Arrays

Chap 8

2

Without Array

• If you want to create Lottery winning numbers…– You need 7 variables (6 for winning numbers

and 1 for the special number)– Every time you choose a winning number, you

have to check if it has been chosen.

– Um… Program becomes ugly!

3

Without Array

• Same things happen when you want to…– Store grades of the whole class– Store data of members– …

• We need to define a group of variables with the same meaning ALL AT ONCE!

4

The Idea of Using an Array

a1 a2 a3 a4 a5 a6a[ ]

a[0] a[1] a[2] a[3] a[4] a[5]

5

Array ( 陣列 )• To define a group of variables with the sa

me meaning at once• Syntax to define an array:dataType arrayName[arraySize];

Ex: int students[6]; // 班級學生人數

6 rooms for this array

students

Each element in this array is of type int

32 35 31 34 32 33

6 classes

6

Accessing Array ( 存取陣列資料 )

Its subscript starts from 0. Referring to an element

Ex: students[4]The element 4 of the array studentsThe 5th element of the array students

students

students[0]students[1]

students[2]

students[3]

students[4]

students[5]

7

怪 怪 怪 怪 怪

Accessing Array ( 存取陣列資料 )

Every students[i] is of type int• students[0]=32; // assign value• students[2]=students[0]-1;// read value

怪students

students[0]students[1]

students[2]

students[3]

students[4]

students[5]

32 31

8

怪 怪 怪 怪 怪

Accessing Array ( 存取陣列資料 )

• printf("%d", students[2]);// It prints out 31

• scanf("%d", &(students[5]));// If 33 is given

• students[5]++;

怪students

students[0]students[1]

students[2]

students[3]

students[4]

students[5]

32 31 3334

9

Typical Array Operations

• Idioms of typical operations on an array a of length N:

for (i = 0; i < N; i++) a[i] = 0; /* clears a */

for (i = 0; i < N; i++) /* reads data */ scanf("%d", &a[i]); /* into a */

for (i = 0; i < N; i++) sum += a[i]; /* sums the elements of a */

10

Example

• Define an integer array of size 100 andset every element as 0.

• Set the value of each element as its subscript.

• Set the value of each element as the square of its subscript.

11

Example

• Define a 70-element integer array score.

• Input the scores of 70 students.

• Print out the scores of 70 students.

12

Subscripts

• A subscript can be an integer,or an integer expression.– students[ 3 ]– students[ i ]– students[ i+1 ]– students[ i+j ]– students[ myFunc( ) ]– students[ sorted[ i ] ]

13

Array Initialization

• You can give initial values when defining.int days[6]={31,28,31,30,31,30};

• If no sufficient values are given, the values of rest elements will be set to be 0.int days[6]={31,28};// initial value of days is {31,28,0,0,0,0}

• So, if you want an all-0 array:int days[6]={0};// initial value of days is {0,0,0,0,0,0}

14

Array Initialization

• If the array size is not given, its size will be the number of elements in the initializer list.

int days[]={31,28,31,30,31,30};will create a 6-element array.

15

Program: Checking a Number for Repeated Digits• After the user enters a number, the

program prints either "Repeated digit" or "No repeated digit":Enter a number: 28212Repeated digit

• The number 28212 has a repeated digit (2); a number like 9357 doesn’t.

16

repdigit.cint main(){ int digit_seen[10] = {0}; int n; int digit; printf("Enter a number: "); scanf("%d", &n); while (n > 0) { digit = n % 10; if (digit_seen[digit]) break; digit_seen[digit] = 1; n /= 10; } if (n > 0) printf("Repeated digit\n"); else printf("No repeated digit\n"); return 0;}

17

repdigit.cint main(void){ bool digit_seen[10] = {false}; long n; int digit; printf("Enter a number: "); scanf("%ld", &n); while (n > 0) { digit = n % 10; if (digit_seen[digit]) break; digit_seen[digit] = true; n /= 10; } if (n > 0) printf("Repeated digit\n"); else printf("No repeated digit\n"); return 0;}

18

Example

• Check if a date month 月 day 日 is valid.

int month;int days[12]={31,28,31,30,31,30,31,31,30,31,30,31};printf(" 請以 月 / 日 的格式輸入日期： ");scanf("%d/%d", &month, &day);if ( month < 1 || month > 12 ) printf(" 不合法的日期。 \n");else if ( day < 1 || day > days[month-1] ) printf(" 不合法的日期。 \n");

month ??

day ??

19

Operator sizeof()• sizeof(z) returns the memory size (in byte

s) required for this variable z.– int a; char b;– sizeof(a) → 4– sizeof(b) → 1

• Or, of data types– sizeof(unsigned short int) → 2– sizeof(bool) → 1

20

Operator sizeof()• So, for an array a, sizeof(a) returns the me

mory size (in bytes) required for this array a.int a[10]; sizeof(a) → 40char b[10]; sizeof(b) → 10

• sizeof(arrayName)/sizeof(array_element0):gives the number of elements in an arrayint a[10];sizeof(a)/sizeof(a[0]) → 10

21

Array Size vs. Number of Data

Ex: int scores[100]; // 學生成績• It defines a 100-element array in advance t

o store scores of students.

• But in fact, the actual number of students is still unknown.

