Fill the two-dimensional array exactly to the expression. Pascal's two-world arrays – matrices. A home for independent virtuousness
When there is a large number of data of the same type, variable data with different names, because they are not ordered by memory addresses, complicates programming. In such cases, we use objects that are called arrays.
- This is a continuous storage of memory to accommodate the sequence of objects of the same type, which is designated by one name.
The massif is characterized by the following basic concepts:
Massive element (meaning of massive element)– the value that is stored in the memory compartment, distributed between the array, as well as the address of this memory compartment.
The skin element of the massif is characterized by three values:
- address of the element - the address of the cob memory in which this element is rotated;
- element index (ordinal number of the element in the array);
- meaning of the element.
Massivu addresses – addresses of the massivu cob element.
Array name – an identifier that is used for subdivision of array elements.
The size of the array is the number of elements in the array
The size of an element is the number of bytes that occupy one array element.
Graphically rearranging the array in the computer's memory can be done by looking at the continuous address page.
Represents a small array of q elements with indices ranging from 0 to q-1. A skin element takes up k bytes of computer memory, and the elements are replaced in memory sequentially.
The addresses of the i-th element of the array have values
Array addresses are the address of the cob (zero) element of the array. For the multiplication of elements in the array, the serial number (index) of the element is calculated, the first value of which is equal to 0. So, if an array contains q elements, then the indexes of the array elements change between 0 and q-1.
Dovzhina array - the number of bytes that are allocated to memory to save all elements of the array.
Dovzhina Massivu = Size of Element * Quantity of Elements
To determine the size of an array element, you can use the function
int sizeof(type);
For example,
sizeof(char) = 1;
sizeof(int) = 4;
sizeof(float) = 4;
sizeof(double) = 8;
Stunning and initialization of arrays
To dumb down the array in the language, the following syntax is used:
name type [dimension] = (initialization);
Initialization is a set of cob values of array elements, assigned to the figured arches, and separated by comas.
int a = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9); // array a with 10 integers
Since the number of initial values indicated in the figured arms, the least number of elements in the array are indicated in the square arms, then all the elements that are lost in the array (for which the initial has not been removed) The studied values are set to zero. This power must be manually used to assign zero values to all elements of the array.
int b = (0); // array b with 10 elements, initialized to 0
If an array of pronunciations is deafened, then the constant cob values of its elements are indicated through the figure arms. In this case, a number of elements in the square arms may be omitted.
int a = (1, 2, 3, 4, 5, 6, 7, 8, 9);
When expanding the array to elements, the index of the required element is indicated in the square arms.
Butt in C
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#include
int main()
{
int a = (5, 4, 3, 2, 1); // array a contains 5 elements
printf("%d%d%d%d\n", a, a, a, a, a);
getchar();
return 0;
}
Result of the program:
However, it is often necessary to specify the values of array elements during the programming process. Whose vikorist has a stunned mass without initialization. In this case, the inset of a number of elements in the square arms is bound.
int a;
To determine the cob values of the elements of an array, a parametric cycle is often used:
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#include
int main()
{
int a;
int i;
// Entering elements into the array
for (i = 0; i<5; i++)
{
printf("a[%d] = ", i);
scanf("%d", &a[i]);
}
// Display elements of the array
for (i = 0; i<5; i++)
printf("%d", a[i]); // There is a gap in the format
getchar(); getchar();
return 0;
}
Result of Vikonannya program 
Rich world massifs
You may have access to a wide range of world wide areas. The importance of a rich-dimensional array compared to a one-dimensional array is that in a one-dimensional array the element's position is indicated by one index, and in a rich-dimensional array - by a decal. The butt of the rich massif is the matrix.
The zagal form of the stupor of the rich world massif
name type[dimension1][dimension2]...[dimensionm];
Elements of the rich world array are rotated in the successive parts of the operative memory of the growing address. In the computer's memory, the elements of a rich array are rotated, for example, an array that has 2 rows and 3 columns,
int a;
will be retouched in memory at the coming rank
The number of elements in the induced two-dimensional array appears as
Number of rows * Number of rows = 2 * 3 = 6.
The number of bytes of memory required to allocate the array is calculated as
Number of elements * Element size = 6 * 4 = 24 bytes.
Initialization of the world's richest massifs
The values of the elements of a multidimensional array, as in the one-dimensional expression, can be specified by constant values in the case of the column, placed in the shape of the bow (). However, in this case, a number of elements in the rows and columns may be strictly indicated in the square arms.
