CSCI 1120

Introduction to Computing Using C++

Tutorial 6: Predefined Function

20th Oct. 2020

Predefined Functions
• Review about functions
• C++ Standard Libraries
• Calling predefined functions
• Math library function examples
• Random number generation

2
Functions: Function Prototypes
• Function prototype consists of
• Function name
• Parameters
• Information the function takes in
• C++ is “strong typed” – error to pass a parameter of the wrong type
• Return type
• Type of information the function passes back to caller (default int)
• void signifies the function returns nothing
• Only needed if function definition comes after the function call in the
program

3
Functions: Header Files
• Header files
– Contain function prototypes for library functions
– <cstdlib> , <cmath>, etc.
– Load with #include <filename>
• Example:
#include <cmath>
• Custom header files
– Defined by the programmer
– Save as filename.h
– Loaded into program using
#include "filename.h"

4
C++ Standard Libraries
• C++ provides a huge set of libraries:
– Standard ANSI C library ported over to C++. These libraries are name with a prefix "c" and
without the ".h", e.g., <cmath> for C's <math.h>, <cstdlib> for C's <stdlib.h>, etc
– C++ new Libraries, such as <iostream>, <iomanip>, <string>, <fstream>, <sstream>.
– C++ Standard Template Library (STL): consists of containers, iterators, algorithms and function
objects.
– Boost C++ libraries.

5
Calling Predefined Functions
• To call a function, you have to know the following info about the
function (usually from manuals)
• name, functionality, parameters, return value

• You may also need to know which header file(s) to include

• e.g.: To use math functions, you have to include "cmath" as
#include <cmath>

• Optionally, you may need to find out

• What namespace to use
• Which "library file" to add to your project (for non-standard C++ functions)

6
Math Library Functions
• Math library functions
– Allow the programmer to perform common mathematical calculations
– Are used by including the header file <cmath>
• Functions called by writing
functionName (argument)
• Example
cout << sqrt( 900.0 );
– Calls the sqrt (square root) function. The preceding statement would print 30
– The sqrt function takes an argument of type double and returns a result of
type double, as do all functions in the math library

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Math Function Examples
1 #include <iostream>
2 #include <cmath> // Need this line to use math functions
3 using namespace std;
4 You can store the returned value
5 int main() { in a variable or use the returned
6 double x; value directly in an expression.
7 x = sqrt(10);
8
9 cout << "x = square root of 10 = " << x << endl;
10 cout << "Ceiling of x = " << ceil(x) << endl;
11 cout << "2 to the power x = " << pow(2.0, x) << endl;
12 cout << "log(x + 10) = " << log10(x + 10) << endl;
13 x = square root of 10 = 3.16228
14 return 0; Ceiling of x = 4
15 } 2 to the power x = 8.95242
8
log(x + 10) = 1.11933
Functions Description Examples

ceil( x ) rounds x to the smallest integer ceil(9.2) is 10.0

not less than x ceil(-9.8) is -9.0
⌈x⌉
floor ( x ) rounds x to the largest integer not floor(9.2) is 9.0
greater than x floor(-9.8) is -10.0
⌊x⌋
exp( x ) exponential function exp(1.0) is 2.71828
ex
fabs( x ) absolute value of x fabs(5.1) is 5.1
|x| fabs(0.0) is 0.0
fabs(-8.76) is 8.76
pow( x, y ) x raised to power y pow(2, 7) is 128.0
xy pow(9, .5) is 3.0

sqrt( x ) square root of x sqrt(900.0) is 30.0

√x sqrt(9.0) is 3.0

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Functions Description Examples

log ( x ) natural logarithm of x (base e) log(2.718282) ≈ 1.0

loge x or ln x log(exp(3.0)) is 3.0
ln e = 1
ln ex = x * ln e = x
log10 ( x ) logarithm of x (base 10) log(10.0) is 1.0
log10 x log(100.0) is 2.0

sin( x ) trigonometric sine, cosine and sin(0.0) is 0.0

cos( x ) tangent of x (x in radians) cos(0.0) is 1.0
tan( x ) sin x tan(0.0) is 0.0
cos x
tan x Let pi = 3.141592654
90° = π/ 2 sin(pi / 2) ≈ 1.0
180° = π cos(pi / 2) ≈ 0.0
270° = 3 * π / 4 tan(pi / 2) ≈ a large #

Ref: http://www.cplusplus.com/reference/cmath/ 10
Random Number Generation
• rand function
i = rand();
– Load <cstdlib>
– Generates a pseudorandom number between 0 and RAND_MAX (usually 32767)
• A pseudorandom number is a preset sequence of "random" numbers
• The same sequence is generated upon every program execution
• srand function
– Jumps to a seeded location in a "random" sequence
srand( seed );
srand( time( 0 ) ); //must include <ctime>
– time( 0 )
• The time at which the program was compiled
– Changes the seed every time the program is compiled, thereby allowing rand to
generate random numbers
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Random Number Generation
• rand() (#include <cstdlib>)
x = rand();
• x is assigned an integer between 0 and RAND_MAX (usually 32767)

• Scaling and shifting

rand() % range
• Generates a random number in the interval [0, range – 1]
• e.g.: x = rand() % 100; // x in [0, 99]

start + rand() % (end - start + 1)

• Generates a random number in the interval [start, end]
• e.g.: x = 10 + rand() % 8 // x in [10, 17]

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Sample Problem – Distribution of rand()

• Use rand() to simulate the process of throwing a dice for 6000

times

• Calculate the number of times each dice number appears in the

simulation.
• What outcome do you expect?

