@@ -509,4 +509,86 @@ class Array
self[idx, 0] = args
self
end
+
+ ##
+ # call-seq:
+ # ary.bsearch {|x| block } -> elem
+ #
+ # By using binary search, finds a value from this array which meets
+ # the given condition in O(log n) where n is the size of the array.
+ #
+ # You can use this method in two use cases: a find-minimum mode and
+ # a find-any mode. In either case, the elements of the array must be
+ # monotone (or sorted) with respect to the block.
+ #
+ # In find-minimum mode (this is a good choice for typical use case),
+ # the block must return true or false, and there must be an index i
+ # (0 <= i <= ary.size) so that:
+ #
+ # - the block returns false for any element whose index is less than
+ # i, and
+ # - the block returns true for any element whose index is greater
+ # than or equal to i.
+ #
+ # This method returns the i-th element. If i is equal to ary.size,
+ # it returns nil.
+ #
+ # ary = [0, 4, 7, 10, 12]
+ # ary.bsearch {|x| x >= 4 } #=> 4
+ # ary.bsearch {|x| x >= 6 } #=> 7
+ # ary.bsearch {|x| x >= -1 } #=> 0
+ # ary.bsearch {|x| x >= 100 } #=> nil
+ #
+ # In find-any mode (this behaves like libc's bsearch(3)), the block
+ # must return a number, and there must be two indices i and j
+ # (0 <= i <= j <= ary.size) so that:
+ #
+ # - the block returns a positive number for ary[k] if 0 <= k < i,
+ # - the block returns zero for ary[k] if i <= k < j, and
+ # - the block returns a negative number for ary[k] if
+ # j <= k < ary.size.
+ #
+ # Under this condition, this method returns any element whose index
+ # is within i...j. If i is equal to j (i.e., there is no element
+ # that satisfies the block), this method returns nil.
+ #
+ # ary = [0, 4, 7, 10, 12]
+ # # try to find v such that 4 <= v < 8
+ # ary.bsearch {|x| 1 - (x / 4).truncate } #=> 4 or 7
+ # # try to find v such that 8 <= v < 10
+ # ary.bsearch {|x| 4 - (x / 2).truncate } #=> nil
+ #
+ # You must not mix the two modes at a time; the block must always
+ # return either true/false, or always return a number. It is
+ # undefined which value is actually picked up at each iteration.
+
+ def bsearch(&block)
+ return to_enum :bsearch unless block_given?
+
+ low = 0
+ high = self.size
+ satisfied = false
+ while low < high
+ mid = low + ((high - low) / 2).truncate
+ val = self[mid]
+ v = block.call(val)
+ if v.is_a?(Integer)
+ return val if v == 0
+ smaller = v < 0
+ elsif v == true
+ satisfied = true
+ smaller = true
+ elsif v == false || v == nil
+ smaller = false
+ end
+ if smaller
+ high = mid
+ else
+ low = mid + 1
+ end
+ end
+ return nil if low == self.size
+ return nil unless satisfied
+ self[low]
+ end
end
@@ -206,3 +206,19 @@ assert("Array#insert") do
b = ["a", "b", "c", "d"]
assert_equal ["a", "b", "c", "d", nil, nil, 99], b.insert(6, 99)
end
+
+assert("Array#bsearch") do
+ # Find minimum mode
+ a = [0, 4, 7, 10, 12]
+ assert_include [4, 7], a.bsearch {|x| x >= 4 }
+ assert_equal 7, a.bsearch {|x| x >= 6 }
+ assert_equal 0, a.bsearch {|x| x >= -1 }
+ assert_nil a.bsearch {|x| x >= 100 }
+
+ # Find any mode
+ a = [0, 4, 7, 10, 12]
+ assert_include [4, 7], a.bsearch {|x| 1 - (x / 4).truncate }
+ assert_nil a.bsearch {|x| 4 - (x / 2).truncate }
+ assert_equal(nil, a.bsearch {|x| 1 })
+ assert_equal(nil, a.bsearch {|x| -1 })
+end