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   2021
/ 
 
(    , ++    )
 : 3   :75
:      ,            
   󰌹       
1.        ?        
?       󰌹       󰌹 
 󰌹
2. (A)       ?   
(B)              
  
    ?
3.   󰌹      ?  
        ?
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4.            󰌹   
       
5.    ?  󰌹    A  󰌹   : 37, 52,
28, 75, 61, 24, 9, 59  A          
- 
6.           󰌹  󰌹  
   
7. (A)   ? C++          
?
(B)         ?
()          
8.   ?        ? 
    󰌹       󰌹   
            
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   2021
/ 
 
(    , ++    )
 : 3   :75
:      ,            
   󰌹       
1.        ?        
?       󰌹       󰌹 
 󰌹
:1.   ?
 󰌹           10 -  
—name1, name2, name3,     ,   
     
                 
    

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            (-)     
         1000  ,    1002, 1004, 1006... 
  (2-   )
     ?
       
        
 ,           
       
             ,       ()
         
2. 󰌹 
        :
. -  (1 )
 1D        : int marks[5];  5   :
marks[0], marks[1], … marks[4]
      :
󰌹
0
1
2
3
4

50
60
72
85
90
     
.   (2, 3, )
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 2D        󰌹      : int a[3][4];
     3   4  ,   
 :
0
 1
2
R0
 1
2
 3  (   )    ,       

3.  󰌹        
  2      ,     , 󰌹   
    
                 ?
               
   :
. -  ( , ++, ,     )
         ,     ,   
 
  󰌹,   󰌹
[3][3]
1 2 3
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4 5 6
7 8 9
-    :
1 2 3 4 5 6 7 8 9
. -  (,   )
,     
       :
1 4 7 2 5 8 3 6 9
4. 2D   -  ()
-  :
 A[i][j]   :
LOC(A[i][j]) =   + [ (i ×   ) + j ] ×    
:
i =  
j =  
NumberOfColumns =       
SizeOfEachElement =     (  󰌹, int  󰌹 4 )

 󰌹  A[3][3] ,  ( 4 )
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  = 1000 A[1][2]    
  :
 = 1000 + [(1 × 3) + 2 ] × 4 = 1000 + (3 + 2) × 4 = 1000 + 5 × 4 = 1000 + 20
= 1020
󰌹 A[1][2]   1020    
5.   󰌹     
 C   󰌹           (     
     )
   󰌹 /  

1.       󰌹  
  
2.   󰌹 
3.    
 
#include <stdio.h>
  () {
int arr[100], n, pos, ;
printf("    : ");
scanf("%d", &n);
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printf("  : ");
for(int i=0; i<n; i++)
scanf("%d", &arr[i]);
printf("󰌹  󰌹    (0  %d): ", n);
scanf("%d", &pos);
printf("󰌹  󰌹   : ");
scanf("%d", &value);
//   
 
for(int i=n; i>pos; i--) {
arr[i] = arr[i-1];
}
arr[pos] = ;
++;
printf("   : ");
for(int i=0; i<n; i++)
printf("%d ", arr[i]);
0  ;
}
   󰌹  /  

1.         
 
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2.    1 
 
#include <stdio.h>
  () {
int arr[100], n, pos;
printf("    : ");
scanf("%d", &n);
printf("  : ");
for(int i=0; i<n; i++)
scanf("%d", &arr[i]);
printf(" 󰌹    (0  %d): ", n-1);
scanf("%d", &pos);
// 
 󰌹 
for(int i=pos; i<n-1; i++) {
arr[i] = arr[i+1];
}
--;
printf("   : ");
for(int i=0; i<n; i++)
printf("%d ", arr[i]);
0  ;
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}

               
-,             :
  ?
󰌹  (   )
          
  - 
  󰌹     󰌹 
  , , 󰌹 󰌹, ,         󰌹 
  
2. (A)       ?   
(B)              
  
