Commit e487b576fadc2fd48100667ff233e4a0bb4f0aa5 | zig

author	John Schmidt <john.schmidt.h@gmail.com> 2024-01-27 22:43:35+01:00
committer	John Schmidt <john.schmidt.h@gmail.com> 2024-02-07 21:00:24+01:00
log	e487b576fadc2fd48100667ff233e4a0bb4f0aa5
tree	27084584f2dd67cb33f5903d2c950f5149f6ce04
parent	664c18544c2622352a4e38254496a349006d331b

Changes to lowerBound/upperBound/equalRange

The old definitions had some problems:

- In `lowerBound`, the `lhs` (left hand side) argument was passed on the
  right hand side.
- In `upperBound`, the `greaterThan` function needed to return
  `greaterThanOrEqual` for the function work, so either the name or the
  implementation is incorrect.

To fix both problems, define the functions in terms of a `lessThan` function that returns `lhs < rhs`.
The is more consistent with the rest of `sort.zig` and it's also how C++ implements lower/upperBound (1)(2).

(1) https://en.cppreference.com/w/cpp/algorithm/lower_bound
(2) https://en.cppreference.com/w/cpp/algorithm/upper_bound

- Rewrite doc comments.
- Add a couple of more test cases.
- Add docstring for std.sort.binarySearch

1 files changed, 108 insertions(+), 124 deletions(-)

