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U:RDoc::TopLevel[ i I"bsearch.rdoc:ETcRDoc::Parser::Simpleo:RDoc::Markup::Document:@parts[8S:RDoc::Markup::Heading: leveli: textI"Binary Searching;To:RDoc::Markup::BlankLine o:RDoc::Markup::Paragraph;[I"AA few Ruby methods support binary searching in a collection:;T@ o:RDoc::Markup::List: @type: NOTE:@items[o:RDoc::Markup::ListItem:@label[I"Array#bsearch;T;[o; ;[I"5Returns an element selected via a binary search ;TI"$as determined by a given block.;To;;[I"Array#bsearch_index;T;[o; ;[I"BReturns the index of an element selected via a binary search ;TI"$as determined by a given block.;To;;[I"Range#bsearch;T;[o; ;[I"5Returns an element selected via a binary search ;TI"$as determined by a given block.;T@ o; ;[I"FEach of these methods returns an enumerator if no block is given.;T@ o; ;[ I"\Given a block, each of these methods returns an element (or element index) from +self+ ;TI"'as determined by a binary search. ;TI"7The search finds an element of +self+ which meets ;TI"^the given condition in <tt>O(log n)</tt> operations, where +n+ is the count of elements. ;TI"6+self+ should be sorted, but this is not checked.;T@ o; ;[I" There are two search modes:;T@ o;;;;[o;;[I"Find-minimum mode;T;[o; ;[I":method +bsearch+ returns the first element for which ;TI"the block returns +true+; ;TI"-the block must return +true+ or +false+.;To;;[I"Find-any mode;T;[o; ;[I"6method +bsearch+ some element, if any, for which ;TI"the block returns zero. ;TI"+the block must return a numeric value.;T@ o; ;[I"QThe block should not mix the modes by sometimes returning +true+ or +false+ ;TI"Hand other times returning a numeric value, but this is not checked.;T@ o; ;[I"<b>Find-Minimum Mode</b>;T@ o; ;[I"DIn find-minimum mode, the block must return +true+ or +false+. ;TI":The further requirement (though not checked) is that ;TI"0there are no indexes +i+ and +j+ such that:;T@ o;;:BULLET;[o;;0;[o; ;[I"&<tt>0 <= i < j <= self.size</tt>.;To;;0;[o; ;[I"TThe block returns +true+ for <tt>self[i]</tt> and +false+ for <tt>self[j]</tt>.;T@ o; ;[I"KLess formally: the block is such that all +false+-evaluating elements ;TI",precede all +true+-evaluating elements.;T@ o; ;[I"FIn find-minimum mode, method +bsearch+ returns the first element ;TI"(for which the block returns +true+.;T@ o; ;[I"Examples:;T@ o:RDoc::Markup::Verbatim;[I"a = [0, 4, 7, 10, 12] ;TI"$a.bsearch {|x| x >= 4 } # => 4 ;TI"$a.bsearch {|x| x >= 6 } # => 7 ;TI"%a.bsearch {|x| x >= -1 } # => 0 ;TI"(a.bsearch {|x| x >= 100 } # => nil ;TI" ;TI"r = (0...a.size) ;TI"&r.bsearch {|i| a[i] >= 4 } #=> 1 ;TI"&r.bsearch {|i| a[i] >= 6 } #=> 2 ;TI"&r.bsearch {|i| a[i] >= 8 } #=> 3 ;TI"*r.bsearch {|i| a[i] >= 100 } #=> nil ;TI"!r = (0.0...Float::INFINITY) ;TI"/r.bsearch {|x| Math.log(x) >= 0 } #=> 1.0 ;T:@format0o; ;[I"2These blocks make sense in find-minimum mode:;T@ o;;[ I"a = [0, 4, 7, 10, 12] ;TI">a.map {|x| x >= 4 } # => [false, true, true, true, true] ;TI"?a.map {|x| x >= 6 } # => [false, false, true, true, true] ;TI">a.map {|x| x >= -1 } # => [true, true, true, true, true] ;TI"Da.map {|x| x >= 100 } # => [false, false, false, false, false] ;T;0o; ;[I"This would not make sense:;T@ o;;[I"Aa.map {|x| x == 7 } # => [false, false, true, false, false] ;T;0o; ;[I"<b>Find-Any Mode</b>;T@ o; ;[I">In find-any mode, the block must return a numeric value. ;TI":The further requirement (though not checked) is that ;TI"0there are no indexes +i+ and +j+ such that:;T@ o;;;;[ o;;0;[o; ;[I"&<tt>0 <= i < j <= self.size</tt>.;To;;0;[o; ;[I"=The block returns a negative value for <tt>self[i]</tt> ;TI"/and a positive value for <tt>self[j]</tt>.;To;;0;[o; ;[I"WThe block returns a negative value for <tt>self[i]</tt> and zero <tt>self[j]</tt>.;To;;0;[o; ;[I"[The block returns zero for <tt>self[i]</tt> and a positive value for <tt>self[j]</tt>.;T@ o; ;[I"+Less formally: the block is such that:;T@ o;;;;[o;;0;[o; ;[I"KAll positive-evaluating elements precede all zero-evaluating elements.;To;;0;[o; ;[I"OAll positive-evaluating elements precede all negative-evaluating elements.;To;;0;[o; ;[I"KAll zero-evaluating elements precede all negative-evaluating elements.;T@ o; ;[I"=In find-any mode, method +bsearch+ returns some element ;TI"Lfor which the block returns zero, or +nil+ if no such element is found.;T@ o; ;[I"Examples:;T@ o;;[I"a = [0, 4, 7, 10, 12] ;TI"1a.bsearch {|element| 7 <=> element } # => 7 ;TI"4a.bsearch {|element| -1 <=> element } # => nil ;TI"3a.bsearch {|element| 5 <=> element } # => nil ;TI"4a.bsearch {|element| 15 <=> element } # => nil ;TI" ;TI"!a = [0, 100, 100, 100, 200] ;TI"r = (0..4) ;TI"/r.bsearch {|i| 100 - a[i] } #=> 1, 2 or 3 ;TI")r.bsearch {|i| 300 - a[i] } #=> nil ;TI")r.bsearch {|i| 50 - a[i] } #=> nil ;T;0o; ;[I".These blocks make sense in find-any mode:;T@ o;;[ I"a = [0, 4, 7, 10, 12] ;TI"=a.map {|element| 7 <=> element } # => [1, 1, 0, -1, -1] ;TI"Aa.map {|element| -1 <=> element } # => [-1, -1, -1, -1, -1] ;TI">a.map {|element| 5 <=> element } # => [1, 1, -1, -1, -1] ;TI"<a.map {|element| 15 <=> element } # => [1, 1, 1, 1, 1] ;T;0o; ;[I"This would not make sense:;T@ o;;[I"<a.map {|element| element <=> 7 } # => [-1, -1, 0, 1, 1];T;0: @file@:0@omit_headings_from_table_of_contents_below0