二分查找和插入

# 二分查找（又称折半查找）是在一个有序表里查找元素的复杂度为O(log(n))的算法。先从中# 二分查找（又称折半查找）是在一个有序表里查找元素的复杂度为O(log(n))的算法。先从中间位置开始比较，相等则返回，如小于中间值，则将接下来的查找范围设定为前一子表，大于则为后一子表，以下如此类推。
# 维基百科参考：http://en.wikipedia.org/wiki/Binary_search_algorithm
class Array
  # 迭代版本
  def binary_search_in_iterative num, insert = true
    min, max = 0, self.size - 1
    while min <= max
      mid =  (min + max) / 2
      if num < self[mid]
        max = mid - 1
      elsif num == self[mid]
        return mid
      else
        min = mid + 1
      end
    end

    insert_item num, min, mid if insert
    return nil if min > max
  end

  # 递归版本
  def binary_search_in_recursive num, insert = true, min = nil, max = nil
    min ||= 0
    max ||= self.size - 1
    mid = (min + max) / 2

    if min > max
      insert_item num, min, mid if insert
      return nil
    end

    if num > self[mid]
      binary_search_in_recursive num, insert, mid + 1 , max
    elsif num < self[mid]
      binary_search_in_recursive num, insert, min, mid - 1
    else
      return mid
    end
  end

  def insert_item num, min, mid
    min = mid if self[min].nil?
    self[min..min] = (self[min] < num) ? [self[min], num] : [num, self[min]]
  end
end



require 'benchmark'

array = (0..6**7).to_a

puts "数组是从0到#{array[-1]}的之间的所有整数"
[-1, -6**3, 0, 4**5, 6**6].each do |num|
  puts "匹配#{num}"
  Benchmark.bm do |x|
    x.report("index    ") { array.index num }
    x.report("iterative") { array.binary_search_in_iterative num, false }
    x.report("recursive") { array.binary_search_in_recursive num, false }
  end
  puts
end


__END__
以下是运行本程序的结果


数组是从0到279936的之间的所有整数
匹配-1
      user     system      total        real
index      0.010000   0.000000   0.010000 (  0.014947)
iterative  0.000000   0.000000   0.000000 (  0.000048)
recursive  0.000000   0.000000   0.000000 (  0.000065)

匹配-216
      user     system      total        real
index      0.010000   0.000000   0.010000 (  0.014744)
iterative  0.000000   0.000000   0.000000 (  0.000028)
recursive  0.000000   0.000000   0.000000 (  0.000040)

匹配0
      user     system      total        real
index      0.000000   0.000000   0.000000 (  0.000005)
iterative  0.000000   0.000000   0.000000 (  0.000019)
recursive  0.000000   0.000000   0.000000 (  0.000032)

匹配1024
      user     system      total        real
index      0.000000   0.000000   0.000000 (  0.000059)
iterative  0.000000   0.000000   0.000000 (  0.000031)
recursive  0.000000   0.000000   0.000000 (  0.000048)

匹配46656
      user     system      total        real
index      0.000000   0.000000   0.000000 (  0.003513)
iterative  0.000000   0.000000   0.000000 (  0.000022)
recursive  0.000000   0.000000   0.000000 (  0.000045)


从上面可以看到，迭代都比递归快一倍左右，不难看出Ruby里默认的数组查找是直接在线性时间里遍历查找的，查看Array#index对应的C源码一看便知。


static VALUE
rb_ary_index(argc, argv, ary)
    int argc;
    VALUE *argv;
    VALUE ary;
{
    VALUE val;
    long i;

    if (argc  == 0) {
	RETURN_ENUMERATOR(ary, 0, 0);
	for (i=0; i<RARRAY(ary)->len; i++) {
	    if (RTEST(rb_yield(RARRAY(ary)->ptr[i]))) {
		return LONG2NUM(i);
	    }
	}
	return Qnil;
    }
    rb_scan_args(argc, argv, "01", &val);
    for (i=0; i<RARRAY(ary)->len; i++) {
	if (rb_equal(RARRAY(ary)->ptr[i], val))
	    return LONG2NUM(i);
    }
    return Qnil;
}