2.
2023
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(C++ )
: 3 :75
: - ,
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1. ? ?
f(x) = 5x4 + 7x +3 0 (x¹)
15
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Quick Sort
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C++
2023
/
(C++ )
: 3 :75
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-
1. ? ?
f(x) = 5x4 + 7x +3 0 (x¹)
15
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f(x) = 5x⁴ + 7x + 3 O(x⁴)
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O(x⁴)
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2.
f(x) = 5x⁴ + 7x + 3
:
x , x⁴ x
:
• 7x
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≤ 7x⁴
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[5] = {10, 20, 30, 40, 50};
, arr 5 -
• :
1000 4 , :
o [0] → 1000
o [1] → 1004
o [2] → 1008
o [3] → 1012
o [4] → 1016
,
2. -
• :
2.
[2][3] = {
{1, 2, 3},
{4, 5, 6}
};
2x3
• :- (C )
,
o [0][0] → 1000
o [0][1] → 1004
o [0][2] → 1008
o [1][0] → 1012
o [1][1] → 1016
o [1][2] → 1020
,
3. -
• :
[2][2][3] = {
{
{1, 2, 3},
{4, 5, 6}
},
{
{7, 8, 9},
{10, 11, 12}
}
};
2x2x3
• : - , [0][0]
, [0][1], [1][0],
,
2.
(C )
# <stdio.h>
() {
[5] = {10, 20, 30, 40, 50};
[2][3] = {{1, 2, 3}, {4, 5, 6}};
[2][2][3] = {
{{1, 2, 3}, {4, 5, 6}},
{{7, 8, 9}, {10, 11, 12}}
};
printf("1D : %d\n", arr[2]); // : 30
printf("2D : %d\n", [1][2]); // : 6
printf("3D : %d\n", [1][0][2]); // : 9
0;
}
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• 60 → 0 ( ) -
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5. Quick Sort Quick Sort 15, 10, 13, 9, 12, 7
Quick Sort
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1
= 15
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• 15 → : 10, 13, 9, 12, 7
•
15
:
7, 10, 13, 9, 12 | 15
( , ) 15
'
' ' Quick Sort :
10, 13, 9, 12, 7
2.
2
: 10, 13, 9, 12, 7 = 10
:
• 10 → 9, 7
• 10 → 13, 12
:
7, 9 | 10 | 13, 12
10 '
' :
: 7, 9 : 13, 12
3
7 , 9 = 7
?
→ 9
:
7 | 9
4
13 , 12 = 13
→ 12 →
:
12 | 13
2.
:
7, 9, 10, 12, 13, 15
:
7, 9, 10, 12, 13, 15
, ' ,
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= O(n log n)
-
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2.
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= 1
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= O(n²)
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:
15, 10, 13, 9, 12, 7
: 7, 9, 10, 12, 13, 15
:
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• → O(n log n)
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6.
?
:
-
:
[5, 12, 18, 23, 45, 67, 89]
2.
45 :
• 5 →
• 12 →
• 18 →
• 23 →
• 45 → !
5
, - :
1.
2. →
3. →
4. →
;
, ,
:
[5, 12, 18, 23, 45, 67, 89]
45 :
• = 23 → 45 > 23 →
• - = [45, 67, 89] = 67 → 45 < 67 →
• - = [45] = 45 → !
5 3
• : , n
, O(n)
2.
• : n , O(log n)
:
• 1,000 :
o → 1,000
o → 10 (₂(1000) ≈ 10 )
',
(, , , ):
1. > :
-1 //
2. ← ( + ) / 2
3. arr[mid] = key:
4.
<arr[mid]:
BinarySearchRecursive (arr, low, mid - 1, key)
5. :
BinarySearchRecursive (arr, mid + 1, high, key)
(C )
# <stdio.h>
( [], , , ) {
( > ) -1 ;
= ( + ) / 2;
(arr[mid] == key) ;
(key <arr[mid]) binarySearch(arr, low, mid - 1, key) ;
binarySearch(arr, mid + 1, high, key) ;
}
() {
[] = {5, 12, 18, 23, 45, 67, 89};
n = ()/ ([0]);
2.
= 45;
int = (arr, 0, n-1, );
( != -1)
printf("%d ' \n", );
printf("
\n");
0;
}
1.
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)
2.
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O(log n)
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• 2 → n/2
• 3 → n/4 ... 1
= log₂(n)
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cout << " : " << ;
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= 0;
= "";
cout << "\n ";
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= n;
cout << "\n ";
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= s. ;
= s.name;
cout << "\n ";
}
() {
cout << "\n: " << << " : " << ;
}
};
2.
() {
s1; //
s1.();
s2(101, ""); //
s2.();
s3(s2); //
s3. ();
0;
}
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s1 → runs s2 →
runs s3 s2 →
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# <iostream>
std ;
{
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:
( = 0, = 0) {
= r;
= i;
}
// +
+ (const & obj) {
;
. = + .;
. = + .;
;
}
() {
cout << << " + " << << "i" << endl;
}
};
() {
c1(3, 4), c2(1, 2);
c3 = c1 + c2; // +
2.
cout << " : ";
c3.();
0;
}
:
: 4 + 6i
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# <iostream>
std ;
//
{
:
() {
cout << " " << endl;
}
};
// (-)
: {
:
() {
cout << " " << endl;
}
};
//
{
:
() {
cout << " " << endl;
}
};
// (-) (-)
: , {
:
() {
cout << " " << endl;
}
};
() {
;
m.showPerson(); //
m.showEmployee(); //
m.showDepartment(); //
m.showManager(); //
0;
}
2.
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