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Binary search routines
/*
* Copyright (c) 1998-2002 Carnegie Mellon University. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* THIS SOFTWARE IS PROVIDED BY CARNEGIE MELLON UNIVERSITY ``AS IS' AND
* ANY EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CARNEGIE MELLON UNIVERSITY
* NOR ITS EMPLOYEES BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
*/
/**
* Binary search routines.
*/
public abstract class BinarySearch {
/**
* Search a sorted array of integers.
* @param array Array of integers
* @param offset Starting offset of subarray to search
* @param length Length of subarray to search
* @param x Value to search for
* @return largest index i in subarray (offset <= i <= offset+length)
* such that all elements below i in the subarray are strictly less
* than x. If x is found in the subarray, then array[i] == x (and i is
* the first occurence of x in the subarray). If x is not found,
* then array[i] is where x should be inserted in the sort order.
*/
public static int search (int[] array, int offset, int length, int x) {
// handle 0-length subarray case right away
if (length <= 0)
return offset;
int low = offset;
int high = offset+length-1;
// since length > 0, array[low] and array[high] are valid indices
if (x <= array[low])
return low;
if (x > array[high])
return high+1;
while (low+1 < high) {
// loop invariant: array[low] < x <= array[high],
// offset <= low < high < offset+length
int mid = (low + high)/2;
if (x <= array[mid])
high = mid;
else
low = mid;
}
// now we have array[low] < x <= array[high]
// && (low+1 == high || low == high)
// implies low+1 == high
//debug.assertion (low+1 == high);
return high;
}
}
