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CSCI 230

Department of Computer and Information Science, School of Science, IUPUI. CSCI 230. Functions. Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu. Introduction. Functions Category Programmers Duration Size of Code Trivial 1 1-2 weeks < 500 lines (student homework)

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CSCI 230

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  1. Department of Computer and Information Science,School of Science, IUPUI CSCI 230 Functions Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu

  2. Introduction • Functions Category Programmers Duration Size of Code Trivial 1 1-2 weeks < 500 lines (student homework) Small 1 - 3 Few Weeks 500 -2000 lines (term projects) Medium 2 - 5 Few Months 2000 -10000 (research project) Large 5-25 1 - 3 years 10,000 - 100,000 (current application) Very Large 25-100 3 - 5 years 100,000 - 1M (real-time operations) Extremely Large > 100 > 5 years >1M (advanced military work) • Divide and conquer • Large programs cannot be monolithic • Construct a program from smaller pieces or components. These smaller pieces are called modules • Each piece is more manageable than the original program

  3. Program Modules in C • Functions • Modules in C • Programs combine user-defined functions with library functions • C standard library has a wide variety of functions • Math function, I/O, string function, such as printf(), scanf() • Function calls • Invoking functions • Provide function name and arguments (data) • Function performs operations or manipulations • Function returns results • Write function once and call it many times • Function call analogy: • Boss asks worker to complete task • Worker gets information, does task, returns result • Information hiding: boss does not know details

  4. Math Library Functions • 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

  5. Functions • 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 of functions • Divide and conquer • Manageable program development • Software reusability • Use existing functions as building blocks for new programs • Abstraction - hide internal details (library functions) • Avoid code repetition

  6. Function Definitions • 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– indicates that the function returns nothing • An unspecified return-value-type is always assumed by the compiler to be int • Parameter-list: comma separated list, declares parameters • A type must be listed explicitly for each parameter, unless the parameter is of type int • Declarations and statements: function body (block) • Variables can be declared inside blocks (can be nested) • Functions can not be defined inside other functions • Returning control • If nothing returned • return; • or, until reaches right brace • If something returned • returnexpression;

  7. 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: %d\n", maximum( a, b, c ) ); 14 15 return 0; 16 } 17 18 /* Function maximum definition */ 19 int maximum( int x, int y, int z ) Function prototype (3 parameters) 2. Input values 3. Call function Function definition 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 } Program Output Enter three integers: 22 85 17 Maximum is: 85

  8. Function Prototypes • 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 • The function with the prototype int maximum( int, int, int ); • Takes in 3 ints • Returns an int • Promotion rules and conversions • Converting to lower types can lead to errors

  9. Examples float plus1(float x,y) { float sum; sum = x + y; return sum; } • plus2(int x,y) • { • int sum; • sum = x + y; • return sum; • } • The minimal function is dummy(){} • Again, the return statement can be • return expression; Example:return a*a; • return (expression); Example:return ((a > 0)? a, -a)); • return; • In conclusion, to call a function from another function, you should: • Declare the type of the called function, if not a int function • Use format of function_name(actual parameters)

  10. Old style More Examples: Example 1:… float mySquare(float); main() { float y; printf(%f\n, mySquare(5.0)); } float mySquare(float x) { return x*x; } • float mySquare(x) • float x; • { • return x*x; • } Example 2: /* calculate the sum from 1+2+…+n */ int sum(int n) { int i, sum = 0; for (i=1; i<=n; i++) sum += i; return(sum); } main() { int j,n; printf(“input value n: “); scanf(“%d”,&n); for (j=1; j<=n; j++) printf(“sum from 1 to %d is %d\n”,j,sum(j)); } How can we have both a function and a variable named “sum?”