Butt in C
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#include
int main()
{
int a = (1, 2, 3, 4, 5, 6);
printf("%d%d%d\n", a, a, a);
getchar();
return 0;
}
However, it is more often necessary to enter the values of elements of a rich array during the programming process. With this method, you can manually analyze the insertions of the parametric cycle.
Butt in C
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#define _CRT_SECURE_NO_WARNINGS
#include
int main()
{
int a; // array with 2 rows and 3 rows
int i, j;
// Entering elements into the array
for (i = 0; i<2; i++) // loop in rows
{
for (j = 0; j<3; j++) // cycle through one hundred items
{
printf("a[%d][%d] = ", i, j);
scanf("%d", &a[i][j]);
}
}
// Display elements of the array
for (i = 0; i<2; i++) // loop in rows
{
for (j = 0; j<3; j++) // cycle through one hundred items
{
printf("%d", a[i][j]);
}
printf("\n"); // Transferred to a new row
}
getchar(); getchar();
return 0;
}
Passing an array to a function
Array processing can be manually organized using additional special functions. To process the array as function arguments, you need to pass
- masivu addresses,
- size of the massif.
It is necessary to set up the functions of processing rows, so it is enough to transfer them to the address.
When passing changes as arguments to a function, the data is passed as copies. This means that in the middle of the function the value of the parameter will be changed, but not in any way on the value in the middle of the function that is called.
If changeover addresses (or addresses to an array) are passed to a function, then all operations that involve the function with data that is within the visibility of the assigned address are carried out on the original data, then the output array (or the values of the change other) can be changed by the function that shout out.
Butt on C Given an array of 10 elements. Interchange the maximum and output elements of the array. To search for the maximum element and exchange, use the function.
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#define _CRT_SECURE_NO_WARNINGS
#include
// Exchange function
void change(int * x, int n)
{
// x - pointer to the array (addresses to the array)
// n - size of the array
int i;
int max, index;
max = x;
index = 0;
// Search for the maximum element
for (i = 1; i
if (x[i]>max)
{
max = x[i];
index = i;
}
}
// Exchange
x = x;
x = max;
}
// Head function
int main()
{
int a;
int i;
for (i = 0; i<10; i++)
{
printf("a[%d] = ", i);
scanf("%d", &a[i]);
}
change(a, 10); // click on the exchange function
// Display elements of the array
for (i = 0; i<10; i++)
printf("%d", a[i]);
getchar();
getchar();
return
p = p * x[i];
}
return p;
}
// Head function
int main()
{
int a; // empty array a with 5 elements
int i;
int pr;
// Entering elements into the array
for (i = 0; i<5; i++)
{
printf("a[%d] = ", i);
scanf("%d", &a[i]); // &a[i] - addresses of the i-th element of the array
}
pr = func(a, 5); // Calculation of creativity
printf("\n pr = %d", pr); // I'm creating new elements
getchar(); getchar();
return 0;
}
Divided: Computer Science
Subject: Two-world massif. Reservation of the two-world massif according to a given rule.
Goals: learn how to work with elements of a two-world array, learn to store two-world arrays according to a given rule, learn to deduce the location between the row number and the column number; development of logical thinking of scientists.
HIDDEN WORK
1. Updating knowledge
Arrays whose positions of elements are described by two indices are called two-dimensional. The structure of such an array can be represented by a straight-cut matrix. The leather element of the matrix is uniquely assigned to the row number and sleeper number, row number – i, sleeper number – j.
Let's look at a matrix of size n*m:
| a 11 | a 12 | a 13 | a 14 |
| a 21 | a 22 | a 23 | a 24 |
| a 31 | a 32 | a 33 | a 34 |
Matrix with 3 rows and 4 columns, number of rows n=3, number of columns m=4. A leather element has its own number, which is made up of two numbers - the number of the row in which the element is located, and the number of the row. For example, a23 is an element that stands at the other row and at the third column.
The two-world array of Turbo Pascal can be described in different ways. To describe a two-dimensional array, you need to know what type of element it is and how it is numbered (what type of index it is). There are a number of ways to describe a two-dimensional array.
Const maxN = ...; (Maximum values for the number of rows)
maxM=…; (Maximum values for the number of customers)
1 way
Type Mas = array of<тип элементов>; (one-dimensional array)
Type TMas = array of Mas; (one-dimensional array, elements of which are one-dimensional arrays)
Method 2
Type TMas = array of array of<тип
элементов>;
(one-dimensional array, elements of which are one-dimensional arrays)
3 way
Type<имя типа>= array of<тип элементов>; (Two-World Massif)
Advantage is given to the third method of describing the two-dimensional array.
