[ACM-ICPC] Sort

Transcript

1. Sort ֲࢸݢʢKuoE0ʣ KuoE0.tw@gmail.com KuoE0.ch
2. Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) http://creativecommons.org/licenses/by-sa/3.0/ Latest update: Feb 27, 2013
3. Bubble Sort ᔅ๐ഉং๏
4. Algorithm 1. ኺୈҰݸݩૉ։࢝ൺֱ㑌Ұሣ૬ᬠݩૉ 2. एୈҰݸݩૉେԙୈೋݸݩૉଇަ׵ 3. 㑌࣍ᬇݮधཁൺֱతݩૉሣ௚౸ෆधൺ ֱ
5. Origin 10 2 7 9 1 10 9 7 2 1
6. 7 2 10 1st Iteration 9 1
7. 7 2 10 10 2 1st Iteration 9 1
8. 7 2 10 10 2 1st Iteration 9 1
9. 7 7 2 10 10 2 1st Iteration 9 1 2
10. 7 7 2 10 10 2 1st Iteration 9 1 2
11. 7 7 2 10 10 2 1st Iteration 9 1 2 9 7
12. 7 7 2 10 10 2 1st Iteration 9 1 2 9 7
13. 7 7 2 10 10 2 1st Iteration 9 1 2 9 7 1 9
14. 7 7 2 10 10 2 1st Iteration 9 1 2 9 7 1 9
15. 7 7 2 10 10 2 1st Iteration 2 7 9 1 10 9 1 2 9 7 1 9 10 1
16. 1 7 2 2nd Iteration 10 9
17. 1 7 2 7 2 2nd Iteration 10 9
18. 1 7 2 7 2 2nd Iteration 10 9
19. 1 7 2 7 2 2nd Iteration 10 9 2 9
20. 1 7 2 7 2 2nd Iteration 10 9 2 9
21. 1 1 7 2 7 2 2nd Iteration 10 9 2 9 7
22. 1 1 7 2 7 2 2nd Iteration 10 9 2 9 7
23. 1 1 7 2 7 2 2nd Iteration 2 7 1 9 10 10 9 2 9 7 1 9
24. 3rd Iteration 10 9 7 2 1
25. 3rd Iteration 10 9 7 2 1 2 7
26. 3rd Iteration 10 9 7 2 1 2 7
27. 3rd Iteration 10 9 7 2 1 2 7 1 2
28. 3rd Iteration 10 9 7 2 1 2 7 1 2
29. 3rd Iteration 10 9 7 2 1 2 1 7 9 10 2 7 1 2 1 7
30. 4th Iteration 10 9 7 2 1
31. 4th Iteration 10 9 7 2 1 2 1
32. 4th Iteration 10 9 7 2 1 2 1
33. 4th Iteration 1 2 7 9 10 10 9 7 2 1 2 1 1 2
34. Result 1 2 7 9 10 10 9 7 2 1
35. Source Code for ( int i = 0; i < n; ++i ) for ( int j = 0; j < n - 1 - i; ++j ) if ( A[ j ] > A[ j + 1 ] ) swap( A[ j ], A[ j + 1 ] );
36. Time Complexity for ( int i = 0; i < n; ++i ) for ( int j = 0; j < n - 1 - i; ++j ) if ( A[ j ] > A[ j + 1 ] ) swap( A[ j ], A[ j + 1 ] ); ࠷େ॥؀࣍Ꮠུဟ ୈ 1 ૚᫮ᅲ n ୈ 2 ૚᫮ᅲ n
37. n × n = n2 Time Complexity: O(n2)
38. ኺൣྫதՄᚙݱ... ໣අڐଟ࣌ؒᒾ查༗ংᏐሣ
39. Merge Sort ߹ซഉং๏
40. Algorithm ࠾༻ divide & conquer ࡦུ
41. Divide ሡᙛલᏐྻሣ൒੾ׂᬇ᫮ਐߦ ௚౸ᷮႫҰݸݩૉ
42. 2 9 4 3 8 7 5 1 6 2 9 4 3 8 7 5 1 6 2 9 4 3 8 7 5 1 6 2 9 4 8 3 5 7 6 1 9 2
