functions
- 1. Outline Introduction Program Modules in C Math Library Functions Functions Function Definitions Function Prototypes Header Files Calling Functions: Call by Value and Call by Reference Random Number Generation Recursion Example Using Recursion: The Fibonacci Series Recursion vs. Iteration
- 2. Divide and conquer ◦ Construct a program from smaller pieces or components ◦ Each piece more manageable than the original program
- 3. Functions ◦ Modules in C ◦ Programs written by combining user-defined functions with library functions C standard library has a wide variety of functions Makes programmer's job easier - avoid reinventing the wheel
- 4. Function calls ◦ Invoking functions Provide function name and arguments (data) Function performs operations or manipulations Function returns results ◦ Boss asks worker to complete task Worker gets information, does task, returns result Information hiding: boss does not know details
- 5. Math library functions ◦ perform common mathematical calculations ◦ #include <math.h> Format for calling functions FunctionName (argument); If multiple arguments, use comma-separated list ◦ printf( "%.2f", sqrt( 900.0 ) ); Calls function sqrt, which returns the square root of its argument All math functions return data type double ◦ Arguments may be constants, variables, or expressions
- 6. Functions ◦ Modularize a program ◦ All variables declared inside functions are local variables Known only in function defined ◦ Parameters Communicate information between functions Local variables Benefits ◦ Divide and conquer Manageable program development ◦ Software reusability Use existing functions as building blocks for new programs Abstraction - hide internal details (library functions) ◦ Avoids code repetition
- 7. Function definition format return-value-type function-name( parameter-list ) { declarations and statements } ◦ Function-name: any valid identifier ◦ Return-value-type: data type of the result (default int) void - function returns nothing ◦ Parameter-list: comma separated list, declares parameters (default int)
- 8. Function definition format (continued) return-value-type function-name( parameter-list ) { declarations and statements } ◦ Declarations and statements: function body (block) Variables can be declared inside blocks (can be nested) Function can not be defined inside another function ◦ Returning control If nothing returned return; or, until reaches right brace If something returned return expression;
- 9. 1. Function prototype (3 parameters) 2. Input values 2.1 Call function 3. Function definition Program Output 1 /* Fig. 5.4: fig05_04.c 2 Finding the maximum of three integers */ 3 #include <stdio.h> 4 5 int maximum( int, int, int ); /* function prototype */ 6 7 int main() 8 { 9 int a, b, c; 10 11 printf( "Enter three integers: " ); 12 scanf( "%d%d%d", &a, &b, &c ); 13 printf( "Maximum is: %dn", maximum( a, b, c ) ); 14 15 return 0; 16 } 17 18 /* Function maximum definition */ 19 int maximum( int x, int y, int z ) 20 { 21 int max = x; 22 23 if ( y > max ) 24 max = y; 25 26 if ( z > max ) 27 max = z; 28 29 return max; 30 } Enter three integers: 22 85 17 Maximum is: 85
- 10. Function prototype ◦ Function name ◦ Parameters - what the function takes in ◦ Return type - data type function returns (default int) ◦ Used to validate functions ◦ Prototype only needed if function definition comes after use in program int maximum( int, int, int ); Takes in 3 ints Returns an int Promotion rules and conversions ◦ Converting to lower types can lead to errors
- 11. Header files ◦ contain function prototypes for library functions ◦ <stdlib.h> , <math.h> , etc ◦ Load with #include <filename> #include <math.h> Custom header files ◦ Create file with functions ◦ Save as filename.h ◦ Load in other files with #include "filename.h" ◦ Reuse functions
- 12. Used when invoking functions Call by value ◦ Copy of argument passed to function ◦ Changes in function do not effect original ◦ Use when function does not need to modify argument Avoids accidental changes Call by reference ◦ Passes original argument ◦ Changes in function effect original ◦ Only used with trusted functions For now, we focus on call by value
- 13. rand function ◦ Load <stdlib.h> ◦ Returns "random" number between 0 and RAND_MAX (at least 32767) i = rand(); ◦ Pseudorandom Preset sequence of "random" numbers Same sequence for every function call Scaling ◦ To get a random number between 1 and n 1 + ( rand() % n ) rand % n returns a number between 0 and n-1 Add 1 to make random number between 1 and n 1 + ( rand() % 6) // number between 1 and 6
- 14. srand function ◦ <stdlib.h> ◦ Takes an integer seed - jumps to location in "random" sequence srand( seed ); ◦ srand( time( NULL ) ); //load <time.h> time( NULL )- time program was compiled in seconds "randomizes" the seed
- 15. Recursive functions ◦ Function that calls itself ◦ Can only solve a base case ◦ Divides up problem into What it can do What it cannot do - resembles original problem Launches a new copy of itself (recursion step) Eventually base case gets solved ◦ Gets plugged in, works its way up and solves whole problem
- 16. Example: factorial: 5! = 5 * 4 * 3 * 2 * 1 Notice that 5! = 5 * 4! 4! = 4 * 3! ... ◦ Can compute factorials recursively ◦ Solve base case (1! = 0! = 1) then plug in 2! = 2 * 1! = 2 * 1 = 2; 3! = 3 * 2! = 3 * 2 = 6;
- 17. Fibonacci series: 0, 1, 1, 2, 3, 5, 8... ◦ Each number sum of the previous two fib(n) = fib(n-1) + fib(n-2) - recursive formula long fibonacci(long n) { if (n==0 || n==1) //base case return n; else return fibonacci(n-1) + fibonacci(n-2); }
- 18. f( 3 ) f( 1 )f( 2 ) f( 1 ) f( 0 ) return 1 return 1 return 0 return + +return
- 19. 1. Function prototype 1.1 Initialize variables 2. Input an integer 2.1 Call function fibonacci 2.2 Output results. 3. Define fibonacci recursively Program Output 1 /* Fig. 5.15: fig05_15.c 2 Recursive fibonacci function */ 3 #include <stdio.h> 4 5 long fibonacci( long ); 6 7 int main() 8 { 9 long result, number; 10 11 printf( "Enter an integer: " ); 12 scanf( "%ld", &number ); 13 result = fibonacci( number ); 14 printf( "Fibonacci( %ld ) = %ldn", number, result ); 15 return 0; 16 } 17 18 /* Recursive definition of function fibonacci */ 19 long fibonacci( long n ) 20 { 21 if ( n == 0 || n == 1 ) 22 return n; 23 else 24 return fibonacci( n - 1 ) + fibonacci( n - 2 ); 25 } Enter an integer: 0 Fibonacci(0) = 0 Enter an integer: 1 Fibonacci(1) = 1
- 20. Program Output Enter an integer: 2 Fibonacci(2) = 1 Enter an integer: 3 Fibonacci(3) = 2 Enter an integer: 4 Fibonacci(4) = 3 Enter an integer: 5 Fibonacci(5) = 5 Enter an integer: 6 Fibonacci(6) = 8 Enter an integer: 10 Fibonacci(10) = 55 Enter an integer: 20 Fibonacci(20) = 6765 Enter an integer: 30 Fibonacci(30) = 832040 Enter an integer: 35 Fibonacci(35) = 9227465
- 21. Repetition ◦ Iteration: explicit loop ◦ Recursion: repeated function calls Termination ◦ Iteration: loop condition fails ◦ Recursion: base case recognized Both can have infinite loops Balance ◦ Choice between performance (iteration) and good software engineering (recursion)