commit ba8375328cd6ddf5025a400fc1d1817b88be6d53 (tree)
parent 42fcca49c55eb9250a9ac8868fa6a9201dd9eb7e
Author: Andrew Kelley <andrew@ziglang.org>
Date: Wed, 7 Feb 2024 18:48:41 -0800
Merge pull request #18718 from schmee/bounds
Add upperBound, lowerBound, and equalRange
Diffstat:
| M | lib/std/sort.zig | | | 268 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
1 file changed, 268 insertions(+), 0 deletions(-)
diff --git a/lib/std/sort.zig b/lib/std/sort.zig
@@ -399,6 +399,13 @@ test "sort fuzz testing" {
}
}
+/// Returns the index of an element in `items` equal to `key`.
+/// If there are multiple such elements, returns the index of any one of them.
+/// If there are no such elements, returns `null`.
+///
+/// `items` must be sorted in ascending order with respect to `compareFn`.
+///
+/// O(log n) complexity.
pub fn binarySearch(
comptime T: type,
key: anytype,
@@ -502,6 +509,267 @@ test "binarySearch" {
);
}
+/// Returns the index of the first element in `items` greater than or equal to `key`,
+/// or `items.len` if all elements are less than `key`.
+///
+/// `items` must be sorted in ascending order with respect to `compareFn`.
+///
+/// O(log n) complexity.
+pub fn lowerBound(
+ comptime T: type,
+ key: anytype,
+ items: []const T,
+ context: anytype,
+ comptime lessThan: fn (context: @TypeOf(context), lhs: @TypeOf(key), rhs: T) bool,
+) usize {
+ var left: usize = 0;
+ var right: usize = items.len;
+
+ while (left < right) {
+ const mid = left + (right - left) / 2;
+ if (lessThan(context, items[mid], key)) {
+ left = mid + 1;
+ } else {
+ right = mid;
+ }
+ }
+
+ return left;
+}
+
+test "lowerBound" {
+ const S = struct {
+ fn lower_u32(context: void, lhs: u32, rhs: u32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ fn lower_i32(context: void, lhs: i32, rhs: i32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ fn lower_f32(context: void, lhs: f32, rhs: f32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ };
+
+ try testing.expectEqual(
+ @as(usize, 0),
+ lowerBound(u32, @as(u32, 0), &[_]u32{}, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 0),
+ lowerBound(u32, @as(u32, 0), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 0),
+ lowerBound(u32, @as(u32, 2), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 2),
+ lowerBound(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 2),
+ lowerBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 6),
+ lowerBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 7, 7, 7, 7, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 2),
+ lowerBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 8, 8, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 5),
+ lowerBound(u32, @as(u32, 64), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 6),
+ lowerBound(u32, @as(u32, 100), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 2),
+ lowerBound(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(usize, 1),
+ lowerBound(f32, @as(f32, -33.4), &[_]f32{ -54.2, -26.7, 0.0, 56.55, 100.1, 322.0 }, {}, S.lower_f32),
+ );
+}
+
+/// Returns the index of the first element in `items` greater than `key`,
+/// or `items.len` if all elements are less than or equal to `key`.
+///
+/// `items` must be sorted in ascending order with respect to `compareFn`.
+///
+/// O(log n) complexity.
+pub fn upperBound(
+ comptime T: type,
+ key: anytype,
+ items: []const T,
+ context: anytype,
+ comptime lessThan: fn (context: @TypeOf(context), lhs: @TypeOf(key), rhs: T) bool,
+) usize {
+ var left: usize = 0;
+ var right: usize = items.len;
+
+ while (left < right) {
+ const mid = (right + left) / 2;
+ if (!lessThan(context, key, items[mid])) {
+ left = mid + 1;
+ } else {
+ right = mid;
+ }
+ }
+
+ return left;
+}
+
+test "upperBound" {
+ const S = struct {
+ fn lower_u32(context: void, lhs: u32, rhs: u32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ fn lower_i32(context: void, lhs: i32, rhs: i32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ fn lower_f32(context: void, lhs: f32, rhs: f32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ };
+
+ try testing.expectEqual(
+ @as(usize, 0),
+ upperBound(u32, @as(u32, 0), &[_]u32{}, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 0),
+ upperBound(u32, @as(u32, 0), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 1),
+ upperBound(u32, @as(u32, 2), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 2),
+ upperBound(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 6),
+ upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 7, 7, 7, 7, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 6),
+ upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 8, 8, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 3),
+ upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 6),
+ upperBound(u32, @as(u32, 64), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 6),
+ upperBound(u32, @as(u32, 100), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(usize, 2),
+ upperBound(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(usize, 1),
+ upperBound(f32, @as(f32, -33.4), &[_]f32{ -54.2, -26.7, 0.0, 56.55, 100.1, 322.0 }, {}, S.lower_f32),
+ );
+}
+
+/// Returns a tuple of the lower and upper indices in `items` between which all elements are equal to `key`.
+/// If no element in `items` is equal to `key`, both indices are the
+/// index of the first element in `items` greater than `key`.
+/// If no element in `items` is greater than `key`, both indices equal `items.len`.
+///
+/// `items` must be sorted in ascending order with respect to `compareFn`.
+///
+/// O(log n) complexity.
+///
+/// See also: `lowerBound` and `upperBound`.
+pub fn equalRange(
+ comptime T: type,
+ key: anytype,
+ items: []const T,
+ context: anytype,
+ comptime lessThan: fn (context: @TypeOf(context), lhs: @TypeOf(key), rhs: T) bool,
+) struct { usize, usize } {
+ return .{
+ lowerBound(T, key, items, context, lessThan),
+ upperBound(T, key, items, context, lessThan),
+ };
+}
+
+test "equalRange" {
+ const S = struct {
+ fn lower_u32(context: void, lhs: u32, rhs: u32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ fn lower_i32(context: void, lhs: i32, rhs: i32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ fn lower_f32(context: void, lhs: f32, rhs: f32) bool {
+ _ = context;
+ return lhs < rhs;
+ }
+ };
+
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 0, 0 }),
+ equalRange(i32, @as(i32, 0), &[_]i32{}, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 0, 0 }),
+ equalRange(i32, @as(i32, 0), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 0, 1 }),
+ equalRange(i32, @as(i32, 2), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 2, 2 }),
+ equalRange(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 2, 3 }),
+ equalRange(i32, @as(i32, 8), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 5, 6 }),
+ equalRange(i32, @as(i32, 64), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 6, 6 }),
+ equalRange(i32, @as(i32, 100), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 2, 6 }),
+ equalRange(i32, @as(i32, 8), &[_]i32{ 2, 4, 8, 8, 8, 8, 15, 22 }, {}, S.lower_i32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 2, 2 }),
+ equalRange(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
+ );
+ try testing.expectEqual(
+ @as(struct { usize, usize }, .{ 1, 1 }),
+ equalRange(f32, @as(f32, -33.4), &[_]f32{ -54.2, -26.7, 0.0, 56.55, 100.1, 322.0 }, {}, S.lower_f32),
+ );
+}
+
pub fn argMin(
comptime T: type,
items: []const T,