43. Conquer 1. ར༻ၷݸࢦඪࢦ޲ၷݸ༗ংᏐྻ A ᢛ B 2. ൺֱࢦඪࢦ޲తᏐ值 3. ሡֱখతᏐ值์ೖ৽తᏐྻ Cɼฒሡ֘ࢦඪ ࢦ޲ԼҰᏐ值 4. ௚౸๭Ұࢦඪࢦ޲Ꮠྻ݁ඌɼሡ㠥ҰᏐྻႫ ᰨతᏐ值์౎ೖᏐྻ C
44. Merge Two Sequence 9 8 7 6 5 4 3 2 1
45. Merge Two Sequence 9 8 7 6 5 4 3 2 1
46. Merge Two Sequence 9 8 7 6 5 4 3 2 1
47. Merge Two Sequence 9 8 7 6 5 4 3 2 1
48. Merge Two Sequence 9 8 7 6 5 4 3 2 1
49. Merge Two Sequence 9 8 7 6 5 4 3 2 1
50. Merge Two Sequence 9 8 7 6 5 4 3 2 1
51. Merge Two Sequence 9 8 7 6 5 4 3 2 1
52. Merge Two Sequence 9 8 7 6 5 4 3 2 1
53. Merge Two Sequence 9 8 7 6 5 4 3 2 1
54. 1 2 3 4 5 6 7 8 9 2 3 4 8 9 1 5 6 7 2 4 9 3 8 5 7 1 6 2 9 4 8 3 5 7 6 1 9 2
55. int mergeSort( int L, int R ) { if ( R - L == 1 ) return; int mid = ( R + L ) / 2, C[ R - L ]; mergeSort( L, mid ); mergeSort( mid, R ); for ( int p1 = L, p2 = mid, p = 0; p < R - L; ++p ) { if ( ( p1 != mid && A[ p1 ] < A[ p2 ] ) || p2 == R ) C[ p ] = A[ p1++ ]; else C[ p ] = A[ p2++ ]; } for ( int i = L; i < R; ++i ) A[ i ] = C[ i - L ]; } Source Code
56. Time Complexity total time
57. Time Complexity total time n 2 * (n/2) = n ... n * (n/n) = n
58. Best height }log2n
59. Time Complexity: O(nlog2n)
60. Quick Sort շ଎ഉং๏
61. Algorithm ࠾༻ divide & conquer ࡦུ
62. Divide ኺᏐྻத௅ग़Ұݸݩૉ࡞ҝ pivotɼར ༻ pivot ሡݪᏐྻ෼ҝၷݸࢠᏐྻɿ • ॴ༗ݩૉখԙ pivot తᏐྻ A • ॴ༗ݩૉେԙ pivot తݩૉతᏐྻ B • ౳ԙ pivot తݩૉՄ์ஔࡏ೚Ұݸத
63. 2 9 4 3 8 7 5 1 6
64. 2 9 4 3 8 7 5 1 6 2 7 4 3 5 1 6 9 8
65. 9 8 2 4 3 5 1 6 2 9 4 3 8 7 5 1 6 2 7 4 3 5 1 6 9 8
66. 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 7 4 3 5 1 6 9 8 3
67. 4 5 6 2 1 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 7 4 3 5 1 6 9 8 3
68. 4 5 6 2 1 2 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 7 4 3 5 1 6 9 8 3 1
69. 4 5 6 2 1 2 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 2 7 4 3 5 1 6 9 8 3 1
70. 4 5 6 5 6 2 1 2 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 2 7 4 3 5 1 6 9 8 3 1 4
71. 5 6 4 5 6 5 6 2 1 2 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 2 7 4 3 5 1 6 9 8 3 1 4
