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 int32 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]

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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

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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

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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 */

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Example• Define an integer array of size 100 and

set every element as 0.• Set the value of each element as its subsc

ript.• Set the value of each element as the squa

re of its subscript.

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Example• Define a 70-element integer array score.• Input the scores of 70 students.• Print out the scores of 70 students.

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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 ] ]

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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}

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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.

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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.

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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;}

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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;}

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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 ??

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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

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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

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Array Size vs. Number of DataEx: 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 i

s still unknown.• You need to define an integer variable to s

tore the number of students.

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Practice• Ask the user to input the scores (-1 for

termination) and save them in an array.– Print out all the scores.

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More about Array Index• Example: to calculate the statistics of stud

ents' 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 stud

ents' 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– …

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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 ArraydataType 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

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N-Dimensional ArraydataType 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 doscanf("%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

? ? ?

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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

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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 e

ach 3rd-year class.

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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

010001

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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}};

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Array Initialization• If an initializer isn’t large enough to fill a m

ultidimensional 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

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Array Initialization• If an initializer isn’t large enough to fill a multidim

ensional 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

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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

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Example• Chinese numbers

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Array of Strings• char * subject[3]={ " 國文 ", " 英文 ", " 數學 "};• printf("%s", subject[1]);• PS. More about strings will be introduced l

ater in Chapter 8.

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Random Number GeneratorTo 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) );

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Random Number GeneratorTo 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.

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Practice• Write a program to simulate rolling a dice f

or 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