Mega Code Archive
Finds the value in the range (start,limit) of the largest element (rank) where the count of all smaller element
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/**
* Collection of routines for counting the distribution of the values
* in an int[] array.
*
* @author Fred Toussi (fredt@users dot sourceforge.net)
* @version 1.7.2
* @since 1.7.2
*/
public class ArrayCounter {
/**
* Returns an int[] array of length segments containing the distribution
* count of the elements in unsorted int[] array with values between min
* and max (range). Values outside the min-max range are ignored<p>
*
* A usage example is determining the count of people of each age group
* in a large int[] array containing the age of each person. Called with
* (array, 16,0,79), it will return an int[16] with the first element
* the count of people aged 0-4, the second element the count of those
* aged 5-9, and so on. People above the age of 79 are excluded. If the
* range is not a multiple of segments, the last segment will be cover a
* smaller sub-range than the rest.
*
*/
public static int[] countSegments(int[] array, int elements,
int segments, int start, int limit) {
int[] counts = new int[segments];
long interval = calcInterval(segments, start, limit);
int index = 0;
int element = 0;
if (interval <= 0) {
return counts;
}
for (int i = 0; i < elements; i++) {
element = array[i];
if (element < start || element >= limit) {
continue;
}
index = (int) ((element - start) / interval);
counts[index]++;
}
return counts;
}
/**
* With an unsorted int[] array and with target a positive integer in the
* range (1,array.length), finds the value in the range (start,limit) of the
* largest element (rank) where the count of all smaller elements in that
* range is less than or equals target. Parameter margin indicates the
* margin of error in target<p>
*
* In statistics, this can be used to calculate a median or quadrile value.
* A usage example applied to an array of age values is to determine
* the maximum age of a given number of people. With the example array
* given in countSegments, rank(array, c, 6000, 18, 65, 0) will return an age
* value between 18-64 (inclusive) and the count of all people aged between
* 18 and the returned value(exclusive) will be less than or equal 6000.
*
*/
public static int rank(int[] array, int elements, int target, int start,
int limit, int margin) {
final int segments = 256;
int elementCount = 0;
int currentLimit = limit;
for (;;) {
long interval = calcInterval(segments, start, currentLimit);
int[] counts = countSegments(array, elements, segments, start,
currentLimit);
for (int i = 0; i < counts.length; i++) {
if (elementCount + counts[i] < target) {
elementCount += counts[i];
start += interval;
} else {
break;
}
}
if (elementCount + margin >= target) {
return start;
}
if (interval <= 1) {
return start;
}
currentLimit = start + interval < limit ? (int) (start + interval)
: limit;
}
}
/**
* Helper method to calculate the span of the sub-interval. Simply returns
* the cieling of ((limit - start) / segments) and accounts for invalid
* start and limit combinations.
*/
static long calcInterval(int segments, int start, int limit) {
long range = limit - start;
if (range < 0) {
return 0;
}
int partSegment = (range % segments) == 0 ? 0
: 1;
return (range / segments) + partSegment;
}
}
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