CS1100 Introduction to Programming. Week 8: Modular Programming Sorting Integer Arrays

Transcription

1 CS1100 Introduction to Programming Week 8: Modular Programming Sorting Integer Arrays

2 Goals for the week 1. Functions spread across files. How to compile individual files. Linking object files. 2. Sorting arrays. Selection sort. Insertion sort.

3 Functions across files 3 students collaborate on an assignment on Matrix operations. S 1: Input Output Read Matrix, Print Matrix. S 2: Operations Matrix Multiply, Matrix Add. S 3: Interfacing and Testing Main program, test cases.

4 Functions across files 3 students collaborate on an assignment on Matrix operations. S 1: Input Output Read Matrix, Print Matrix. S 2: Operations Matrix Multiply, Matrix Add. S 3: Interfacing and Testing Main program, test cases. All 3 students agree on the signatures of the functions.

5 Functions across files 3 students collaborate on an assignment on Matrix operations. S 1: Input Output Read Matrix, Print Matrix. S 2: Operations Matrix Multiply, Matrix Add. S 3: Interfacing and Testing Main program, test cases. All 3 students agree on the signatures of the functions. #include<stdio.h> #define N 10 void readmatrix(int rows, int cols, int Mat[][N]); void printmatrix(int rows, int cols, int Mat[][N]); void addmat(int rows, int cols, int Mat1[][N], int Mat2[][N], int output[][n]); void multmat(int rows, int cols, int Mat1[][N], int Mat2[][N], int output[][n]);

6 S 1 writes a file ip.c #include "header.h" void readmatrix(int rows, int cols, int Mat[][N]) { // code to read matrix. } void printmatrix(int rows, int cols, int Mat[][N]) { // code to print matrix. }

7 S 1 writes a file ip.c #include "header.h" void readmatrix(int rows, int cols, int Mat[][N]) { // code to read matrix. } void printmatrix(int rows, int cols, int Mat[][N]) { // code to print matrix. } Compiles the code using gcc -c ip.c Ensures that there are no syntax errors as far as ip.c is concerned.

8 S 2 writes a file ops.c #include "header.h" void addmat(int rows, int cols, int Mat1[][N], int Mat2[][N], int output[][n]) { // code to add two matrices. } void multmat(int rows, int cols, int Mat1[][N], int Mat2[][N], int output[][n]) { } // code to add multiply matrices. Compiles the code using gcc -c ops.c Ensures that there are no syntax errors as far as ops.c is concerned.

9 S 3 writes a file main.c #include "header.h" void main() { int mat1[n][n]; int mat2[n][n]; int mat3[n][n], mat4[n][n]; } readmatrix(n, N, mat1); readmatrix(n, N, mat2); addmat(n, N, mat1, mat2, mat3); multmat(n, N, mat1, mat2, mat4); Compiles the code using gcc -c main.c Ensures that there are no syntax errors as far as main.c is concerned.

10 Finally create an executable Finally compile the program as gcc main.c ip.c ops.c

11 Finally create an executable Finally compile the program as gcc main.c ip.c ops.c Alternatively gcc main.o ip.o ops.o

12 Finally create an executable Finally compile the program as gcc main.c ip.c ops.c Alternatively gcc main.o ip.o ops.o How is this different including the files directly in main as follows? #include ip.c #include ops.c

13 Finally create an executable Finally compile the program as gcc main.c ip.c ops.c Alternatively gcc main.o ip.o ops.o How is this different including the files directly in main as follows? #include ip.c #include ops.c Recommended: Single header file having all the declarations. Include header file in all your.c files.

14 Sorting Integer Arrays

15 Sort the array in decreasing order

16 Sort the array in decreasing order One possible way: Find max, place it at first location. Sort the array from second location to end.

17 Sort the array in decreasing order One possible way: Find max, place it at first location. Sort the array from second location to end. What functions would be useful to implement sorting?

18 Sort the array in decreasing order One possible way: Find max, place it at first location. Sort the array from second location to end. What functions would be useful to implement sorting? getmax element in the array starting from a particular location. swap two values in given array locations.