  11. Header Files • 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. Calling Functions:Call by Value and Call by Reference • 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 Example: addone(int); main () { int i = 5, j; j=addone(i); printf(“%d %d\n”,i, j); 5 6 } addone(int x) { return ++x; }

  13. Calling Functions:Call by Value and Call by Reference • Call by reference (Passing Address) • This is not actually call by reference, although some books called this ‘call-by-reference’ • Passes original argument • Changes in function effect original using & operator to pass address • Only used with trusted functions Example: addone(int); main () { int i = 5, j; j=addone(&i); printf(“%d %d\n”,i, j); 6 6 } addone(int *x) { return ++(*x); } • For now, we focus on call by value

  14. Random Number Generation • 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

  15. Random Number Generation • srand function • <stdlib.h> • Takes an integer seed and jumps to that location in its "random" sequence srand( seed ); • srand( time( NULL ) ); //load <time.h> • time( NULL ) • Returns the time at which the program was compiled in seconds • “Randomizes" the seed

  16. 1 /* Fig. 5.9: fig05_09.c 2 Randomizing die-rolling program */ 3 #include <stdlib.h> 4 #include <stdio.h> 5 6 int main() 7 { 8 int i; 9 unsigned seed; 10 11 printf( "Enter seed: " ); 12 scanf( "%u", &seed ); 13 srand( seed ); 14 15 for ( i = 1; i <= 10; i++ ) { 16 printf( "%10d", 1 + ( rand() % 6 ) ); 17 18 if ( i % 5 == 0 ) 19 printf( "\n" ); 20 } 21 22 return 0; 23 } 1. Initialize seed 2. Input value for seed 3. Use srand to change random sequence 4. Define Loop 5. Generate and output random numbers Program Output Enter seed: 67 6 1 4 6 2 1 6 1 6 4 Enter seed: 867 2 4 6 1 6 1 1 3 6 2 Enter seed: 67 6 1 4 6 2 1 6 1 6 4

  17. Example: A Game of Chance • Craps simulator • Rules • Roll two dice • 7 or 11 on first throw, player wins • 2, 3, or 12 on first throw, player loses • 4, 5, 6, 8, 9, 10 - value becomes player's "point" • Player must roll his point before rolling 7 to win Example: 11 12 10, 6, 11, 6, 10 4, 5, 9, 10, 9, 3, 7

  18. 1 /* Fig. 5.10: fig05_10.c 2 Craps */ 3 #include <stdio.h> 4 #include <stdlib.h> 5 #include <time.h> 6 7 int rollDice( void ); 8 9 int main() 10 { 11 int gameStatus, sum, myPoint; 12 13 srand( time( NULL ) ); 14 sum = rollDice(); /* first roll of the dice */ 15 16 switch ( sum ) { 17 case 7: case 11: /* win on first roll */ 18 gameStatus = 1; 19 break; 20 case 2: case 3: case 12: /* lose on first roll */ 21 gameStatus = 2; 22 break; 23 default: /* remember point */ 24 gameStatus = 0; 25 myPoint = sum; 26 printf( "Point is %d\n", myPoint ); 27 break; 28 } 29 30 while ( gameStatus == 0 ) { /* keep rolling */ 31 sum = rollDice(); 32 1. rollDice prototype 2. Initialize variables 3. Seed srand 4. Define switch statement for win/loss/continue 5. Loop

  19. 33 if ( sum == myPoint ) /* win by making point */ 34 gameStatus = 1; 35 else 36 if ( sum == 7 ) /* lose by rolling 7 */ 37 gameStatus = 2; 38 } 39 40 if ( gameStatus == 1 ) 41 printf( "Player wins\n" ); 42 else 43 printf( "Player loses\n" ); 44 45 return 0; 46 } 47 48 int rollDice( void ) 49 { 50 int die1, die2, workSum; 51 52 die1 = 1 + ( rand() % 6 ); 53 die2 = 1 + ( rand() % 6 ); 54 workSum = die1 + die2; 55 printf( "Player rolled %d + %d = %d\n", die1, die2, workSum ); 56 return workSum; 57 } Program Output Player rolled 6 + 5 = 11 Player wins Player rolled 6 + 6 = 12 Player loses Player rolled 4 + 6 = 10 Point is 10 Player rolled 2 + 4 = 6 Player rolled 6 + 5 = 11 Player rolled 3 + 3 = 6 Player rolled 6 + 4 = 10 Player wins 6. Print win/loss Player rolled 1 + 3 = 4 Point is 4 Player rolled 1 + 4 = 5 Player rolled 5 + 4 = 9 Player rolled 4 + 6 = 10 Player rolled 6 + 3 = 9 Player rolled 1 + 2 = 3 Player rolled 5 + 2 = 7 Player loses