    ?
:󷈷󷈸󷈹󷈺󷈻󷈼
     ,   -   :   
        󰌹 --   ,  
             
    :         ,    
          󰌹,    
           
         
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󼫹󼫺 :     
1.    ?
      󰌹         
   ,        
 󰌹         
   100  ,    10  
   10,000  ,      
󷷑󷷒󷷓󷷔                 
2. - 
      -        - 
                 
   :
O(1):          ,    
  
O(log n):          -  
O(n):           
O(n²):           
3. :     
 
 󰌹             

    -            
 n  ,            
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 : O(n).
󷷑󷷒󷷓󷷔 1,000  ,   1,000      
 
  󰌹    
     :     ,        ;
    ,        
       
 : O(log n).
󷷑󷷒󷷓󷷔 1,000  ,      10    
:
        󰌹  
      󰌹     
          —    󰌹  
    
󼫹󼫺 :  
1.    ?
            
   
󷷑󷷒󷷓󷷔      :
        —     ,    
        —   ,  
    
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        — -    
2.   
(i)   
 : , , , 󰌹
:        
(ii) -  
      󰌹 󰌹   :
a)   
        
:
o 󰌹:     
o 󰌹 󰌹:   
o : ,   (LIFO)
o : ,   ()
b) -  
          
:
o :  (  󰌹,  )
o :   ,  󰌹   
3.         
         󰌹      
   :
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(i)    
  ,    ?
:       󰌹,     
(ii)  
    ,      ?
:
o    󰌹,     
o -  /  󰌹, 󰌹 󰌹   
(iii)  
        
:             ; 󰌹
󰌹  󰌹      
(iv)    
              
:     O(n)  ,        
O(log n)  
(v)   
  ?
:   󰌹 ,  󰌹   󰌹 󰌹  
  
(vi)   
-      ,       
:           
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󽆪󽆫󽆬
            ,   
       󰌹          
    
                  
—      ,       
      
           ,   󰌹
          ,       
3.   󰌹      ?  
        ?
:1.   ?
 󰌹            ,    
         ,         
;       
         
                󰌹   :
LIFO —  ,  
   :
      ,      
         
           
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     
  
    (      )
  (    -     )
  
         :
1.       
2.        
  :
/      
         
             (     
)
,            —    
 
2.    ? (  )
   󰌹     󰌹:
 + 
3 * (4 + 2)
(6 - 2) / 4
       ,   (+, -, *, /)      
      :
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       ,      
   
 󰌹      󰌹,         :
1. (󰌹  )
2. ( 󰌹  )
    ?
  ,      
:
 : A + B : AB+
 : (3 + 4) * 5 : 34+5*
 : (6 - 2) / (1 + 1) : 62-11+/
           
   ?
            

          (  * +  
 )
   
        
 ,  ,      󰌹  󰌹 
3.            ? (-
-)
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     
              
         ,          󰌹
    
 
       
         :
o       
o       
o  
o       
 ,        ,      
4.     (   )
      :
23+5*
  : (2 + 3) * 5       
-- 󰌹


2

2
3

2, 3
+
 3  2    2+3=5    5   
5
5

5, 5
*
 5  5   5*5=25    25 
25
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       : 25    
5.    ( )
:
462/+3*
  :
1.  4  
2. 6  
3.  2  
4.  / 2  6   6/2 = 3 3  : 4, 3
5.  +  3  4 4+3 = 7  7 : 7
6.  3 : 7, 3
7.  * 3  7    7 * 3 = 21 21   
  = 21
6.     󰌹     ?
   󰌹            
      󰌹     :
     ,      󰌹    
       (  )  ,  
󰌹    
,    󰌹      
 ,  +  =  
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4.           󰌹   
       
:󷈷󷈸󷈹󷈺󷈻󷈼
  ,           
                ( ),
                  
   —  ,   (FIFO)  󰌹    
         󰌹        
 ,                
     
      ,  󰌹 󰌹        , 
   -    —        
󼫹󼫺  
      FIFO 󰌹    :
   
      ,      
󷷑󷷒󷷓󷷔   :
    
           
       
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󹶜󹶟󹶝󹶞󹶠󹶡󹶢󹶣󹶤󹶥󹶦󹶧  
         :
1.  –        
2. 󰌹 –       
,  󰌹       ,       󰌹 
      
