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• Here we introduce a BigInt class which can represent integers much larger than the maximum bound for integer type in computers.
• You will deal with only positive BigInt in this problem. The BigInt class uses a dynamic array of char to represent the “big” integers. Each of the elements in the array can only be one of ‘0’, ‘1’, ‘2’, …, ‘9’, i.e., each array element stores just one digit of the “big” integer.
• The BigInt.h file defines the BigInt class as follows:

HW #5

class BigInt { public:

// constructor

BigInt () {

num = NULL;

size = 0;

};

# HW #5

// convert an array of integral digits by tmp to BigInt

// tmp: pointer to the array

// length: the number of digits in the array BigInt (const int* tmp, int length);

BigInt (const BigInt &); // copy constructor

// Assignment

const BigInt & operator=(const BigInt &);

// destructor

~BigInt() { if (num != NULL) delete [ ] num;

};

char & operator[ ] (int index); int length() const { return size; }; char* getNum() { return num; };

# HW #5

private: char* num; // the big integer in char

int size; // number of digits in the big integer

};

1A:

• Implement the overloading of the operator [ ], so that it returns the digits in char of a particular index. For example, if A is a BigInt object, we can get the 5th digit of A from the left in char by calling A[4] (digits are indexed 0, 1, 2, … from the left).

char & BigInt::operator [ ] (int index) { assert (index >=0 && index < size);

1B:

• Implement the constructor which takes in an integer array of digits and converts it to a BigInt object. You may assume that the digits in the array are all integers between 0 and 9.
• Hint: in order to convert a digits to a char type, you can add (‘1’ – 1) to it. For example, if you want to convert the digit 3 to a char in the form of ‘3’, you can use 3 + (‘1’ – 1).

// convert an integer array of digits (0-9) to BigInt

// tmp: pointer to the array

// length: the number of digits in the integer array

BigInt (const* tmp, int length) {

1C:

• In addition to the above, you need to implement prefix increment of BigInt, i.e., you want to support ++bi for a BigInt bi. Write the prototype of the member function in the BigInt class, and its implementation outside the class.

1D:

• You also want to implement postfix increment which supports bi++ for a BigInt bi. Write the prototype of the member function in the BigInt class, and its implementation outside the class.

Part 2:

• Design a class MyVector with two private data members: int length and a pointer to double for memory dynamic allocation.
• Include the following methods in the public section:
• two constructors: one default without parameters and one constructor initializer with one parameter of int type which will be used for specifying the requested vector length, the other parameter of pointer type for specifying that vector.
• a copy constructor;

# HW #5

• destructor;
• assignment operator;
• overload the output operator <<;
• operator* for calculating inner product of two vectors; • operator* for vector multiplication with a constant;
• operator+ for adding two vectors.
• Write a test program which implements all of the above methods.

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