  20. Storage Classes • Storage class specifiers • Storage duration – how long an object exists in memory • Scope – where object can be referenced in program • Linkage – specifies the files in which an identifier is known (more in Chapter 14) • Automatic storage • Object created and destroyed within its block • auto: default for local variables and usually stored in Stack. auto double x, y; • register: tries to put variable into high-speed registers • Can only be used for automatic variables register int counter = 1; Example: f(register int c, register int n) { register int i; … }

  21. Storage Classes • Static storage • Variables exist for entire program execution • Default value of zero • static: local variables defined in functions. • Keep value after function ends • Only known in their own function; Example: static char buf[128]; static int bufp=0; getch1() { … }

  22. 1 /* Fig. 5.12: fig05_12.c 2 A scoping example */ 3 #include <stdio.h> 4 5 void a( void ); /* function prototype */ 6 void b( void ); /* function prototype */ 7 void c( void ); /* function prototype */ 8 9 int x = 1; /* global variable */ 10 11 int main() 12 { 13 int x = 5; /* local variable to main */ 14 15 printf("local x in outer scope of main is %d\n", x ); 16 17 { /* start new scope */ 18 int x = 7; 19 20 printf( "local x in inner scope of main is %d\n", x ); 21 } /* end new scope */ 22 23 printf( "local x in outer scope of main is %d\n", x ); 24 25 a(); /* a has automatic local x */ 26 b(); /* b has static local x */ 27 c(); /* c uses global x */ 28 a(); /* a reinitializes automatic local x */ 29 b(); /* static local x retains its previous value */ 30 c(); /* global x also retains its value */ 1. Function prototypes 2. Initialize global variable 3. Initialize local variable 4. Initialize local variable in block 5. Call functions 6. Output results

  23. 31 32 printf( "local x in main is %d\n", x ); 33 return 0; 34 } 35 36 void a( void ) 37 { 38 int x = 25; /* initialized each time a is called */ 39 40 printf( "\nlocal x in a is %d after entering a\n", x ); 41 ++x; 42 printf( "local x in a is %d before exiting a\n", x ); 43 } 44 45 void b( void ) 46 { 47 staticint x = 50; /* static initialization only */ 48 /* first time b is called */ 49 printf( "\nlocal static x is %d on entering b\n", x ); 50 ++x; 51 printf( "local static x is %d on exiting b\n", x ); 52 } 53 54 void c( void ) 55 { 56 printf( "\nglobal x is %d on entering c\n", x ); 57 x *= 10; 58 printf( "global x is %d on exiting c\n", x ); 59 } Program Output local x in outer scope of main is 5 local x in inner scope of main is 7 local x in outer scope of main is 5 local x in a is 25 after entering a local x in a is 26 before exiting a local static x is 50 on entering b local static x is 51 on exiting b global x is 1 on entering c global x is 10 on exiting c local x in a is 25 after entering a local x in a is 26 before exiting a local static x is 51 on entering b local static x is 52 on exiting b global x is 10 on entering c global x is 100 on exiting c local x in main is 5 7. Function definitions

  24. Scope Rules • File scope • Identifier defined outside function, known in all functions • Used for global variables, function definitions, function prototypes • Function scope • Can only be referenced inside a function body • Used only for labels (start:, case: , etc.) • Block scope • Identifier declared inside a block • Block scope begins at declaration, ends at right brace • Used for variables, function parameters (local variables of function) • Outer blocks "hidden" from inner blocks if there is a variable with the same name in the inner block • Function prototype scope • Used for identifiers in parameter list

  25. extern Storage Class Specifier • If an external variable is to be referred to before it is defined, or if it is defined in a different source file from the one where it is being used, then extern declaration is necessary • extern: default for global variables and functions • Known in any function • Usage: if large number of variables must be shared among functions, external variables are more convenient and efficient than long argument list Example: In file 1: … int sp=0; double val[12]; … In file 2; extern int sp; extern double val[]; int push(f) double f; { … } …

  26. Recursion • Recursive functions • A function can invoke any other function; “ Can a function invoke itself?” • Functions that call themselves either directly or indirectly (through another function) is called a recursive function. • A recursive function is called to solve a problem. The function actually knows how to solve the simplest case(s) - “base case” and simply returns a result. • If a function is called with a complex case, it divides the problem into two conceptual places: • What it can do • What it cannot do: 1. must resembles original problem but slightly simplified 2. function will call itself (recursion step or recursive call) to solve slightly simplified problem 3. process continues until the last recursive call is with the base case 4. that call returns the result of the base case 5. return to previous calling function 6. finally reaches main.c and goes back to 2. • Eventually base case gets solved • Gets plugged in, works its way up and solves whole problem