For example:
Const N=3; M=4;
Type TMas = array of integer; (Two-dimensional array of integer numbers)
The formation of a two-dimensional array can be done in a number of ways: by entering from the keyboard through a random number generator, by a given rule, or by using an additional file.
1) Formation of a two-dimensional array using additional input from the keyboard and an algorithm for row display of matrix elements.
Const N = 10; M = 10;
Type Tmas = array of integer;
Var A: Tmas; i,j:integer;
Begin
(Introduction of matrix elements)
For i:=1 to N do
For j:=1 to M do
Read(A);
(Displaying matrix elements)
For i:=1 to N do begin
For j:=1 to M do
Write(A:4); (First row fights)
Writeln (Move to a new row)
end;
End.
2) A fragment of the program for forming a two-dimensional array through a random number generator.
Begin
Randomize; (Initialization of the random number generator)
(Introduction of matrix elements)
For i:=1 to N do
For j:=1 to M do
A:=random(45)-22;
2. Introduction of new material. Reservation of the massif according to the rule
Let's take a look at a number of fragments of programs for filling the two-world array behind the actual law. For this purpose it is necessary to derive a rule of thumb.
1. Fill massif A with size n*m in such order, for example
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35 36
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39 40
48 47
46 45
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Massiv will follow the “snake” principle. Replacement rule: if the row number is an unpaired number, then A=(i-1)*m+j, otherwise A=i*m-j+1.
program M1A;
n, m, i, j: integer;
begin
readln(n,m);
for i:=1 to n do begin
for j:=1 to m do
begin
if i mod 2 = 1 then
A=(i-1)*m+j
else
A=i*m-j+1;
write(A:3);
end;
writeln;
end;
readln;
end.
Let's look at the program in another way to follow the given rule:
program M1B;
var A:array of integer;
n, m, i, j: integer;
c:integer;
begin
readln(n,m);
c:=1;
for i:=1 to n do
begin
for j:=1 to m do
begin
A:=c;
if (i mod 2 = 0) and (j<>m)then
dec(c)
else
inc(c);
write(A:3);
end;
c:=c+m-1;
writeln;
end;
readln;
end.
2. Store array A using the following principle:
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7 0
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program M2;
var A:array of integer;
n, m, i, j: integer;
c:integer;
begin
readln(n,m);
c:=0;
for i:=1 to n do
begin
for j:=1 to m do
begin
if (i-1+j) mod 2 = 0 then
A:=0
else
begin
inc(c);
A:=c;
end;
write(A:5);
end;
writeln;
end;
readln;
end.
3. Store array A using the following principle:
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var A:array of integer;
n, m, i, j: integer;
c:integer;
begin
readln(n,m);
c:=1;
for j:=1 to m do
begin
for i:=1 to n do
begin
A:=c;
if (j mod 2 = 0) and (i<>n)then
dec(c)
else
inc(c);
end;
c:=c+n-1;
end;
for i:=1 to n do
begin
for j:=1 to m do
write(A:5);
writeln;
end;
readln;
end.
4. Store array A using the following principle:
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var i,j,m,c,d: integer;
begin
c:=1;
readln(m);
for j:=1 to m do
begin
i:=c;
d:=1;
repeat
A:=d;
inc(i);
if i>m then
i:=1;
inc(d);
until i=c;
dec(c);
if c<= 0 then
c:=m-c;
end;
for i:=1 to m do
begin
for j:=1 to m do
write(A:2);
writeln;
end;
end.
5. Store array A using the following principle:
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0 0
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var m,i,j: integer;
A:array of integer;
begin
readln(m);
for i:=1 to m do
begin
for j:=1 to m do
begin
if (i=j) or (m-i+1=j) then
A:=1
else
A:=0;
write(A:2);
end;
writeln;
end;
end.
3. Design for independent achievement
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4) Store the array using the following principle:
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5) Store the array using the following principle:
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32 26
20 14
8 2
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21 15
9 3
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22 16
10 4
35 29
23 17
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24 18
12 6
Home decorations:
1) Store the array using the following principle:
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30 31
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17 20
29 32
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16 21
28 33
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22 27
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24 25
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2) Store the array using the following principle:
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26 25
19 20
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23 24
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3) Store the array using the following principle:
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An array is the structure of data, presented in the form of a group of data of the same type, united under one single name. Massive vicorists are used to process a large number of similar data. I have an array of those who will recognize the same indicators a little later. The surrounding area of this massif is called an array element. The elements of the array can be given to any type. Masses can mother either one or die more than one. It is necessary to divide several dimensional arrays into one-dimensional arrays, two-dimensional arrays, tridimensional arrays, and up to an n-dimensional array. Most often, programmed vicorists have one- and two-world arrays, so we will look at both arrays.
