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
|
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.util;
import org.apache.commons.math3.exception.NullArgumentException;
import java.io.Serializable;
import java.util.Arrays;
/**
* A Simple K<sup>th</sup> selector implementation to pick up the K<sup>th</sup> ordered element
* from a work array containing the input numbers.
*
* @since 3.4
*/
public class KthSelector implements Serializable {
/** Serializable UID. */
private static final long serialVersionUID = 20140713L;
/** Minimum selection size for insertion sort rather than selection. */
private static final int MIN_SELECT_SIZE = 15;
/** A {@link PivotingStrategyInterface} used for pivoting */
private final PivotingStrategyInterface pivotingStrategy;
/** Constructor with default {@link MedianOf3PivotingStrategy median of 3} pivoting strategy */
public KthSelector() {
this.pivotingStrategy = new MedianOf3PivotingStrategy();
}
/**
* Constructor with specified pivoting strategy
*
* @param pivotingStrategy pivoting strategy to use
* @throws NullArgumentException when pivotingStrategy is null
* @see MedianOf3PivotingStrategy
* @see RandomPivotingStrategy
* @see CentralPivotingStrategy
*/
public KthSelector(final PivotingStrategyInterface pivotingStrategy)
throws NullArgumentException {
MathUtils.checkNotNull(pivotingStrategy);
this.pivotingStrategy = pivotingStrategy;
}
/**
* Get the pivotin strategy.
*
* @return pivoting strategy
*/
public PivotingStrategyInterface getPivotingStrategy() {
return pivotingStrategy;
}
/**
* Select K<sup>th</sup> value in the array.
*
* @param work work array to use to find out the K<sup>th</sup> value
* @param pivotsHeap cached pivots heap that can be used for efficient estimation
* @param k the index whose value in the array is of interest
* @return K<sup>th</sup> value
*/
public double select(final double[] work, final int[] pivotsHeap, final int k) {
int begin = 0;
int end = work.length;
int node = 0;
final boolean usePivotsHeap = pivotsHeap != null;
while (end - begin > MIN_SELECT_SIZE) {
final int pivot;
if (usePivotsHeap && node < pivotsHeap.length && pivotsHeap[node] >= 0) {
// the pivot has already been found in a previous call
// and the array has already been partitioned around it
pivot = pivotsHeap[node];
} else {
// select a pivot and partition work array around it
pivot = partition(work, begin, end, pivotingStrategy.pivotIndex(work, begin, end));
if (usePivotsHeap && node < pivotsHeap.length) {
pivotsHeap[node] = pivot;
}
}
if (k == pivot) {
// the pivot was exactly the element we wanted
return work[k];
} else if (k < pivot) {
// the element is in the left partition
end = pivot;
node = FastMath.min(2 * node + 1, usePivotsHeap ? pivotsHeap.length : end);
} else {
// the element is in the right partition
begin = pivot + 1;
node = FastMath.min(2 * node + 2, usePivotsHeap ? pivotsHeap.length : end);
}
}
Arrays.sort(work, begin, end);
return work[k];
}
/**
* Partition an array slice around a pivot.Partitioning exchanges array elements such that all
* elements smaller than pivot are before it and all elements larger than pivot are after it.
*
* @param work work array
* @param begin index of the first element of the slice of work array
* @param end index after the last element of the slice of work array
* @param pivot initial index of the pivot
* @return index of the pivot after partition
*/
private int partition(final double[] work, final int begin, final int end, final int pivot) {
final double value = work[pivot];
work[pivot] = work[begin];
int i = begin + 1;
int j = end - 1;
while (i < j) {
while (i < j && work[j] > value) {
--j;
}
while (i < j && work[i] < value) {
++i;
}
if (i < j) {
final double tmp = work[i];
work[i++] = work[j];
work[j--] = tmp;
}
}
if (i >= end || work[i] > value) {
--i;
}
work[begin] = work[i];
work[i] = value;
return i;
}
}
|