  27. 625 x4 54 x4 51 x1 * * 53 x3 x3 125 51 x1 * * 52 x2 x2 x2 25 51 x1 * * 51 x1 x1 x1 5 5 x1 Recursion (cont.) Example: Compute x y for x > 0 & y > 0 x y = x * x * x * … * x base case: x1= x  x y = x1 * ( x * x * … * x) = x1 * ( x1 * ( x * x * … * x )) = x1 * ( x1 * ( x1 * ( x * x * … * x ))) ex. x 4 = x1 * ( x1 * ( x1 * ( x1 ))) • Fundamental rules of recursion 1.) Base cases 2.) Making progress through recursion 3.) Design rule: assuming all recursive call work (details hidden) 4.) Compound interest rule: do not duplicate recursive calls • Always specify the base case; otherwise, indefinite recursive will occur and cause “stack-overflow” error. y times

  28. x_pow_y(5,4) x_pow_y(5,3) x_pow_y(5,2) x_pow_y(5,1) … x=5; y=4; x_pow_y(5,4); … is (4==1)?  no … is (3==1)?  no … is (2==1)?  no … is (1==1)?  yes  return 5 625 125 25 5 main Base Case Recursion vs. Iteration Recursion: #include <stdio.h> int x_pow_y(int, int); main() { printf(“enter x and y: \n”); scanf(“%d, %d”, x, y); z = x_pow_y(x,y); printf(“z: %d\n”, z); } x_pow_y(int a, int b) { if (b==1) return a; else return (a * x_pow_y(a, b-1)) } • Iteration: • x_pow_y = 1; • for (i = y; i >=1; i--) • x_pow_y*=x; • If x = 5, y = 4 • x_pow_y = 1, x = 5, y = 4, i = 4; • 1.) x_pow_y = 5*1 = 5, i = 3; • 2.) x_pow_y = 5*5 = 25, i = 2; • 3.) x_pow_y = 25*5 = 125, i = 1; • 4.) x_pow_y = 125*5 = 625, i = 0;

  29. Example Using Recursion: Factorial Example: factorials: 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; long factorial(int n) { if (n <= 1) return 1; else return n * factorial(n-1); }

  30. f( 3 ) return f( 2 ) + f( 1 ) return f( 1 ) f( 0 ) return 1 + return 1 return 1 Example Using Recursion: The Fibonacci Series Example: Fibonacci series: Fk = Fk-1 + Fk-2,F0 = 1, F1 = 1 ex: 1, 1, 2, 3, 5, 8… • Each number is the sum of the previous two • Can be solved recursively: fib( n ) = fib( n - 1 ) + fib( n – 2 ) • Set of recursive calls to function fibonacci • Code for the fibaonacci function long fibonacci(long n) { if (n <= 1) return 1; else; return fibonacci(n-1)+ fibonacci(n-2); }

  31. 1 /* Fig. 5.15: fig05_15.c Enter an integer: 0 Fibonacci(0) = 0 Enter an integer: 1 Fibonacci(1) = 1 2 Recursive fibonacci function */ 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 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 ) = %ld\n", 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 } 1. Function prototype 2 Initialize variables 3. Input an integer 4. Call function fibonacci 5. Output results. 6. Define fibonacci recursively

  32. Recursion vs. Iteration • Both are based on the control structures • Repetition (Iteration): explicitly uses repetition (loop). • Selection (Recursion): implicitly use repetition by successive function calls • Both involve termination • Iteration: loop condition fails • Recursion: base case recognized • Both can lead indefinite loops • Loop termination is not met • Base case is not reached • Balance • Choice between performance (iteration) and good software engineering (recursion)

  33. Recursion vs. Iteration • Any problem that can be solved recursively can also be solved iteratively. A recursion is chosen in preference over iteration while the recursive approach more naturally mirrors the problem and results in a program that easier to understand and debug. • Recursion has an overhead of repeated function calls which is expensive in terms of processor time ad memory usage • Another reason to choose recursion is that an iterative solution may not apparent. • If used properly a recursive approach can lead to smaller code size and elegant program (at the case of performance penalty.)

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