One-dimensional arrays C++
A one-dimensional array is an array with one parameter that characterizes the number of elements in a one-dimensional array. In fact, a one-dimensional array is an array that can have more than one row and the nth number of columns. Stovpts in a one-dimensional array are elements of the array. Small picture 1 shows the structure of a single-dimensional array a. The size of this massif is 16 units.
Malyunok 1 - Masivi in C++
Please note that the maximum index of a single-dimensional array a It is more than 15, but the size of the array is 16 middles, since the numbering of the middles of the array always starts from 0. The index of the middle is a completely unknown number, which can be used to expand to the skin middle of the array and the eye nuvati be-yaki dii above her (in the middle).
//syntax for emptying a one-dimensional array C++: /*data type*/ /*name of a one-dimensional array*/; // butt of the stunning one-dimensional array depicted by baby 1: int a;
de, int-integers;
A - the name of a single-dimensional array;
16 - the size of a one-dimensional array, 16 middles.
Immediately after the name of the array, there are square arms, in which the size of the one-dimensional array is set, and the array is divided to solve the changes.
//another way to dumb down single-dimensional arrays int mas, a;
Two one-dimensional arrays of mas with sizes of 10 and 16 per line have been announced. Moreover, in this method, all arrays require a new type of data, int - int.
// arrays can be initialized when empty: int a = (5, -12, -12, 9, 10, 0, -9, -12, -1, 23, 65, 64, 11, 43, 39, -15 ); //Initialization of a single-dimensional array
The initialization of the one-dimensional array is indicated at the curly arms after the sign. one, the skin element of the massif is strengthened at the anterior coma.
Int a=(5,-12,-12,9,10,0,-9,-12,-1,23,65,64,11,43,39,-15); //Initializes the array without specifying its size.
Once the compiler itself determines the size of the one-dimensional array. The size of the array need not be specified only for its initialization, but in case of emergency the array is required to indicate the size of the array. Let's develop a simple program for processing a one-dimensional array.
// array.cpp: defines the entry point for the console program. #include "stdafx.h" #include
// code Code::Blocks
// Dev-C++ code
// array.cpp: defines the entry point for the console program. #include
U rows 10 - 11 An integer one-dimensional array with the dimensions of array1, the size of which is equal to 16 numbers, is empty and initialized, so that such an array can store 16 numbers. Whether the processing of the massif is done at once or in cycles. What is the cycle of selection for processing the massif? It’s best suited for this task. The medical doctor counter will be victorized to expand to the elements of the one-dimensional array array1. If the continuation of the for loop has a negative sign, there are no fragments of the sixteenth index in the one-dimensional array array1. Since the numbering of the middles starts from zero, then the array has 16 elements. In the cycle for the cout operator, there are other elements of a one-dimensional array (there are 2 small ones).
Processing massiva indexes element massiva array1 5 array1 -12 array1 -12 array1 9 array1 10 array1 0 array1 -9 array1 -12 array1 -1 array1 23 array1 65 array1 64 array1 arra1 press whatever key. . .
Malyunok 2 - Masivi in C++
Let's build another program to process a single-dimensional C++ array. The program must sequentially read ten entered numbers from the keyboard. All entered numbers are summed up and the result is displayed on the screen.
// array_sum.cpp: defines the entry point for the console program. #include "stdafx.h" #include
// code Code::Blocks
// Dev-C++ code
// array_sum.cpp: defines the entry point for the console program. #include
Before concluding the processing of the array, it is necessary to vote, and the size of the one-dimensional array is more than 10, since this is determined by the mental task. The variable sum accumulates the sum of elements of a one-dimensional array. The first for loop fills a one-dimensional array with numbers entered from the keyboard, rows 12 - 13. The counter variable is used for sequential access to the elements of the same-dimensional array array1, starting from index 0 to 9 inclusive. Another for loop displays an array of elements on the screen, rows 15 - 16. The third loop for sequentially reads the elements of a one-dimensional array and sums them, the sum accumulates in the variable sum. rows 17 - 18. The result of the robotic program is to marvel at the baby 3.
Enter elementi massiva: 0 1 2 3 4 5 6 7 8 9 array1 = (0 1 2 3 4 5 6 7 8 9 ) sum = 45 To continue, press any key. . .