13
1 #include <iostream>
2 using namespace std;
3 #include <iomanip> // Needed by setw()
4 #include <cstdlib>
5
6 int main() {
7
8 // # of times the outcome is 1, 2, 3, 4, 5, or 6
9 int freq1 = 0, freq2 = 0, freq3 = 0,
10 freq4 = 0, freq5 = 0, freq6 = 0;
11
12 int face; // face value of the dice
13 int i = 1;
14
15 while (i <= 6000) {
16 face = 1 + rand() % 6;
17
18
14
19 if (face == 1) freq1++;
Reserve 13 spaces for
20 else if (face == 2) freq2++;
the next output.
21 else if (face == 3) freq3++;
22 else if (face == 4) freq4++; The output is right
23 else if (face == 5) freq5++; justified in the reserved
24 else freq6++; space.
25 No use if next output is
26 i++; too big to fit into the
27 } // End of while loop reserved space.
28
29 cout << "Face" << setw(13) << "Frequency\n"
30 << " 1" << setw(13) << freq1 << endl
31 << " 2" << setw(13) << freq2 << endl
32 << " 3" << setw(13) << freq3 << endl
33 << " 4" << setw(13) << freq4 << endl
34 << " 5" << setw(13) << freq5 << endl
35 << " 6" << setw(13) << freq6 << endl;
36
37 return 0;
38 }
39 15
Face Frequency
1 1003
2 1017
3 983
4 994
5 1004
6 999

13 character-wide

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srand() and Random Number Sequence
• rand() only generates pseudorandom number
sequence.

• A seed value controls what sequence of numbers to be

generated.

• To get different random sequences, call

srand(seed);
• seed is a non-negative integer number.
• Same seed  same sequence of random numbers
• Every call to srand() resets the random number
sequence
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1 #include <iostream>
using namespace std;
2
#include <cstdlib>
3 #include <iomanip>
4 int main() {
5 unsigned int seed;
6 int i = 1;
7 cout << "Enter seed: ";
8 cin >> seed;
9 srand( seed ); // Initialize random number generator
10
11 while (i <= 10) {
cout << setw(10) << ( 1 + rand() % 6 );
12
13 // prints 5 #'s per line
14 if (i % 5 == 0)
15 cout << endl;
16 i++;
17 } // end of while
18 return 0;
19 }
18
Enter seed: 67
6 1 4 6 2
1 6 1 6 4

Enter seed: 432

4 6 3 1 6
3 1 5 4 2

Enter seed: 67
6 1 4 6 2
1 6 1 6 4

rand() yields the same

sequence of pseudorandom
numbers if it is initialized
with the same seed value.

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 macOS

Windows

With the same seed value, the

sequence of pseudorandom
numbers may not be the same
across different systems.
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1 #include <iostream>
using namespace std; Use the current time to set the seed
2
#include <cstdlib>
3 #include <ctime> Need to include "ctime" as
4 #include <iomanip> #include <ctime>
5
6 int main() {
int i = 1; time(0)returns the current time in
7 seconds since 1st Jan 1970.
8 srand(time(0));
9
10 while (i <= 10) {
11 cout << setw(10) << ( 1 + rand() % 6 );
12 // prints 5 #'s per line
13 if (i % 5 == 0)
14 cout << endl; Advantage: No need to ask user for a
15 seed value
i++;
16 } // end of while
17 return 0;
18 }
19 21
 The first output

Wait a “second” to get the second output

22
Example – randGenPuzzle() function in assignment 3

• Recall that we have provided a randGenPuzzle() function to you in

assignment 3, which can return a solvable 8-puzzle.

• The randGenPuzzle() makes use of rand() function to generate a

random 8-puzzle game.

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Example – randGenPuzzle() function in assignment 3
Generate a random digit in the
range [0, 8].

while loop: generate each digit of p

one by one.
Example:
s=3, divm=1000, p=3, mask=1000,
divp=10.

s=4, divm=10000, p=43, mask=11000,

divp=100.

s=1, divm=10, p=143,mask=11010,

divp=1000.
…..

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Sample Problem:

• Generate a random variable in [0,1]

x = (double)rand() / RAND_MAX
• Suppose there is a machine, which generates 3 with probability 0.2, 5
with probability 0.5, and 7 with probability 0.3. How to solve the
problem?

25
Sample Problem: code
int main() {
int i, a, b, c, k;
double x;
a = 0; b = 0; c = 0;
srand(time(NULL));
for (i = 1; i <= 10000; i ++){
x = (double)rand() / RAND_MAX; // generate random variable
if (x <= 0.2){
k = 3; a ++; // count the number of 3
}
if (x > 0.2 && x < 0.7){
k = 5; b ++; // count the number of 5
}
if (x >= 0.7){
k = 7; c ++; // count number of 7
}
}
cout<< a <<" "<< b << " " << c << endl;
return 0;
} 26
Sample Problem 2
• Generate a random permutation of the sequence (1, 2, …, n):

-- To shuffle an array a of n elements (indices 0..n-1):

for i from n−1 downto 1 do
j ← random integer such that 0 ≤ j ≤ i
exchange a[j] and a[i]

27
 Sample Code
#include<iostream> // To shuffle an array a of n elements
#include<cstdlib> (indices 0..n-1):
using namespace std; for (int i = n - 1; i > 0; i--) {
int j = rand() % i;
void printArray(int x[], int n) { swap(randperm[j], randperm[i]);
for (int i = 0; i < n; i++) { }
cout << x[i] << " "; // print the random permuration sequence
} cout << "Random Permutation: ";
cout << endl; printArray(randperm, n);
}
return 0;
int main() { }
int n = 10;
int randperm[10]; // declare the array
// assign (0, 1, ..., n-1) to the array
for (int i = 0; i < n; i++) {
randperm[i] = i;
}
cout << "Original Array: ";
printArray(randperm, n);

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