Midterm: Simpilified Big Number Calculator (extra homework, 15% grade)
-
Inputs:
- The function to be calculated, listed below:
- Display two nubmers only (
display only) (50%, with exceptions handled) - Plus (
+) (30%) - Greatest Common Divider (
gcd) (20%)
- Display two nubmers only (
- Two non-negative integers \( a, b \). Two numbers will not more than 50 digits.
- If the calculated function is greatest common divider, \( a, b \) should be natural numbers (自然數), otherwise, the two numbers should be integer.
- The function to be calculated, listed below:
-
Outputs:
- The calculated function. (i.e.
display only,+,gcd) - Two nubmers. \( a, b \)
- The corrsponding calculation result.
- The calculated function. (i.e.
-
File name:
midterm_1_<student_id>.cpp(e.g.midterm_1_106062802.cpp) -
The program should inform the user to select the function and type the numbers, \( a, b \) to be calculated. Output the typed numbers and the calculation result of the selected function.
-
The program supports the calculation repeatly. User can select the function
0to exit the program. -
The program should check user's input, output the error message and inform the user to input again if the input is invalid. If the input is invalid, the program should inform the user with
Invalid input: <the wrong input>right after the input and inform the user to type the same input again. -
The format of the error message is shown in the Exception section.
-
The program should assume the user's input is any non-space character (i.e. not space, tab) string.
-
The program should be finished within 30 seconds. Any test cases will garuntee the program is finished within 30 seconds.
Format
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: <1-3>⏎
You selected: <display only,+,gcd>
Input integer number (a): <a>⏎
Input integer number (b): <b>⏎
(a) = <a>
(b) = <b>
(a) <+, gcd> (b) = <result>
Example
Display
$ ./a.out
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 1⏎
You selected: display only
Input integer number (a): 0000000000000⏎
Input integer number (b): 00000001⏎
(a) = 0
(b) = 1
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 1⏎
You selected: display only
Input integer number (a): 123456789012345678901234567890⏎
Input integer number (b): 987654321098765432109876543210⏎
(a) = 123456789012345678901234567890
(b) = 987654321098765432109876543210
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 1⏎
You selected: display only
Input integer number (a): 12345678901234567890123456789012345678901234567890⏎
Input integer number (b): 98765432109876543210987654321098765432109876543210⏎
(a) = 12345678901234567890123456789012345678901234567890
(b) = 98765432109876543210987654321098765432109876543210
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 0⏎
$
Plus
$ ./a.out
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 2⏎
You selected: +
Input integer number (a): 111⏎
Input integer number (b): 222⏎
(a) = 111
(b) = 222
(a) + (b) = 333
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 2⏎
You selected: +
Input integer number (a): 123⏎
Input integer number (b): 987⏎
(a) = 123
(b) = 987
(a) + (b) = 1110
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 2⏎
You selected: +
Input integer number (a): 123456789012345678901234567890⏎
Input integer number (b): 987654321098765432109876543210⏎
(a) = 123456789012345678901234567890
(b) = 987654321098765432109876543210
(a) + (b) = 1111111110111111111011111111100
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 2⏎
You selected: +
Input integer number (a): 12345678901234567890123456789012345678901234567890⏎
Input integer number (b): 98765432109876543210987654321098765432109876543210⏎
(a) = 12345678901234567890123456789012345678901234567890
(b) = 98765432109876543210987654321098765432109876543210
(a) + (b) = 111111111011111111101111111110111111111011111111100
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 0⏎
$
Greatest Common Divider
$ ./a.out
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 3⏎
Input integer number (b): 27⏎
(a) = 3
(b) = 27
(a) gcd (b) = 3
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 47⏎
Input integer number (b): 7⏎
(a) = 47
(b) = 7
(a) gcd (b) = 1
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 123492001107001353123492001107001353⏎
Input integer number (b): 99396000891001089099396000891001089⏎
(a) = 123492001107001353123492001107001353
(b) = 99396000891001089099396000891001089
(a) gcd (b) = 3012000027000033003012000027000033
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 7369130657357778596659⏎
Input integer number (b): 2305843009213693951⏎
(a) = 7369130657357778596659
(b) = 2305843009213693951
(a) gcd (b) = 1
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 2305843009213693951⏎
Input integer number (b): 7369130657357778596659⏎
(a) = 2305843009213693951
(b) = 7369130657357778596659
(a) gcd (b) = 1
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 12345678901234567890123456789012345678901234567890⏎
Input integer number (b): 1234567890123456789012345678901234567890123456789⏎
(a) = 12345678901234567890123456789012345678901234567890
(b) = 1234567890123456789012345678901234567890123456789
(a) gcd (b) = 1234567890123456789012345678901234567890123456789
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 987654321098765432109876543210⏎
Input integer number (b): 123456789012345678901234567890⏎
(a) = 987654321098765432109876543210
(b) = 123456789012345678901234567890
(a) gcd (b) = 9000000000900000000090
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 0⏎
$
Exceptions
$ ./a.out
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: +⏎
Invalid input: +
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 00000001⏎
Invalid input: 00000001
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: -2⏎
Invalid input: -2
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 4⏎
Invalid input: 4
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 1⏎
You selected: display only
Input integer number (a): +_)(*(&#$)(*@()*@!⏎
Invalid input: +_)(*(&#$)(*@()*@!