󹺰󹺱  󰌹 
󰌹  :
         
      :
o ( )
o  (   )
        :
o    (    )    
o     (      )    
󷷑󷷒󷷓󷷔           :
    ,    
       -     
󽁌󽁍󽁎  
         -   
 
1.    ()
       
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:
1.         
2.    ,           
3. ,      󰌹     
󷷑󷷒󷷓󷷔:
: [10 20 30]
 40 [10 20 30 40]
   40      
2.  ()
         
:
1.         ,     
2. ,      
3.           
󷷑󷷒󷷓󷷔:
: [10 20 30 40]
 10   [20 30 40]
    20      
3.  (  )
         
       󰌹        
󷷑󷷒󷷓󷷔:
: [20 30 40]
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 20  
4. IsEmpty (      )
   = NULL   true  
:      ,  IsEmpty True.
5. IsFull (       )
󰌹  ,       " "   
󰌹   ,  IsFull   
🖼-    
  {
;
 * ;
};
  {
 * ;
 * ;
};
//  
  ( * ,  ) {
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
 -> = ;
newNode->next = NULL;
 (q->rear == NULL) {
q->  = q-> =  ;
 ;
}
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q->rear->next = newNode;
q->rear = newNode;
}
//  
int dequeue(struct Queue* q) {
 (q->front == NULL) {
printf("      ");
-1  ;
}
struct Node* temp = q->front;
int  = temp->data;
q->  = q-> ->;
 (q->front == NULL) q->rear = NULL;
();
 ;
}
󷷑󷷒󷷓󷷔     󰌹            
󽆪󽆫󽆬
             󰌹  
  , 󰌹        󰌹    
      󰌹  ,     ,   
               
 ,        󰌹 —     , 
       
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5.    ?  󰌹    A  󰌹   : 37, 52,
28, 75, 61, 24, 9, 59  A          
- 
:   ?
 󰌹               ,   
      —          
 󰌹  ,   -      󰌹  :
 1    2  
  1  ,      
  2    3       - 
   
     ,            —
        󰌹     
 , -   -           
          ,        
  
  
 󰌹        󰌹   :
A = [37, 52, 28, 75, 61, 24, 9, 59]
      
  -      
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    --  
 1
      :


   
37  52
37 < 52 - 
37, 52, 28, 75, 61, 24, 9, 59
52  28

37, 28, 52, 75, 61, 24, 9, 59
52  75
- 
37, 28, 52, 75, 61, 24, 9, 59
75  61

37, 28, 52, 61, 75, 24, 9, 59
75  24

37, 28, 52, 61, 24, 75, 9, 59
75  9

37, 28, 52, 61, 24, 9, 75, 59
75  59

37, 28, 52, 61, 24, 9, 59, 75
 1  :
[37, 28, 52, 61, 24, 9, 59, 75]
   75      
 2



37  28

28, 37, 52, 61, 24, 9, 59, 75
37  52
- 
28, 37, 52, 61, 24, 9, 59, 75
52  61
- 
28, 37, 52, 61, 24, 9, 59, 75
61  24

28, 37, 52, 24, 61, 9, 59, 75
61  9

28, 37, 52, 24, 9, 61, 59, 75
61  59

28, 37, 52, 24, 9, 59, 61, 75
 2  :
[28, 37, 52, 24, 9, 59, 61, 75]
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    61      
 3



28  37
- 
28, 37, 52, 24, 9, 59, 61, 75
37  52
- 
28, 37, 52, 24, 9, 59, 61, 75
52  24

28, 37, 24, 52, 9, 59, 61, 75
52  9

28, 37, 24, 9, 52, 59, 61, 75
52  59
- 
28, 37, 24, 9, 52, 59, 61, 75
 3  :
[28, 37, 24, 9, 52, 59, 61, 75]
 4



28  37
- 
28, 37, 24, 9, 52, 59, 61, 75
37  24

28, 24, 37, 9, 52, 59, 61, 75
37  9

28, 24, 9, 37, 52, 59, 61, 75
37  52
- 
28, 24, 9, 37, 52, 59, 61, 75
 4  :
[28, 24, 9, 37, 52, 59, 61, 75]
 5