19 Selection sort

20 Selection sort

21 Selection sort

22 Selection sort Pseudo-code while (i n ) maxindex = findmaxindex(array, i, n); swap(array, maxindex, i);

23 Selection sort main-program 1 #i n c l u d e s o r t h e a d e r. h 2 3 main ( ) { 4 i n t a r r a y [N] = {15, 8, 3, 12, 30, 7, 9, 17, 32, 1 9 } ; 5 6 p r i n t A r r a y ( a r r a y ) ; 7 i n t i = 0 ; 8 f o r ( i =0; i <N; i ++) { 9 i n t j = f i n d M a xindex ( a r r a y, i, N 1) ; 10 i f ( j!= i ) { 11 swap ( a r r a y, i, j ) ; 12 } 13 } p r i n t A r r a y ( a r r a y ) ; 16 }

24 Selection sort helper functions 1 #i n c l u d e s o r t h e a d e r. h 2 / f u n c t i o n s f o r s e l e c t i o n s o r t / 3 i n t f i n d M a x I n d e x ( i n t a r r a y [N], i n t s t a r t, i n t end ) { 4 i n t max = a r r a y [ s t a r t ] ; 5 i n t maxindex = s t a r t ; 6 i n t i = s t a r t ; 7 w h i l e ( i <= end ) { 8 i f ( a r r a y [ i ] > max ) { 9 max = a r r a y [ i ] ; 10 maxindex = i ; 11 } 12 i ++; 13 } 14 r e t u r n maxindex ; 15 }

25 Selection sort helper functions 1 #i n c l u d e s o r t h e a d e r. h 2 / common p r i n t f u n c t i o n / 3 v o i d p r i n t A r r a y ( i n t a r r a y [N] ) { 4 i n t i ; 5 f o r ( i =0; i < N; i ++) { 6 p r i n t f ( %d\ t, a r r a y [ i ] ) ; 7 8 } 9 p r i n t f ( \n ) ; 10 } v o i d swap ( i n t a r r a y [N], i n t index1, i n t i n d e x 2 ) { 13 i n t temp = a r r a y [ i n d e x 1 ] ; 14 a r r a y [ i n d e x 1 ] = a r r a y [ i n d e x 2 ] ; 15 a r r a y [ i n d e x 2 ] = temp ; 16 }

26 Selection sort header file 1 #i n c l u d e <s t d i o. h> 2 3 #d e f i n e N 10 4 i n t f i n d M a x I n d e x ( i n t a r r a y [N], i n t s t a r t, i n t end ) ; 5 v o i d swap ( i n t a r r a y [N], i n t index1, i n t i n d e x 2 ) ;

27 Selection sort number of comparisons Which input do we consider? Do number of comparisons depend on the particular permutation of input? How does the method perform when the array is nearly sorted? Consider a worst-case input. Irrespective of whether the array is sorted or not, the method always needs n(n 1) 2 comparisons.

28 Insertion Sort

29 Insertion Sort

30 Insertion Sort

31 Insertion Sort

32 Insertion Sort Although final result is the same, intermediate steps are different from selection sort.

33 Insertion sort main program 1 #i n c l u d e s o r t h e a d e r. h 2 3 v o i d i n s e r t M a x ( i n t a r r a y [ ], i n t i n d e x ) ; 4 main ( ) { 5 i n t a r r a y [N] = {15, 8, 3, 12, 30, 7, 9, 17, 32, 1 9 } ; 6 7 p r i n t A r r a y ( a r r a y ) ; 8 i n t i ; 9 f o r ( i =1; i <N; i ++) { 10 i n s e r t M a x ( a r r a y, i ) ; 11 } p r i n t A r r a y ( a r r a y ) ; 14 }

34 Insertion sort number of comparisons 1 #i n c l u d e s o r t h e a d e r. h 2 3 v o i d i n s e r t M a x ( i n t a r r a y [ ], i n t i n d e x ) { 4 i n t temp = a r r a y [ i n d e x ] ; 5 i n t j = i n d e x ; 6 w h i l e ( j > 0 && a r r a y [ j 1] < temp ) { 7 a r r a y [ j ] = a r r a y [ j 1]; 8 j ; 9 } 10 a r r a y [ j ] = temp ; 11 } What happens if array[index-1] array[index]? InsertMax does a single comparison and returns to main. Thus if array is sorted, each time insertmax returns after a single comparison. Number of comparisons n for best case scenario.

35 Merging two sorted arrays Given two sorted arrays each of size N, create another array of size 2N which contains the merge of the two arrays. void merge(int A[], int B[], int C[]);