fundamental of programming...

Lecturer: Mahdi Soltani

Sharif University of TechnologyDepartment of Computer Engineering

Fundamental of Programming (C)

Lecture 7

Array typical problems, Search, Sorting

Array typical problems, Search, Sorting – Lecture 8

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Outline• Array typical problems

• Search

• Sorting

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Find Maximum• Find maximum value in data array

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Find Average

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Number of elements greater than average

• After finding the average as shown in previous slide, use the following code

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Find pair sum Find sum of every pair in data and write into pair array

data[0]=5

data[1]=7

data[2]=15

data[3]=5

…

…

data[98]=3

data[99]=12

pair[0]=12

pair[1]=20

…

pair[49]=15

}}

}

.

.

.

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solution

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Randomly re-shuffle numbers 30 timesdata[0]=5

data[1]=7

data[2]=15

data[3]=5

…

…

data[98]=3

data[99]=12

.

.

.

data[0]=12

data[1]=7

data[2]=5

data[3]=15

…

…

data[98]=3

data[99]=5

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solution

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Reverse an array

6 3 1 9 7 2

0 21 3 4 5

2 7 9 1 3 6

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Reverse an Array

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Print sum of top-bottom pairsA[0]=3

A[1]=6

…

A[49]=5

A[50]=3

A[98]=4

A[99]=5

+ + +….

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Group avg• Suppose we have a sorted array of hundred

grades.

• We want to find the average oftop ten, second top ten students etc.

}Grade[0]

Grade[1]

….

Grade[9]

Grade[10]

…

Grade[19]

Grade[20]

…

Grade[90]

….

Grade[99]

}

}

Array typical problems, Search, Sorting – Lecture 8

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#include <stdio.h>

#define SIZE 20

void main(void){

int number[SIZE];

double average;

int sum, large_size, small_size, i;

}

sum = large_size = small_size = 0;

for(i = 0; i < SIZE; i++){

int tmp;

scanf("%d", &tmp);

number[i] = tmp;

sum += number[i];}

average

for(i =

= (1.0 * sum) / SIZE;

0; i < SIZE; i++)

= %d\n", small_size, large_size);

برنامه‌ای‌بنویسید‌که‌بیست‌عدد‌از‌ورودیتر‌از‌دریافت‌کند‌و‌تعداد‌اعداد‌کوچکتر‌و‌بزرگ

.میانگین‌را‌چاپ‌کند

if(number[i] >= average)

large_size++;

else

small_size++;

printf("average = %f\n", average);

printf("Small Size = %d, Larg Size

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Array Elements in Functions

int number[20];

number[i] is an integer

variable

Array element can be used for

call by value input

Array element can be use for

output

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Arrays in Functions

Array cannot be used as output type of

function

int [] f(int x, int y); //compile error

Arrays can be used in input list of functions

Arrays are not passed by Call By Value

Arrays are passed by Call By Reference

If we change array elements in a function

The element is changed in the caller function

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Arrays in FunctionsSize of array could be different from the real oneBut dangerous things would happen

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Exercise

a[0]=3

a[1]=5

c=? 8

b=

n=2

i=0 1 2

sum=0 3 8

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Exercise

a[0]=3 20

a[1]=5

c=? 8

b=

n=2

i=0 1 2

sum=0 3 8

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و‌گیرد‌میرا‌10به‌طول‌رایه‌آتابعی‌که‌یک‌مقداردهی‌9تا‌0اعضای‌آن‌را‌با‌اعداد‌

.میکند

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Array Size in Functions If array is an input parameter of

a function

It cannot find out the size of the

array

Array size should be passed

from caller function to called

function

Using definitions

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Array Size in Functions (cont’d) If array is declared in a function It knows the size of the array

It can find out the size of the array using sizeof

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ت‌و‌تابعی‌بنویسید‌که‌یک‌آرایه‌را‌دریاف.محل‌بزرگترین‌عنصر‌آن‌را‌بازگرداند

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Search function• Liner search

• Binary search

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Unordered list – linear search

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Ordered list – linear search

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Binary Search

Key = 76

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Binary Search

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Sort function• Selection Sort

• Bubble Sort

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Selection Sort

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Implementation

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Bubble sort • Bubble sort Several passes through the array

– Successive pairs of elements are compared • If increasing order (or identical ), no change

• If decreasing order, elements exchanged

– Repeat

34

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Bubble Sort

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Implementation

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Merge two sorted array• Assume we have A and B arrays containing

sorted numbers

• For example– A = { 3, 5, 7, 9, 12}

– B = {4, 5, 10}

• Merge these two arrays as a single sorted array C, for example– C = {3, 4, 5, 5, 7, 9, 10, 12}

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Solution

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Intersection Set • Suppose we have two sets (groups) represented by A

and B

• E.g., A is the set of students taking Math,

B is the set of students taking Science.