72. 5 6 5 4 5 6 5 6 2 1 2 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 2 7 4 3 5 1 6 9 8 3 1 4 6
73. 5 6 5 4 5 6 5 6 2 1 2 9 8 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 5 2 7 4 3 5 1 6 9 8 3 1 4 6
74. 5 6 5 4 5 6 5 6 2 1 2 9 8 9 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 2 5 2 7 4 3 5 1 6 9 8 3 1 4 6 8
75. 5 6 5 4 5 6 5 6 2 1 2 9 8 9 2 4 3 5 1 6 2 4 5 1 6 2 9 4 3 8 7 5 1 6 9 2 5 2 7 4 3 5 1 6 9 8 3 1 4 6 8
76. Conquer ༝ԙࢠᏐྻቮඃ pivot ෼ҝၷஈɼҰஈ খԙ౳ԙ pivot తᏐྻ Aɼ㠥Ұஈେԙ ౳ԙ pivot తᏐྻ Bɻ
77. Conquer ༝ԙࢠᏐྻቮඃ pivot ෼ҝၷஈɼҰஈ খԙ౳ԙ pivot తᏐྻ Aɼ㠥Ұஈେԙ ౳ԙ pivot తᏐྻ Bɻ A B C
78. 2 2
79. 2 2 1
80. 2 2 1
81. 1 2 1 2 2 5 2 5 1 6
82. 1 2 1 2 2 5 2 5 1 6
83. 5 6 1 2 1 2 5 6 2 5 2 5 1 6 4
84. 5 6 1 2 1 2 5 6 2 5 2 5 1 6 4
85. 4 5 6 5 6 1 2 1 2 4 5 6 5 6 2 5 2 5 1 6 4 3
86. 4 5 6 5 6 1 2 1 2 4 5 6 5 6 2 5 2 5 1 6 4 3
87. 1 2 3 4 5 6 4 5 6 5 6 1 2 1 2 4 5 6 5 6 1 2 3 4 5 6 9 2 5 2 5 9 1 6 4 3 8
88. 1 2 3 4 5 6 4 5 6 5 6 1 2 1 2 4 5 6 5 6 1 2 3 4 5 6 9 2 5 2 5 9 1 6 4 3 8
89. 8 9 1 2 3 4 5 6 8 9 4 5 6 5 6 1 2 1 2 4 5 6 5 6 1 2 3 4 5 6 9 2 5 2 5 9 7 1 6 4 3 8
90. 8 9 1 2 3 4 5 6 8 9 4 5 6 5 6 1 2 1 2 4 5 6 5 6 1 2 3 4 5 6 9 2 5 2 5 9 7 1 6 4 3 8
91. 8 9 1 2 3 4 5 6 8 9 4 5 6 5 6 1 2 1 2 4 5 6 5 6 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 9 2 5 2 5 9 7 1 6 4 3 8
92. void quickSort( int L, int R ) { if ( R - L <= 1 ) return; int pivot = N[ L ], p1 = L + 1, p2 = R - 1; do { while ( N[ p1++ ] <= pivot ) ; while ( N[ p2-- ] > pivot ) ; if ( p1 < p2 ) swap( N[ p1 ], N[ p2 ] ); } while ( p1 < p2 ); quickSort( L + 1, p1 ); quickSort( p1, R ); for ( int i = L + 1; i < p1; ++i ) swap( N[ i - 1 ], N[ i ] ); } Source Code
93. 9 3 How to Divide 4 1 5 8 6 7 2
94. 9 3 How to Divide 4 1 5 8 6 4 7 2
95. 9 3 How to Divide 4 1 5 8 6 4 7 2
96. 9 3 How to Divide 4 1 5 8 6 4 7 2
97. 9 3 How to Divide 4 1 5 8 6 4 7 2
98. 9 3 How to Divide 4 1 5 8 6 4 7 2
99. 9 3 How to Divide 4 1 5 8 6 4 7 2
