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/**************************************************************************/
/* */
/* The Why platform for program certification */
/* */
/* Copyright (C) 2002-2011 */
/* */
/* Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud 11 */
/* Claude MARCHE, INRIA & Univ. Paris-sud 11 */
/* Yannick MOY, Univ. Paris-sud 11 */
/* Romain BARDOU, Univ. Paris-sud 11 */
/* */
/* Secondary contributors: */
/* */
/* Thierry HUBERT, Univ. Paris-sud 11 (former Caduceus front-end) */
/* Nicolas ROUSSET, Univ. Paris-sud 11 (on Jessie & Krakatoa) */
/* Ali AYAD, CNRS & CEA Saclay (floating-point support) */
/* Sylvie BOLDO, INRIA (floating-point support) */
/* Jean-Francois COUCHOT, INRIA (sort encodings, hyps pruning) */
/* Mehdi DOGGUY, Univ. Paris-sud 11 (Why GUI) */
/* */
/* This software is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU Lesser General Public */
/* License version 2.1, with the special exception on linking */
/* described in file LICENSE. */
/* */
/* This software is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. */
/* */
/**************************************************************************/
//@+ CheckArithOverflow = yes
/* @ lemma mean_property :
@ \forall integer x y; x <= y ==> x <= (x+y)/2 <= y ;
@*/
/* @ lemma mean_property_2 :
@ \forall integer x y; x <= y ==> x <= x+(y-x)/2 <= y;
@*/
/*@ predicate is_sorted{L}(int[] t) =
@ t != null &&
@ \forall integer i j;
@ 0 <= i && i <= j && j < t.length ==> t[i] <= t[j];
@*/
class BinarySearch {
/* binary_search(t,n,v) search for element v in array t
between index 0 and n-1
array t is assumed to be sorted in increasing order
returns an index i between 0 and n-1 where t[i] equals v,
or -1 if no element in t is equal to v
*/
/*@ requires
@ 0 <= n <= t.length &&
@ \forall integer k1 k2;
@ 0 <= k1 <= k2 <= n-1 ==> t[k1] <= t[k2];
@ behavior correctness:
@ ensures
@ (\result >= 0 && t[\result] == v) ||
@ (\result == -1 && \forall integer k; 0 <= k < n ==> t[k] != v);
@*/
static int binary_search(int t[], int n, int v) {
int l = 0, u = n-1;
/*@ loop_invariant
@ 0 <= l && u <= n-1 &&
@ \forall integer k; 0 <= k < n ==> t[k] == v ==> l <= k <= u;
@ loop_variant
@ u-l ;
@*/
while (l <= u ) {
int m = l + (u - l) / 2;
if (t[m] < v) l = m + 1;
else if (t[m] > v) u = m - 1;
else return m;
}
return -1;
}
/* idiomatic code, using t.length instead of n as argument */
/*@ requires t != null;
@ ensures -1 <= \result < t.length;
@ behavior success:
@ ensures \result >= 0 ==> t[\result] == v;
@ behavior failure:
@ assumes
@ \forall integer k1 k2;
@ 0 <= k1 <= k2 <= t.length-1 ==> t[k1] <= t[k2];
@ ensures \result == -1 ==>
@ \forall integer k; 0 <= k < t.length ==> t[k] != v;
@*/
static int binary_search2(int t[], int v) {
int l = 0, u = t.length - 1;
/*@ loop_invariant
@ 0 <= l && u <= t.length - 1;
@ for failure:
@ loop_invariant
@ \forall integer k; 0 <= k < t.length ==> t[k] == v ==> l <= k <= u;
@ loop_variant
@ u-l ;
@*/
while (l <= u ) {
int m = l + (u - l) / 2;
if (t[m] < v) l = m + 1;
else if (t[m] > v) u = m - 1;
else return m;
}
return -1;
}
/* search in a field */
public int t[];
// pb with recursive def of type and logic in Jessie
// @ invariant t_is_sorted: is_sorted(t);
/*@ requires t != null && t.length <= 2147483647 && is_sorted(t);
@ behavior search_success:
@ ensures
@ \result >= 0 ==> t[\result] == v;
@ behavior search_failure:
@ ensures \result < 0 ==> (\forall integer k;
@ 0 <= k < t.length ==> t[k] != v);
@*/
public int binary_search3(int v) {
int l = 0, u = t.length-1;
/*@ loop_invariant
@ 0 <= l && u <= t.length-1 &&
@ \forall integer k;
@ 0 <= k < t.length && t[k] == v ==> l <= k <= u;
@ loop_variant u-l ;
@*/
while (l <= u ) {
int m = l + (u-l) / 2;
if (t[m] < v) l = m + 1;
else if (t[m] > v) u = m - 1;
else return m;
}
return -1;
}
}
/*
Local Variables:
compile-command: "make BinarySearch"
End:
*/
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