Input integer number (a): -0.0⏎
Invalid input: -0.0
Input integer number (a): 123⏎
Input integer number (b): 0.1⏎
Invalid input: 0.1
Input integer number (b): 0⏎
(a) = 123
(b) = 0
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 3⏎
You selected: gcd
Input integer number (a): 0⏎
Invalid input: 0
Input integer number (a): 987654321098765432109876543210⏎
Input integer number (b): 0⏎
Invalid input: 0
Input integer number (b): 987654321098765432109876543210⏎
(a) = 987654321098765432109876543210
(b) = 987654321098765432109876543210
(a) gcd (b) = 987654321098765432109876543210
Big number calculator
1) display only
2) plus (+)
3) greatest common divider (gcd)
0) exit
Please select the operator: 0⏎
$
Pseudo code
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cctype>
using namespace std;
int main()
{
vector<int> num_a, num_b;
string input_buffer;
int select_function;
while (true)
{
// select function
cout << "Big number calculator" << endl
<< "1) display only" << endl
<< "2) plus (+)" << endl
<< "3) greatest common divider (gcd)" << endl
<< "0) exit" << endl
<< "Please select the operator: ";
cin >> input_buffer;
// start of check selected function is valid
// end of check selected function is valid
// start of inform selected function
// end of inform selected function
// clear buffer
input_buffer.clear();
// input number (a)
// check if input is valid
// if not valid, inform user and continue to input
// convert string to int
// remove leading zeros
// check if input is valid for gcd
// clear buffer
input_buffer.clear();
// input number (b)
// check if input is valid
// if not valid, inform user and continue to input
// convert string to int
// remove leading zeros
// check if input is valid for gcd
// clear buffer
input_buffer.clear();
// print number (a) (b)
// calculation
// plus
// gcd
// compaire a and b
// if a == b, break
// if a > b
// a = a - b
// if a < b
// b = b - a
// remove leading zeros
// if a == 0, b is the result
// else if b == 0, a is the result
// clean up (a) and (b)
}
}
C++ References
- unzip
html-book-20201016.zip. - open
html-book-20201016/reference/en/index.html. - Find what you want.
Reference Code:
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cctype>
using namespace std;
int main()
{
vector<int> num_a, num_b;
string input_buffer;
int select_function;
while (true)
{
// select function
cout << "Big number calculator" << endl
<< "1) display only" << endl
<< "2) plus (+)" << endl
<< "3) greatest common divider (gcd)" << endl
<< "0) exit" << endl
<< "Please select the operator: ";
cin >> input_buffer;
// start of check selected function is valid
if (input_buffer == "0")
{
select_function = 0;
}
else if (input_buffer == "1")
{
select_function = 1;
}
else if (input_buffer == "2")
{
select_function = 2;
}
else if (input_buffer == "3")
{
select_function = 3;
}
else
{
cout << "Invalid input: " << input_buffer << endl
<< endl;
continue;
}
// end of check selected function is valid
// start of inform selected function
if (select_function == 0)
{
cout << endl;
break;
}
else if (select_function == 1)
{
cout << "You selected: display only" << endl;
}
else if (select_function == 2)
{
cout << "You selected: +" << endl;
}
else if (select_function == 3)
{
cout << "You selected: gcd" << endl;
}
// end of inform selected function
// clear buffer
input_buffer.clear();
// input number (a)
while (true)
{
cout << "Input integer number (a): ";
cin >> input_buffer;
bool valid = true;
// check if input is valid
for (int i = 0; i < input_buffer.size(); i++)
{
if (!isdigit(input_buffer[i]))
{
