def binary_search(array = [], term)
  low = 0
  high = array.length
  mid = (low + high)/2.ceil

  if term > array[mid] # term偏大
    low = mid + 1
  elsif term < array[mid] # term 偏小
    high = mid -1
  elsif term == array[mid]
    return mid
  else
    return "数组中没有此元素"
  end
end

# 二分法
def binary_search(array, term)
  low = 0
  high = array.length - 1

  loop do
    mid = (low + high)/2.ceil

    if term > array[mid] # term偏大
      low = mid + 1
    end
    if term < array[mid] # term偏小
      high = mid - 1
    end

    # 循环结束条件
    # 1. 找到 term， 跳出循环
    # 2. 数组遍历完了，跳出循环

    if term == array[mid]
      return mid
    end
    if low > high
      return "数组中没有此元素"
    end
  end
end

### 测试
```ruby
a = [1,2,3,4,5],
b = [3, 6, 9, 29, 38, 42]
binary_search(a, 2)
# `=> 1`
binary_search(b, 29)
# `=> 3`
binary_search(b, 22)
# `=> "数组中没有此元素"`

def binary_coin(n)

  array = (1..n).to_a  # 范围转换数组花费时间比较长

  low = 0
  high = array.length - 1

  loop do
    mid = (low+ high)/2.ceil
    k = array[mid]
    if (1+ k) * k / 2 == n                      # 边界条件1
      return @result = k
    elsif (1+ k) * k / 2 > n && k * (k-1)/2 < n # 边界条件2
      return @result = k - 1
    elsif(1+ k) * k / 2 > n                    # mid偏大
      high = mid - 1
    else                                        # mid偏小
      low =  mid + 1
    end
  end
end

(1..10).to_a.each do |x|
  puts binary_coin(x)
end
puts 'binary_coin(100000000)'
puts binary_coin(100000000)