Malyunok 3 - Masivi in C++
First, all 10 numbers were entered sequentially, after which a one-dimensional array was displayed, and the sum of numbers was added to the array.
Two-world arrays C++
How far we have seen the one-world massifs with which we can forever be surrounded. It is possible that you need to process the data from the table. The table has two characteristics: the number of rows and the number of columns. Also in a two-dimensional array, in addition to the number of elements in the array, there are such characteristics as the number of rows and the number of columns in the two-dimensional array. So, visually, there is a two-world array - the primary table with rows and columns. In fact, a two-dimensional array is a one-dimensional array of one-dimensional arrays. The structure of a two-dimensional array with dimensions a, size m by n is shown below (division 4).
Malyunok 4 - Masivi in C++
de, m - number of rows of a two-world array;
n - the number of people in the two-world massif;
m * n – number of elements in the array.
// syntax for emptying a two-dimensional array /*data type*/ /*name of array*/;
In a deafened two-dimensional array, just as in a deafened one-dimensional array, it is necessary to enter:
- data type;
- I'm massive.
Therefore, the first square arms indicate a number of rows of a two-dimensional array, while the other square arms indicate a number of rows of a two-dimensional array. The two-dimensional array is visually subdivided by another pair of square arms. Let's take a look at the butt of the stunned two-world massif. Perhaps we need to evaluate a two-dimensional array with as many elements as 15. This two-dimensional array can have three rows and five columns or five rows and three columns.
// Butt of stunned dvomirny array: int a;
- a - the name of a whole array
- the number of first square arms indicates the number of rows of a two-dimensional array, each having 5;
- The number for the other square arms shows the number of elements of the two-dimensional array, for one of them there are 3.
// initialization of a two-dimensional array: int a = ((4, 7, 8), (9, 66, -1), (5, -5, 0), (3, -3, 30), (1, 1, 1) );
This array has 5 rows, 3 columns. After the sign of assignment, shaped arches are placed in the middle, in the middle of which there are as many pairs of shaped arms as there are rows in a two-dimensional array, and these arms are divided into clumps. In a pair of shaped arches in the skin, elements of the two-dimensional array are recorded through the coma. All shaped arms have a number of elements that can be combined. Since the array has five rows, then there are also five internal pairs of arms. The inner arches have three elements, and some of the arches have three elements. Graphically, our array will look like a double table (division 5).
Malyunok 5 - Masivi in C++
In the skin center of the bilayer massif a the value is shown, in the lower right box the address of the company is shown. The address of the middle of the two-dimensional array is the name of the array, the row number and the column number.
We have developed a very complicated program for processing a two-dimensional massif called “Labyrinth”. The labyrinth contains stimuli based on a two-dimensional array. The size of the labyrinth will be chosen at the discretion of the authorities.
// array2.cpp: defines the entry point for the console program. #include "stdafx.h" #include
// code Code::Blocks
// Dev-C++ code
// array2.cpp: defines the entry point for the console program. #include
The correct and wrong ways could be designated by one or the same number, for example, zero, or, for precision, the correct way of values by the number 2. The initialization of the array was done manually, just to simplify the program. Since the program is processing a two-dimensional array, it requires two cycles to switch between the elements of the two-dimensional array. The first for loop consists of alternating between the rows of a two-dimensional array. The fragments of rows in the two-dimensional array are 33, then the change-doctor i is incremented from 0 to 33, row 46. In the middle of the first loop there is a for loop, which alternates between the elements of a row of a two-dimensional array. In another for loop, in the middle there is a unary operation of transformation of the data type - static_cast<>() , which is another symbol numbered 176. The operation of converting data types is duplicated to increase the width of the labyrinth. The result of the robotic program (div. Figure 6).
Malyunok 6 - Masivi in C++
Masiv (also Index array, inodes table, row) - naming (ordering) a set of the same type of change (data), retrieved from memory one by one, access to which is subject to index. In the simplest way massif It works continuously and saves units of data of the same type.
Index w masiwu - tse number whole, which indicates a specific array element
The number of indexes in the array to be searched may vary. Arrays with one index are called one-dimensional, two - two-dimensional etc.
One-dimensional The array does not strictly match vector in mathematics, two-dimensional - matrices . Most often the massif becomes stagnant one or else two indexes, sometimes three, even more indices are encountered even rarely.