100. 9 3 How to Divide 4 1 5 8 6 4 7 2
101. 9 3 How to Divide 4 1 5 8 6 4 7 2
102. 9 3 How to Divide 4 1 5 8 6 4 7 2
103. 9 3 How to Divide 4 1 5 8 6 4 7 2 4 1 3 2 5 8 7 9 6
104. 5 6 7 8 9 3 2 1 4 How to Conquer
105. 5 6 7 8 9 3 2 1 4 How to Conquer
106. 5 6 7 8 9 3 2 1 4 How to Conquer
107. 5 6 7 8 9 3 2 1 4 How to Conquer
108. void quickSort( int L, int R ) { if ( R - L <= 1 ) return; int pivot = N[ R - 1 ], p = L; for ( int i = L; i < R - 1; ++i ) { if ( N[ i ] <= pivot ) { swap( N[ i ], N[ p ] ); ++p; } } swap( N[ R - 1 ], N[ p ] ); quickSort( L, p ); quickSort( p + 1, R ); } In-place Version
109. 9 4 3 6 5 1 8 7 How to Divide 2
110. 9 4 3 6 5 1 8 7 How to Divide 2 6
111. 9 4 3 6 5 1 8 7 How to Divide 2 2 6
112. 9 4 3 6 5 1 8 7 How to Divide 2 2 6
113. 9 4 3 6 5 1 8 7 How to Divide 2 2 2 6
114. 9 9 4 3 6 5 1 8 7 How to Divide 2 2 2 6
115. 9 9 4 4 3 6 5 1 8 7 How to Divide 2 2 2 9 6
116. 9 9 4 4 3 6 5 1 8 7 How to Divide 2 2 2 9 6
117. 9 9 4 4 3 6 5 1 8 7 How to Divide 2 2 2 9 4 6
118. 9 9 4 4 3 3 6 5 1 8 7 How to Divide 2 2 2 9 4 6
119. 9 9 4 4 3 3 6 5 1 8 7 How to Divide 2 2 2 9 4 6
120. 9 9 4 4 3 3 6 5 1 8 7 How to Divide 2 2 2 9 4 3 6
121. 9 9 4 4 3 3 6 5 1 8 7 8 How to Divide 2 2 2 9 4 3 6
122. 9 9 4 4 3 3 6 5 1 8 7 8 8 How to Divide 2 2 2 9 4 3 6
123. 9 9 4 4 3 3 6 5 1 8 7 8 7 8 How to Divide 2 2 2 9 4 3 6
124. 9 9 4 4 3 3 6 5 1 8 7 8 7 8 7 How to Divide 2 2 2 9 4 3 6
125. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 9 4 3 6
126. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 9 4 3 6
127. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 5 9 4 3 6
128. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 5 9 4 3 1 6
129. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 5 9 4 3 1 6
130. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 5 9 4 3 1 1 6
131. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 5 9 4 3 1 1 6
132. 9 9 4 4 3 3 6 5 1 5 8 7 8 7 8 7 How to Divide 2 2 2 5 9 4 3 1 1 6 2 5 4 3 1 8 9 7