• Find set C, the intersection of A and B, i.e., students taking both Math and Science

For each element ID in A

Search that ID in B

if found, put ID into C 3 6 9 17 2

458

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Solution

6 3 1 9 7 2

4 2 5 6 1 8

6 1 2

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Multidimensional Arrays in Functions

Can be used as input of functionsAll dimensions except the first one must be given

void func(int a[10][20][5]);

Input is a 10x20x5 integer matrix

void func(int a[][20][30], int size); void func(int

size1, int size2, int

a[size1][size2]);

Input is a matrix of integers that both rows and columns are

variable

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Multidimensional Arrays in Functions

The first subscript therefore only indicates the amount of storage that is needed when the array is declared

Others are required because the computer needs to know how far along to increment the pointer for each "row"

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#define

}

SIZE 5

void swap(int a[SIZE][SIZE], int i, int j){

int tmp;

tmp = a[i][j];

a[i][j]

a[j][i]

= a[j][i];

= tmp;

}

void transpose(int a[][SIZE]){

for(i =

int i, j;

0; i < SIZE; i++)

for(j = i; j < SIZE; j++)

swap(a, i, j);

ماتريس ترانهاده محاسبه

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2-Dim Arrays as Arguments to Functions

void print_m(int m[][4], int r, int c)

{

int i,j;

for (i=0; i < r; i++) {

for (j=0; j < c; j++)

printf("%.5d ",m[i][j]);

printf("\n");

}

printf("\n");

return;

}

int i, j, matrix[3][4];

for (i=0; i<3; i++)

for (j=0; j<4; j++)

matrix[i][j] = i;

print_m(matrix, 3, 4);

void print_m(int m[3][4], int r, int c)

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Matrix sum• Compute the addition of two matrices

3 0 33

0 6 6 3

2 0 4 4

0 1 2 3

0

1

2

0 1 20

-1 2 4 3

0 -1 3 1

0

1

2

0 1 2 3

+

3 -1 13

1 4 2 0

2 1 1 3

0

1

2

0 1 2 3

=

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solution

int matrix1[3][4],

matrix2[3][4],

sum[3][4];

// initialize matrix1 and matrix2

for (i=0; i<3; i++)

for (j=0; j<4; j++)

sum[i][j]=

matrix1[i][j]+matrix2[i][j];

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Exchange Two Rows

4 6 2

0 5 3

0 8 1

2 1 4

4 6 2

2 1 4

0 8 1

0 5 3

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Matrix multiplicationdouble a[3][2], b[2][4], c[3][4];

• Find c = a * b;

x =

3*2 + 4*4=22 3*3 + 4*5=29

2 3 7 1

4 5 6 8

3 4

5 2

1 6

22 29 45 35

18 40 47 21

26 33 43 49

5*2 + 2*4=18

3*7 + 4*6=45 3*1 + 4*8=35

5*3 + 2*5=40 5*7 + 2*6=47 5*1 + 2*8=21

1*2 + 6*4=26 1*3 + 6*5=33 1*7 + 6*6=43 1*1 + 6*8=49

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Matrix Multiplication

x =2 3 7 1

4 5 6 8

3 4

5 2

1 6

22 29 45 35

18 40 47 21

26 33 43 49

i=0

i

jj

3 42

4x

j=0

k

k =

c[i][j] =

a[i][k=0]*b[k=0][j] +

a[i][k=1]*b[k=1][j]

0 1 2 3

i

0

1

2

0 1 2 3

0

1

2

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Matrix Multiplication cont’d#define N 3

#define M 2

#define L 4

void matrix_mul(a[N][M], int b[M][L], int c[N][L])

{

int i, j, k;

for(i=0; i < N; i++) {

for(j=0; j < L; j++) {

c[i][j] = 0;

for(k=0; k < M; k++) {

c[i][j] = c[i][j] + a[i][k] * b[k][j];

}

}

}

return;

}