The array is described as follows:
The most common type of index is a range, for example:
Better to describe array B, What develops with 5 elements and symbolic array R, What develops with 34 elements. For Masiwu U 5 * 6 = 30 bytes of memory will be seen (since under the changeable type Real appears 6 bytes of memory), for array R - 1*34=34 bytes of memory (under changeable type Char - 1 byte). Basic type The elements of the array can be structured in any way, for example, or structured, except for the file! The massif can be voiced on Wikoristanny Vlasny type:
Cycle It can be called a sequence of instructions that is highly concise, organized in some way (for example, to aid mental transition).
A single cycle of the body is called iteration. Viraz, which means you will be screwed up next time iteration, or cycle end - tse umova exit chi the end of the cycle(Also, it is possible and intellectual continuation). The memory that saves the line number of the iteration is called healer iteration the cycle is simple doctor cycle. Cycle it is not obligatory to take revenge doctor.
Cycles rage:
- Cycle with a doctor, in which the changeable action changes its value from the specified value cob value up to Kintsevogo meaning of action croc, and the skin value of the body change cycle is completed once. Implemented by the operator for
butt. Save massif:
And so you can remember two-dimensional array: 
- Cycle with change of mind, who is concluding while the true work of the mind is indicated in front of his cob. Implemented by the operator while.
- Cycle with postumova, In which mind is rechecked after the body is completed in the cycle, and, then, the body is reconstituted at least once. In mov Pascal this cycle is implemented by the operator repeat...until
The first operation skip iteration, if in thread iteration cycle It is necessary to skip all commands until the end of the completed loop. In this case, the cycle itself is not to blame for interruption, but rather for continuation, but the output is to blame for the initial rank. Implemented by the operator continue.
Also in cycles the command is often victorious pre-string exit from the loop For example, if, when the body is finished, the cycle shows a break, after any further work the cycle does not harm the sense. Implemented by the operator EXIT or else break.
Let's turn to the cob, or rather to the cob butt. We need to figure out what to do with this little piece of software:
Coming from what has been said, vikorystvovany two-world massif A- this is the matrix size n x n. The cycle is being vicorized with a doctor from one to n, may have been indicated earlier.
Mid-cycle: change h stores the values of a two-dimensional array with an index (c:=A), right now . Then, at the place of this element in the array, the values of the element of the same array are entered, as well as with the index (A:=A), or when k:=1 (A:=A). Tobto. elements of the first row are included, because The first number in the index indicates the row number in the matrix - [ i j), and to the other for the station number - . Finally, at the place of the element with the index , be entered as the primary value of the array element A with index , like we brought it to the end of the meal h (A:=c).
And with every iteration of our meaning cycle i increases by one. Simple for the crocs. Start now :
h:=A A:=A A:=c
h:=A A:=A A:=c
h:=A A:=A A:=c
Yes n times before . Tobto. The values of the diagonals of the matrix are straight to the right and downwards. I The elements of this diagonal change with the values of the elements first matrix drains(or k-That row). So, the correct answer is - option 3: This algorithm changes places diagonal elementskth column of the table.
Pascal treats a two-dimensional array as a one-dimensional array, the type of elements of which is also an array (an array of arrays). The positions of elements in Pascal's two-dimensional arrays are described by two indexes. They can be presented in the form of a rectangular table or matrix.
Let's look at Pascal's two-dimensional array with dimensions 3*3, then there will be three rows in it, and three elements in each row:
A leather element has its own number, like in single-layer arrays, but the number is also made up of two numbers - the number of the row in which the element is located, and that number is combined. In this way, the number of the element is indicated by the crossbar of the row and column. For example, a 21 is an element that stands in the other row and in the first column.
Description of Pascal's two-world array.
There are a number of ways to detonate Pascal's two-dimensional array.
We can already describe one-dimensional arrays, the elements of which can be of any type, and therefore, the elements themselves can be arrays. Let's take a look at the following description of the different types:
An example of a description of Pascal's two-world arrayType
Vector = array of<тип_элементов>;
Matrix = array of vector;
Var m: matrix;
We named Pascal's two-dimensional array m, which consists of 10 rows, each with 5 rows. In this case, m [i] can be added to the skin i-th row, and m [i, j] can be applied to the j-th skin element in the middle of the i-th row.
The values of types for two-dimensional Pascal arrays can be specified in one row:
Type
Matrix = array of array of< тип элементов >;
or even simpler:
type
matrix = array of<тип элементов>;
Rolling up to the elements of a two-dimensional array looks like: M [i, j]. This means that we want to remove the element added to the i-th row and j-th column. Here we can’t confuse the rows with the countertops, because we can once again reduce the beast to the next element. For example, going up to the element M can create the correct form of the entry, or you can call the request from the robot program.