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28  24

24, 28, 9, 37, 52, 59, 61, 75
28  9

24, 9, 28, 37, 52, 59, 61, 75
28  37
- 
24, 9, 28, 37, 52, 59, 61, 75
 5  :
[24, 9, 28, 37, 52, 59, 61, 75]
 6



24  9

9, 24, 28, 37, 52, 59, 61, 75
24  28
- 
9, 24, 28, 37, 52, 59, 61, 75
 6  :
[9, 24, 28, 37, 52, 59, 61, 75]
 7



9  24
- 
9, 24, 28, 37, 52, 59, 61, 75
 7  :
       
  
[9, 24, 28, 37, 52, 59, 61, 75]
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
        -     󰌹 
    -   -       , 
                
 
   ,         ,   
 -  ,       
6.           󰌹  󰌹  
   
:󷈷󷈸󷈹󷈺󷈻󷈼
                 
  ,         ,       
 ,           ,   
         
     1960  󰌹  ,        
                󰌹 '
 '   —    -   ,   
    󰌹 
      ,         ,  
      
󼫹󼫺    
           󰌹    
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       
    
       
    
      
      󰌹          
   
󷷑󷷒󷷓󷷔        :        
( ),               
       ,      
󹶜󹶟󹶝󹶞󹶠󹶡󹶢󹶣󹶤󹶥󹶦󹶧  󰌹 
   --    :
:  
1.      
2.    
o   ,  ,     ,      
  
3.   󰌹 
o       :
    
 
    
 
4.       
5.        
 
  
6.             (     
)
 
 󰌹        :
[35, 12, 43, 8, 51]
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1.  = 35 
2. :
o  : [12, 8]
o : [35]
o  : [43, 51] : [12, 8] [35] [43, 51]
3. [12, 8]     :
o  = 12
o  : [8], : [12],  : [] : [8, 12]
4. [43, 51]     :
o  = 43
o  : [], : [43],  : [51] : [43, 51]
5.     :
[8, 12, 35, 43, 51]
󷷑󷷒󷷓󷷔     !
󽁌󽁍󽁎  󰌹 
(arr, , ):
  < :
 = (arr, , )
(arr, low, pivotIndex - 1)
QuickSort(arr, pivotIndex + 1, high)
 (arr, , ):
 = arr[high] //        
i =  - 1
j =    - 1  󰌹:
 arr[j] <= :
i = i + 1
arr[i]  arr[j]    
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arr[i + 1]  arr[high]   
(i + 1) 
󹵍󹵉󹵎󹵏󹵐   
         
1.  
         󰌹  
 : O(n log n)
:        [10, 20, 30, 40, 50]  
2.  
         󰌹   (  󰌹 ,
   󰌹  )
 : O(n log n)
    
3.   
         
          󰌹 
 : O(n²)
: [10, 20, 30, 40, 50]           
    
󷷑󷷒󷷓󷷔      󰌹,          " 
"     (,        )
4.  
   -   ( 󰌹     
)
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     : O(log n)
󽆪󽆫󽆬
        —   -  
            ,   
       ,    󰌹    
 :   , 󰌹     
               
   
7. (A)   ? C++          
?
(B)         ?
()          
:
C++       -   (OOP)   
 OOP             󰌹   
  , , , —  C++     
  󰌹               
      󰌹, C++ ,  󰌹 (/) 
       
  ,  OOP      :
1.      C++         
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2.        ?
3.   ,     ?
(A)   ? C++           ?
  ?
C++       :
1.  ( )   󰌹,    ,      
2.  ()    ,     
      ,          
    •   •       

   :
 " "           :
: , , 
: call(), message(), clickPhoto()
   󰌹       ,    
C++      
 ,             
:
  {
//  
//   
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};
  () {
ClassName objectName; //  
}
:
  {
:
 ;
 ;
 () {
cout << ": " <<  << ", : " << ;
}
};
  () {
 c1; //    
c1.model = " 󰌹";
c1.speed = 180;
c1.show(); //    
}
     ?
C++     (.)        
.
. ()
:
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c1.speed = 150; //   
c1.show(); //     
  C++          
(B)         ?
C++ ,    󰌹          
               