• You need to define an integer variable to store the number of students.

22

Practice

• Ask the user to input the scores (-1 for termination) and save them in an array.– Print out all the scores.

23

More about Array Index

• Example: to calculate the statistics of students' scores– 90~99 ### 人– 80~89 ### 人– 70~79 ### 人– 60~69 ### 人– …

• Given score[i] → number[??]++;

• int score[100];• int number[10];

number[0]: 0~9 人數number[1]: 10~19 人數number[2]: 20~29 人數…

number[score[i]/10]++;

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More about Array Index

• Example: to calculate the statistics of students' scores– 91~100 ### 人– 81~90 ### 人– 71~80 ### 人– 61~70 ### 人– …

• Given score[i] → number[??]++;

• int score[100];• int number[10];

number[0]: 1~10 人數number[1]: 11~20 人數number[2]: 21~30 人數…

number[(score[i]-1)/10]++;

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Practice in Array Index

• 計算成績分布– 0~14 ### 人– 15~29 ### 人– 30~44 ### 人– 45~59 ### 人– …

• score[i]: ?? → number[??]++;

• int score[100];

• int number[10]; – number[0]: 0~14 人數– number[1]: 15~29 人數– …

26

Practice

• Calculate the statistics of students' scores and graph it with histograms.範圍 人數 圖表90~99 5 *****80~89 12 ************70~79 18 ******************60~69 9 *********…

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0 1 … 38 390 …

1 …

2 …

3 …

4 …

5 …

2-Dimensional Array

dataType arrayName[size1][size2];Ex. int grade[6][40]; // 各班級所有學生的成績

grade

grade[3][1]=73;grade[0][38]=98;

代表班級代表學生座號

73

98 →→→→row

↓ ↓ ↓ ↓ ↓column

28

N-Dimensional Array

dataType arrayName[size1][size2]…[sizeN];

Ex. int grade[6][3][40]; // 成績 [班級 ][科目 ][座號 ]

• To save the English score of the 23th student in the 1st class, you should do

scanf("%d",&score[ 0 ][ 1 ][22]);

代表班級

代表科目 { 國文 , 英文 , 數學 }

代表學生座號

? ? ?

29

Practice

• 印出所有學生各科成績：

1 年 1 班 1 號同學國文 98 分1 年 1 班 1 號同學英文 95 分1 年 1 班 1 號同學數學 92 分1 年 1 班 2 號同學國文 89 分1 年 1 班 2 號同學英文 78 分…

2 年 3 班 5 號同學數學 97 分

30

Practice

• Calculate the average Math scores among the 1st year students.

• Calculate the mean of total scores in 二年一班 .

• Calculate the average English scores of each 3rd-year class.

31

Ex: Prepare an Identity Matrix

• A pair of nested for loops is perfect:

#define N 10 double ident[N][N];int row, col; for (row = 0; row < N; row++) for (col = 0; col < N; col++) if (row == col) ident[row][col] = 1.0; else ident[row][col] = 0.0;

100

010

001

32

Array Initialization

• Example:int m[5][9] = {{1, 1, 1, 1, 1, 0, 1, 1, 1}, {0, 1, 0, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 1, 0, 0, 1, 0}, {1, 1, 0, 1, 0, 0, 0, 1, 0}, {1, 1, 0, 1, 0, 0, 1, 1, 1}};

33

Array Initialization

• If an initializer isn’t large enough to fill a multidimensional array, the remaining elements are given the value 0.

int m[5][9] = {{1, 1, 1, 1, 1, 0, 1, 1, 1}, {0, 1, 0, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 1, 0, 0, 1, 0}};// the last two rows will contain zeros

34

Array Initialization

• If an initializer isn’t large enough to fill a multidimensional array, the remaining elements are given the value 0.

int m[5][9] = {{1, 1, 1, 1, 1, 0, 1, 1, 1}, {0, 1, 0, 1, 0, 1, 0, 1}, {0, 1, 0, 1, 1, 0, 0, 1}, {1, 1, 0, 1, 0, 0, 0, 1}, {1, 1, 0, 1, 0, 0, 1, 1, 1}};// m[1][8], m[2][8], and m[3][8] will contain zeros

35

Array Initialization

• We can even omit the inner braces :int m[5][9] = {1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1};

– It is risky, since an extra element (or even worse, a missing element) will affect the rest of the initializer

36

Example

• Chinese numbers

37

Array of Strings

• char * subject[3]={ " 國文 ", " 英文 ", " 數學 "};

• printf("%s", subject[1]);

• PS. More about strings will be introduced later in Chapter 8.

38

Random Number Generator

To get a random number ( 亂數 ):• Add #include <stdlib.h>• Add #include <time.h>• Add a line in the beginning of main(): srand( (unsigned)time(NULL) );

39

Random Number Generator

To get a random number ( 亂數 ):• Use rand() to get a random number.

– The value is between 0 and RAND_MAX.– For a random number between 0~7, use rand()%8

– For a random number between 1~8, use rand()%8+1 , and so on.

40

Practice

• Write a program to simulate rolling a dice for 1000 times. Print out how many times each value has occurred.

1 occurs 169 times2 occurs 143 times3 occurs 179 times4 occurs 167 times5 occurs 180 times6 occurs 162 times