Basic operations with Pascal's two-dimensional arrays
Everything that has been said about the main actions with one-dimensional arrays is also true for matrices. The only action that can be performed on matrices of the same type as a whole is the price. So, when programs describe two matrices of the same type, for example,
type
matrix = array of integer;
var
a, b: matrix;
then during the editing of the program you can assign matrices a matrix values b(a: = b). All other actions are added element by element, and all valid operations can be added to the elements, as defined for the type of these array elements. This means that if an array consists of whole numbers, then on its elements you can perform operations intended for whole numbers, if an array consists of symbols, then prior to them you can carry out operations intended for working with symbols.
Introduction of Pascal's two-world array.
To sequentially introduce elements of a single-dimensional array, we used a for loop, in which we changed the index values from 1 to the rest. The position of an element in a two-dimensional Pascal array is indicated by two indices: the row number and the column number. This means that we will need to consistently change the row number from 1 to the remaining one and in the skin row sort through the elements of the rows from 1 to the remaining one. Now, we need two for loops, with one of them nested within the other.
Let's take a look at the example of entering Pascal's two-dimensional array from the keyboard:
Example of a program for entering Pascal's two-dimensional array from the keyboardtype
matrix = array of integer;
var
a: matrix;
i, j: integer; (Index massif)
begin
for i:=1 to 5 do (loop to iterate through all rows)
readln(a[i, j]); (enter from the keyboard the element that is in the i-th row and j-th column)
Pascal's two-world massif can be stored in a simple way. Use the random (N) function, and also assign the value of a particular virus to the skin element of the matrix. The method of filling Pascal's two-dimensional array is selected depending on the task at hand, but in any case, the values of the skin element in the skin row and skin layer are to blame.
Bringing Pascal's two-world array to the screen.
The derivation of the elements of Pascal's two-dimensional array also proceeds sequentially, it is necessary to stretch the elements of the skin row and skin column. Who would like to have the elements, like those in one row, hand in hand, then. in a row, and the sleeper elements were arranged one after another. For what needs to be done, here is the sequence of actions (let’s look at a fragment of the program for the array, described in the previous example):
Example of Pascal's two-world programfor i:=1 to 5 do (loop to iterate through all rows)
begin
for j:=1 to 10 do (sorting through all elements of the row by sleepers)
write(a[i, j]: 4); (the other elements should be in the i-th row of the matrix in one screen row, with which 4 positions are entered to display the skin element)
writeln; (First change the row number in the matrix, you need to move the cursor to the head of the new screen row)
end;
Respect ( It's important!): Quite often, students' programs experience problems when input from the keyboard or display on the screen is forced to occur in the following order: readln(a), writeln(a), de A- This is important for the massif type. In this case, they are surprised by the compiler's information that it is impossible to capture or enforce a change to this type. Perhaps you will understand why you can’t earn something if you see N kuklov standing in a row, and in your hands, for example, a kettle of water. Can you follow the command “pour water” and fill all the heaps at once? If you didn't get it wet, you'd have to pour some okramo into the leather jacket. The filling and display of array elements must also be done sequentially and element by element, because In the EOM memory, the elements of the array grow in successive sequences.
A tribute to Pascal's two-world array in memory
The elements of the abstract array in the machine's memory are physically expanded sequentially with the description. In this case, the skin element takes up a large number of bytes in memory, which indicates its size. For example, if an array consists of elements of the integer type, then each element takes up two bytes. And the entire array takes up S 2 bytes, where S is the number of elements in the array.
How many places will you take the massif, what with the massifs, then. matrix? Obviously: S i^S j, where S i is the number of rows, and S j is the number of elements in each row. For example, for massive type
Matrix = array of integer;
12 bytes of memory are required.
How can we remember the elements of this massif? Let's take a look at the layout of the array M type matrix in memory.
Under the M type integer skin element there are two memory compartments. The location of the memory is “from below to above.” The elements are placed in the order of index changes, which illustrates the scheme of nested loops: the first row is placed first, then the other, the third... In the middle of the row, the elements go in order: the first, the other, etc.
As we know, access to any change is possible only by entering the address in the middle of the memory in which the change is saved. A specific memory is visible for change when used by programs, so that mutual correspondence is established between the changeable memory and the computer address. If we have named the change as an array, then the program knows the address of the cob of the array, then the first element. How is access to all other elements of the array achieved? When actually accessing the memory in which the two-dimensional array element is stored, the system calculates its addresses using the formula:
Addr + SizeElem * Cols * (I -1) + SizeElem * (J -1),
de Addr – the actual root address in which the array resides in memory; I, J – element indices in a two-dimensional array; SizeElem – size of the array element (for example, two bytes for elements of type integer); Cols – number of elements in a row.
