1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
//############################################################################
// Programmation IV - 2002 - Week 05
//############################################################################
// $Id$
module M0 {
def partition[a](xs: List[a], pred: a => boolean): Pair[List[a], List[a]] = {
if (xs.isEmpty)
Pair(List(),List())
else {
val tailPartition = partition(xs.tail, pred);
if (pred(xs.head))
Pair(xs.head :: tailPartition._1, tailPartition._2)
else
Pair(tailPartition._1, xs.head :: tailPartition._2)
}
}
def quicksort[a] (less : (a,a) => boolean) (xs : List[a]) : List[a] = {
if (xs.isEmpty)
xs
else {
val pivot = xs.head;
val sub = partition(xs.tail, (elem : a => less(elem, pivot)));
quicksort(less)(sub._1) ::: List(pivot) ::: quicksort(less)(sub._2)
}
}
def test = {
System.out.println(partition[int](List(1,2,3,4,5,6,7,8), (x => x < 0)));
System.out.println(partition[int](List(1,2,3,4,5,6,7,8), (x => x < 5)));
System.out.println(partition[int](List(1,2,3,4,5,6,7,8), (x => x < 9)));
System.out.println();
System.out.println(partition[int](List(8,7,6,5,4,3,2,1), (x => x < 0)));
System.out.println(partition[int](List(8,7,6,5,4,3,2,1), (x => x < 5)));
System.out.println(partition[int](List(8,7,6,5,4,3,2,1), (x => x < 9)));
System.out.println();
System.out.println(partition[int](List(7,2,1,5,4,3,8,6), (x => x < 0)));
System.out.println(partition[int](List(7,2,1,5,4,3,8,6), (x => x < 5)));
System.out.println(partition[int](List(7,2,1,5,4,3,8,6), (x => x < 9)));
System.out.println();
System.out.println(quicksort[int]((x,y) => x < y)(List(7,2,1,5,4,3,8,6)));
System.out.println();
}
}
//############################################################################
module M1 {
def partition[a](xs: List[a], pred: a => boolean): Pair[List[a], List[a]] = {
xs.foldRight[Pair[List[a], List[a]]](Pair(List(), List())) {
(x, p) => if (pred (x)) Pair(x :: p._1, p._2) else Pair(p._1, x :: p._2)
}
}
def quicksort[a] (less : (a,a) => boolean) (xs : List[a]) : List[a] = {
if (xs.isEmpty)
xs
else {
val pivot = xs.head;
val sub = partition(xs.tail, (elem : a => less(elem, pivot)));
quicksort(less)(sub._1) ::: List(pivot) ::: quicksort(less)(sub._2)
}
}
def test = {
System.out.println(partition[int](List(1,2,3,4,5,6,7,8), (x => x < 0)));
System.out.println(partition[int](List(1,2,3,4,5,6,7,8), (x => x < 5)));
System.out.println(partition[int](List(1,2,3,4,5,6,7,8), (x => x < 9)));
System.out.println();
System.out.println(partition[int](List(8,7,6,5,4,3,2,1), (x => x < 0)));
System.out.println(partition[int](List(8,7,6,5,4,3,2,1), (x => x < 5)));
System.out.println(partition[int](List(8,7,6,5,4,3,2,1), (x => x < 9)));
System.out.println();
System.out.println(partition[int](List(7,2,1,5,4,3,8,6), (x => x < 0)));
System.out.println(partition[int](List(7,2,1,5,4,3,8,6), (x => x < 5)));
System.out.println(partition[int](List(7,2,1,5,4,3,8,6), (x => x < 9)));
System.out.println();
System.out.println(quicksort[int]((x,y) => x < y)(List(7,2,1,5,4,3,8,6)));
System.out.println();
}
}
//############################################################################
module M2 {
def powerset[a] (s : List[a]) : List[List[a]] = {
if (s.isEmpty)
List(List())
else {
val x = s.head;
val withoutX = powerset(s.tail);
withoutX ::: withoutX.map(s1 : List[a] => x::s1)
}
}
def test = {
System.out.println(powerset(List()));
System.out.println(powerset(List(1)));
System.out.println(powerset(List(1,2)));
System.out.println(powerset(List(1,2,3)));
System.out.println(powerset(List(1,2,3,4)));
System.out.println();
}
}
//############################################################################
module M3 {
type Placement = List[Pair[int,int]];
def queens(n: int): List[Placement] = {
def placeQueens(row: int): List[Placement] = {
if (row == 0)
List(List())
else {
def isSafe(column: int, placement: Placement): boolean =
placement forall {
pos => pos._2 != column
&& abs(pos._2 - column) != row - pos._1
}
def adjoinRow(placement: Placement): List[Placement] =
range(1, n)
filter (column => isSafe(column, placement))
map (column => Pair(row, column) :: placement);
placeQueens(row - 1) flatMap adjoinRow
}
}
placeQueens(n)
}
def range(lo: int, hi: int): List[int] =
if (lo > hi) List()
else lo :: range(lo + 1, hi);
def abs(x: int) = if (x < 0) 0 - x else x;
def test = {
System.out.println("queens(1) = " + queens(1));
System.out.println("queens(2) = " + queens(2));
System.out.println("queens(3) = " + queens(3));
System.out.println("queens(4) = " + queens(4));
System.out.println();
}
}
//############################################################################
module Test {
def main(args: Array[String]): unit = {
M0.test;
M1.test;
M2.test;
M3.test;
()
}
}
//############################################################################
|