     :
1.  
●          ●         ●  
    󰌹             
 
:
  {
:
 () {}
};
, display()    main()           
2.  
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●            ●      
     ●      
:
  {
:
;
};
  󰌹 :
 ;
obj.secret = 10; // 
    
  ( 
)



 
  (    )
   

  (  󰌹 )
 ()

   󰌹 󰌹  
   

/  󰌹
  
  

 
  󰌹  
     󰌹:
    (          )
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 deposit(), withdraw() (         
)
           
()       
, OOP       
  ?
   ( )    ( )      
   
   :     ,          
     
    ?
     :           
   , :

  
    󰌹  - 󰌹 , C++     (Vehicle)
  Car, Bike, Truck        
  :
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1.   : 
  󰌹,    
2.  ( )
-     
3.  
          
4.    
        
   
 :
  {
:
 ;
 () {
cout << ": " << speed;
}
};
 :
  :   {
:
 ;
};
    :
  () {
 1;
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c1.speed = 120; //    
c1. = "";
c1.showSpeed(); //     
}
   (  )
      󰌹    󰌹   󰌹   
   Car    Vehicle       
      󰌹     ()    ,
       󰌹 
       󰌹    -    
,   C++ ,          

C++ ,       󰌹      
                
      󰌹        
      , 󰌹       
         :     , 
, :         󰌹  
   C++    -      
           
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8.   ?        ? 
    󰌹       󰌹   
            
:  󰌹  ,          
   󰌹 +, -, *  ==           
      ,    ,     󰌹 ? 
                ?
         -  󰌹
             , 󰌹 
             ,  
 ,               
  
󼫹󼫺   ?
  C++         -
  (   )  󰌹       
 
󷷑󷷒󷷓󷷔  :
 , +     
    ,       ,   
 ,            
      -  󰌹  
󷘹󷘴󷘵󷘶󷘷󷘸   
 󰌹      󰌹   :

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  {
 , ;
:
Complex(int r=0, int i=0) : real(r), imag(i) {}
  + ( & c) {
 ( + .,  + .)  ;
}
};
,   󰌹:

 c1(2, 3), c2(4, 5);
 c3 = c1 + c2;
   ,      +    "    
  "
󷷑󷷒󷷓󷷔     ,  -      
󼫹󼫺      ?
1.      
o    ,  addComplex(c1, c2)    
   
o   ,   c1 + c2 󰌹 
o     -       
2.    
o       󰌹 +       
   󰌹  ?
o   -     
      
3.    
Easy2Siksha.com
o        
o             
4. FLEXIBILITY
o       󰌹      
o :             󰌹 == 
 
󷷑󷷒󷷓󷷔 :      ,    
󼫹󼫺 󰌹     
C++               :
1. 󰌹 
+, -, *, /, %
:    ,    
2.  
==, !=, <, >, <=, >=
:        
3.  
&&, ||, !
:   󰌹  󰌹     
4.  
&, |, ^, ~, <<, >>
:   (cout)  󰌹 <<   
5.  
Easy2Siksha.com
      󰌹 =      
6. 󰌹/ 
++, -- (   )
7.  
        󰌹 []      
8.    
           󰌹 ()    
 
9.  
->, *    󰌹     
󼫹󼫺  󰌹     
                󰌹
      
  󰌹     :
:: ( )
( )
.* (    󰌹 )
?: (  )
   (  )
 (   )
󼫹󼫺         ?
1.     
Easy2Siksha.com
o ::  .   C++         󰌹 
o          
2.   
o  sizeof        ,    
 
o :   sizeof       
    , 󰌹     
3.    
o            ( ?:)
o                
 
󷷑󷷒󷷓󷷔 :              
        
󽆪󽆫󽆬
  C++          
   -        , 󰌹
      ,      —  
        
                ,  C++
              
    —          
,        
    󰌹         
       ,   󰌹    ”