Viraz SizeElem * Cols * (I -1) + SizeElem * (J -1) is called the displacement of the cob massif.
How much memory is available for the array?
Let's look not so much at how much memory is visible under the array (which we discussed in the previous section), but at the maximum permissible size of the array, which is responsible for the care of memory.
For robotic programs, memory is seen in segments of 64 KB each, and the least one of them is designated as data segment. The axis of this segment is the same data that is processed by the program. Of course, programs cannot be expanded more than once in one segment. Therefore, since there is only one change in the segment, it is described as an array, and it is not possible to extract more than 65536 bytes. And yet, in addition to the array in the data segment, there will be descriptions of other changes, so the actual memory storage, which can be seen under the array, will be found under the formula: 65536-S, where S is the memory storage, which can be seen under the array. ours changeable.
What do you need to know? In order not to be surprised, when compiling, the translator will display a notification about the compilation of a long-standing array, if there is a description in the program (correct according to the syntax):
Type myArray = array of integer;
You already know that, using double-byte numbers of whole numbers, you can actually read an array with many elements, which is equal to 65536/2 –1=32767. And it’s just because there won’t be any other changes. Two-world arrays of guilty mothers have even smaller boundaries between indexes.
Apply decoupling problems from Pascal's two-dimensional arrays.
Zavdannya: Find the number of non-zero elements of the matrix.
Decision:
- For the most important task, we need the following changes: a matrix, which consists, for example, of whole elements; P – addition of elements subsumed under 0; I, J – array indexes; N, M – number of rows and columns in the matrix.
- The input data is N, M - their values are entered from the keyboard; matrix – the introduction of the matrix can be formalized as a procedure for filling the matrix with a special order, then. for the additional random() function.
- The output data will be the changeable P (solid) value.
- To verify the correctness of the program's display, you need to display the matrix on the screen, for which we will formulate the procedure for displaying the matrix.
- Progress of the task:
Let's discuss the initial implementation of the main program, the implementation of procedures will be discussed a little later:
- enter the values N and M;
- We introduce Pascal's two-dimensional array, which goes to the vvod (a) procedure, where a is a matrix;
- Let's create a matrix, for which we go to the print(a) procedure;
- Nadamo cob value change P =1;
- We will sequentially iterate through all rows I from 1st to Nth, for the skin row we will iterate through all the columns J from 1st to M, for the skin element of the matrix it is mentally verifiable: what is a ij ? 0, tvir P will be multiplied by the element a ij (P = P * a ij);
- The values of the additional non-zero elements of the matrix are displayed on the screen - P;
Now let's talk about procedures.
Respect (this is important!) A procedure parameter can be changed to the assigned type, which means that in order to pass an array to the procedure as a parameter, its type is subject to descriptions behind it. For example:
Type
Matrix = array of integer;
procedure primer(a: matrix);
..............................
Let us now turn to our procedures.
The procedure for entering a matrix is called a vvod parameter of the procedure - a matrix, and as a result, it is transferred to the main program, and the parameter must be passed on. So the header of our procedure looks like this:
Procedure vvod (var m: matrix);
To implement the insertion cycles of the procedure, we need local changers, for example, k and h. The algorithm for filling the matrix has already been discussed, so we will not repeat it.
The procedure for displaying a matrix on the screen is called print, the parameter of the procedure is the matrix, and in this case the input parameter is also passed along the values. The title of this procedure will look like this:
Procedure print (m: matrix);
And again, for the implementation of investment cycles in the middle of the procedure, we will need more doctors, let them be called that way - k and h. The algorithm for displaying the matrix on the screen has been described more quickly in this description.
Butt of Pascal's two-world programProgram produced;
Type
Matrix = array of integer;
Var
A: matrix;
N, m, i, j: byte;
P: integer;
Procedure vvod (var m: matrix);
Var k, h: byte;
Begin
For i:=1 to n do (change n for the procedure, which is global and also “visible”)
For j:=1 to m do (change m for the procedure is global, and therefore “visible”)
M:= random(10);
End;
Procedure print (m: matrix);
Var k, h: byte;
Begin
For i:=1 to n do
begin
For j:=1 to m do
Write(M:4);
Writeln;
end;
End;
Begin (start of the main program)
Writeln("Enter matrix size:");
Readln(N, M);
Vvod(a);
Print(a);
P:=1;
For i:=1 to N do
For j:=1 to M do
If a<>0 then p:=p*a;
Writeln(p);
End.
