson, we explore how to represent and manipulate large integers using lists in Haskell.

#### Big-Integer Representation

We use a list `[d1, d2, ..., dn]` where each element `di` is a digit between `0` and `9`, to represent the positive big-integer `d1d2...dn`.

```haskell
type BigInt = [Int]
```

#### Example

The list `[9, 9, 9, 9, 9, 9, 9, 9, 9, 8]` represents the big-integer `9999999998`. Your task is to implement the function:

```haskell
bigAdd :: BigInt -> BigInt -> BigInt
```

This function should take two integer lists (each integer being between `0` and `9`) and return a list representing the sum of the two big-integers. This involves completing the implementation to provide appropriate values to `f`, `base`, and `args`.

#### Desired Behavior

The function should exhibit the following behavior:

```haskell
ghci> bigAdd [9, 9] [1, 0, 0, 2]
[1, 1, 0, 1]

ghci> bigAdd [9, 9, 9, 9] [9, 9]
[1, 0, 9, 9, 8]
```

By mastering the manipulation of these lists, you'll be able to handle computations involving large numbers efficiently in Haskell.

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