133. 6 How to Conquer 1 4 2 3 5 8 7 9 1 4 2 3 5 8 7 9
134. 6 How to Conquer 1 4 2 3 5 8 7 9 1 4 2 3 5 8 7 9
135. Time Complexity total time
136. Time Complexity total time n 2 * (n/2) = n ... n * (n/n) = n
137. Best height }log2n
138. Worst height }n
139. Time Complexity: O(nlog2n) ~ O(n2)
140. Average Time Complexity: O(nlog2n)
141. Builtin Function ೗Ռ㟬७ហ૝ཁഉংඁྃ...
142. qsort (C/C++) •include <stdlib.h> or <cstdlib> •compare function void qsort (void* base, size_t num, size_t size, int (*compar)(const void*,const void*));
143. void qsort (void* base, size_t num, size_t size, int (*compar)(const void*,const void*)); base: ࢦ޲ཉഉংྻදى࢝Ґஔ೭ࢦඪ num: ཉഉংతݩૉᏐྔ size: ֤ݩૉେখ compar: ൺֱവࣜతവࣜࢦඪ
144. Compare Function Function prototype: int function_name(const void* p1, const void* p2); return value means less than 0 p1 < p2 equal to 0 p1 == p2 greater than 0 p1 > p2
145. Example int cmp( const void* p1, const void* p2 ) { return *(int*)p1 - *(int*)p2; } int main() { int n, N[ 10010 ]; while ( scanf( “%d”, &n ) != EOF ) { int x; for ( int i = 0; i < n; ++i ) { scanf( “%d”, &x ); N[ i ] = x; } qsort( N, n, sizeof( int ), cmp ); } return 0; }
146. sort (STL) •include <algorithm> •compare function for customized behavior template <class RandomAccessIterator> void sort (RandomAccessIterator first, RandomAccessIterator last); template <class RandomAccessIterator, class Compare> void sort (RandomAccessIterator first, RandomAccessIterator last, Compare comp);
147. template <class RandomAccessIterator> void sort (RandomAccessIterator first, RandomAccessIterator last); first: ࢦ޲ཉഉংྻදى࢝Ґஔ೭ iterator last: ࢦ޲ཉഉংྻද݁ඌҐஔ೭ iterator ࢦඪՄඃ᫚ܕҝ iterator! ґর֘ࢿྉܕผతখԙӡࢉࢠ (<) ࡞ҝഉংґᎦʂ Sort by operator <
148. Customized Data Type Function prototype for operator <: bool operator< ( const type_name &p ) const; return value means TRUE this < p FALSE this >= p
149. Example (builtin type) int main() { int n, N[ 10010 ]; while ( scanf( “%d”, &n ) != EOF ) { int x; for ( int i = 0; i < n; ++i ) { scanf( “%d”, &x ); N[ i ] = x; } sort( N, N + n ); } return 0; }
150. Example (custom type) struct T { int x, y; bool operator< ( const T &p ) const { return x == p.x ? x < p.x : y < p.y; } }; T pt[ 10010 ]; int main() { int n; while ( scanf( “%d”, &n ) != EOF ) { int x, y; for ( int i = 0; i < n; ++i ) { scanf( “%d %d”, &x, &y ); pt[ i ].x = x, pt[ i ].y = y; } sort( pt, pt + n ); } return 0; }
151. template <class RandomAccessIterator, class Compare> void sort (RandomAccessIterator first, RandomAccessIterator last, Compare comp); first: ࢦ޲ཉഉংྻදى࢝Ґஔ೭ iterator last: ࢦ޲ཉഉংྻද݁ඌҐஔ೭ iterator comp: ൺֱവࣜ Sort by Compare Function ࢦඪՄඃ᫚ܕҝ iterator!
152. Customized Data Type Function prototyp: bool function_name ( type_name p1, type_name p2 ); return value means TRUE p1 < p2 FALSE p1 >= p2
153. Example (descending) bool descending( int p1, int p2 ) { return p1 >= p2; } int main() { int n, N[ 10010 ]; while ( scanf( “%d”, &n ) != EOF ) { int x; for ( int i = 0; i < n; ++i ) { scanf( “%d”, &x ); N[ i ] = x; } sort( N, N + n, descending ); } return 0; }
154. Reference • ๯๐ഉং - ҡجඦՊɼࣗ༝తඦՊશॻ • ᓤซഉং - ҡجඦՊɼࣗ༝తඦՊશॻ • շ଎ഉং - ҡجඦՊɼࣗ༝తඦՊશॻ • qsort - C++ Reference • sort - C++ Reference
155. 10810 - Ultra-QuickSort Practice Now
156. Thank You for Your Listening.