valid = false;
break;
}
}
if (!valid)
{
cout << "Invalid input: " << input_buffer << endl
<< endl;
continue;
}
// convert string to int
for (int i = 0; i < input_buffer.size(); i++)
{
num_a.push_back(input_buffer[i] - '0');
}
// remove leading zeros
while (num_a.size() > 1 && num_a[0] == 0)
{
num_a.erase(num_a.begin());
}
reverse(num_a.begin(), num_a.end());
// check if input is valid for gcd
if (select_function == 3 && num_a.size() == 1 && num_a[0] == 0)
{
cout << "Invalid input: " << input_buffer << endl
<< endl;
num_a.clear();
continue;
}
break;
}
// clear buffer
input_buffer.clear();
// input number (b)
while (true)
{
cout << "Input integer number (b): ";
cin >> input_buffer;
bool valid = true;
// check if input is valid
for (int i = 0; i < input_buffer.size(); i++)
{
if (!isdigit(input_buffer[i]))
{
valid = false;
break;
}
}
if (!valid)
{
cout << "Invalid input: " << input_buffer << endl
<< endl;
continue;
}
// convert string to int
for (int i = 0; i < input_buffer.size(); i++)
{
num_b.push_back(input_buffer[i] - '0');
}
// remove leading zeros
while (num_b.size() > 1 && num_b[0] == 0)
{
num_b.erase(num_b.begin());
}
reverse(num_b.begin(), num_b.end());
// check if input is valid for gcd
if (select_function == 3 && num_b.size() == 1 && num_b[0] == 0)
{
cout << "Invalid input: " << input_buffer << endl
<< endl;
num_b.clear();
continue;
}
break;
}
// clear buffer
input_buffer.clear();
// print number (a)
cout << "(a) = ";
for (int i = num_a.size() - 1; i >= 0; i--)
{
cout << num_a[i];
}
cout << endl;
// print number (b)
cout << "(b) = ";
for (int i = num_b.size() - 1; i >= 0; i--)
{
cout << num_b[i];
}
cout << endl;
// calculation
if (select_function == 2)
{
// plus
vector<int> result;
int carry = 0;
for (int i = 0; i < max(num_a.size(), num_b.size()); i++)
{
int sum = carry;
if (i < num_a.size())
{
sum += num_a[i];
}
if (i < num_b.size())
{
sum += num_b[i];
}
result.push_back(sum % 10);
carry = sum / 10;
}
if (carry != 0)
{
result.push_back(carry);
}
cout << "(a) + (b) = ";
for (int i = result.size() - 1; i >= 0; i--)
{
cout << result[i];
}
cout << endl;
}
else if (select_function == 3)
{
// gcd
while (true)
{
// compaire a and b
int comp = 0;
if (num_a.size() > num_b.size())
{
comp = 1;
}
else if (num_a.size() < num_b.size())
{
comp = -1;
}
else
{
for (int i = num_a.size() - 1; i >= 0; i--)
{
if (num_a[i] > num_b[i])
{
comp = 1;
break;
}
else if (num_a[i] < num_b[i])
{
comp = -1;
break;
}
}
}
// if a == b, break
if (comp == 0)
{
break;
}
// if a > b
else if (comp == 1)
{
// a = a - b
int carry = 0;
for (int i = 0; i < num_a.size(); i++)
{
int sub = num_a[i] - carry;
if (i < num_b.size())
{
sub -= num_b[i];
}
if (sub < 0)
{
sub += 10;
carry = 1;
}
else
{
carry = 0;
}
num_a[i] = sub;
}
}
// if a < b
else
{
// b = b - a
int carry = 0;
for (int i = 0; i < num_b.size(); i++)
{
int sub = num_b[i] - carry;
if (i < num_a.size())
{
sub -= num_a[i];
}
if (sub < 0)
{
sub += 10;
carry = 1;
}
else
{
carry = 0;
}
num_b[i] = sub;
}
}
// remove leading zeros
for (int i = num_a.size() - 1; i >= 0; i--)
{
if (num_a[i] != 0)
{
break;
}
num_a.pop_back();
}
for (int i = num_b.size() - 1; i >= 0; i--)
{
if (num_b[i] != 0)
{
break;
}
num_b.pop_back();
}
// if a == 0, b is the result
if (num_a.size() == 1 && num_a[0] == 0)
{
num_a.swap(num_b);
break;
}
// else if b == 0, a is the result
else if (num_b.size() == 1 && num_b[0] == 0)
{
break;
}
}
cout << "(a) gcd (b) = ";
for (int i = num_a.size() - 1; i >= 0; i--)
{
cout << num_a[i];
}
cout << endl;
}
// clean up (a) and (b)
num_a.clear();
num_b.clear();
cout << endl;
}
}