lib
- std
  - sort.zig

lib/std/sort.zig+108-124

 @@ -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,
 @@ -502,25 +509,25 @@ test "binarySearch" {
     );
 }
-/// Returns the index pointing to the first element in the range [first,last)
+/// Returns the index of the first element in `items` greater than or equal to `key`,
-/// which does not compare less than val.
+/// or `items.len` if all elements are less than `key`.
-/// The function optimizes the number of comparisons performed by using a binary search O(log n).
+///
-/// An example lessThan function:
+/// `items` must be sorted in ascending order with respect to `compareFn`.
-/// fn lower_u32(_: void, key: u32, lhs: u32) bool { return lhs < key; }
+///
+/// O(log n) complexity.
 pub fn lowerBound(
     comptime T: type,
     key: anytype,
     items: []const T,
     context: anytype,
-    comptime lessThan: fn (context: @TypeOf(context), key: @TypeOf(key), lhs: T) bool,
+    comptime lessThan: fn (context: @TypeOf(context), lhs: @TypeOf(key), rhs: T) bool,
 ) usize {
     var left: usize = 0;
     var right: usize = items.len;
-    var mid: usize = undefined;
     while (left < right) {
-        mid = left + (right - left) / 2;
+        const mid = left + (right - left) / 2;
-        if (lessThan(context, key, items[mid])) {
+        if (lessThan(context, items[mid], key)) {
             left = mid + 1;
         } else {
             right = mid;
 @@ -532,87 +539,85 @@ pub fn lowerBound(
 test "lowerBound" {
     const S = struct {
-        fn lower_u32(context: void, key: u32, lhs: u32) bool {
+        fn lower_u32(context: void, lhs: u32, rhs: u32) bool {
             _ = context;
-            return lhs < key;
+            return lhs < rhs;
         }
-        fn lower_i32(context: void, key: i32, lhs: i32) bool {
+        fn lower_i32(context: void, lhs: i32, rhs: i32) bool {
             _ = context;
-            return lhs < key;
+            return lhs < rhs;
         }
-        fn lower_f32(context: void, key: f32, lhs: f32) bool {
+        fn lower_f32(context: void, lhs: f32, rhs: f32) bool {
             _ = context;
-            return lhs < key;
+            return lhs < rhs;
         }
     };
-    // u32
-    // test no data
     try testing.expectEqual(
-        @as(?usize, 0),
+        @as(usize, 0),
         lowerBound(u32, @as(u32, 0), &[_]u32{}, {}, S.lower_u32),
     );
-    // test below the first element
     try testing.expectEqual(
-        @as(?usize, 0),
+        @as(usize, 0),
         lowerBound(u32, @as(u32, 0), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test equal to the first element
     try testing.expectEqual(
-        @as(?usize, 0),
+        @as(usize, 0),
         lowerBound(u32, @as(u32, 2), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test between two numbers
     try testing.expectEqual(
-        @as(?usize, 2),
+        @as(usize, 2),
         lowerBound(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test equal to a number not at the ends
     try testing.expectEqual(
-        @as(?usize, 2),
+        @as(usize, 2),
         lowerBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test equal to the last element
     try testing.expectEqual(
-        @as(?usize, 5),
+        @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),
     );
-    // test above the last element
     try testing.expectEqual(
-        @as(?usize, 6),
+        @as(usize, 6),
         lowerBound(u32, @as(u32, 100), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // i32
     try testing.expectEqual(
-        @as(?usize, 2),
+        @as(usize, 2),
         lowerBound(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // f32
     try testing.expectEqual(
-        @as(?usize, 1),
+        @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 pointing to the first element in the range [first,last)
+/// Returns the index of the first element in `items` greater than `key`,
-/// which compares greater than val.
+/// or `items.len` if all elements are less than or equal to `key`.
-/// The function optimizes the number of comparisons performed by using a binary search O(log n).
+///
-/// An example greaterThan function:
+/// `items` must be sorted in ascending order with respect to `compareFn`.
-/// fn upper_u32(_: void, key: u32, rhs: u32) bool { return key >= rhs; }
+///
+/// O(log n) complexity.
 pub fn upperBound(
     comptime T: type,
     key: anytype,
     items: []const T,
     context: anytype,
-    comptime greaterThan: fn (context: @TypeOf(context), key: @TypeOf(key), rhs: T) bool,
+    comptime lessThan: fn (context: @TypeOf(context), lhs: @TypeOf(key), rhs: T) bool,
 ) usize {
     var left: usize = 0;
     var right: usize = items.len;
-    var mid: usize = undefined;
     while (left < right) {
-        mid = (right + left) / 2;
+        const mid = (right + left) / 2;
-        if (greaterThan(context, key, items[mid])) {
+        if (!lessThan(context, key, items[mid])) {
             left = mid + 1;
         } else {
             right = mid;
 @@ -624,165 +629,144 @@ pub fn upperBound(
 test "upperBound" {
     const S = struct {
-        fn upper_u32(context: void, key: u32, rhs: u32) bool {
+        fn lower_u32(context: void, lhs: u32, rhs: u32) bool {
             _ = context;
-            return key >= rhs;
+            return lhs < rhs;
         }
-        fn upper_i32(context: void, key: i32, rhs: i32) bool {
+        fn lower_i32(context: void, lhs: i32, rhs: i32) bool {
             _ = context;
-            return key >= rhs;
+            return lhs < rhs;
         }
-        fn upper_f32(context: void, key: f32, rhs: f32) bool {
+        fn lower_f32(context: void, lhs: f32, rhs: f32) bool {
             _ = context;
-            return key >= rhs;
+            return lhs < rhs;
         }
     };
-    // u32
-    // test no data
     try testing.expectEqual(
-        @as(?usize, 0),
+        @as(usize, 0),
-        upperBound(u32, @as(u32, 0), &[_]u32{}, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 0), &[_]u32{}, {}, S.lower_u32),
     );
-    // test below the first element
     try testing.expectEqual(
-        @as(?usize, 0),
+        @as(usize, 0),
-        upperBound(u32, @as(u32, 0), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 0), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test equal to the first element
     try testing.expectEqual(
-        @as(?usize, 1),
+        @as(usize, 1),
-        upperBound(u32, @as(u32, 2), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 2), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test between two numbers
     try testing.expectEqual(
-        @as(?usize, 2),
+        @as(usize, 2),
-        upperBound(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test equal to a number not at the ends
     try testing.expectEqual(
-        @as(?usize, 3),
+        @as(usize, 6),
-        upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 7, 7, 7, 7, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test equal to the last element
     try testing.expectEqual(
-        @as(?usize, 6),
+        @as(usize, 6),
-        upperBound(u32, @as(u32, 64), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 8, 8, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // test above the last element
     try testing.expectEqual(
-        @as(?usize, 6),
+        @as(usize, 3),
-        upperBound(u32, @as(u32, 100), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_u32),
+        upperBound(u32, @as(u32, 8), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // i32
     try testing.expectEqual(
-        @as(?usize, 2),
+        @as(usize, 6),
-        upperBound(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.upper_i32),
+        upperBound(u32, @as(u32, 64), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // f32
     try testing.expectEqual(
-        @as(?usize, 1),
+        @as(usize, 6),
-        upperBound(f32, @as(f32, -33.4), &[_]f32{ -54.2, -26.7, 0.0, 56.55, 100.1, 322.0 }, {}, S.upper_f32),
+        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 range containing all elements equivalent to value in the range [first,last)
+/// Returns a tuple of the lower and upper indices in `items` between which all elements are equal to `key`.
-/// The function optimizes the number of comparisons performed by using a binary search O(2 * log n).
+/// If no element in `items` is equal to `key`, both indices are the
-/// Example lessThan & greaterThan functions:
+/// index of the first element in `items` greater than `key`.
-/// fn lower_u32(_: void, key: u32, lhs: u32) bool { return lhs < key; }
+/// If no element in `items` is greater than `key`, both indices equal `items.len`.
-/// fn upper_u32(_: void, key: u32, rhs: u32) bool { return key >= rhs; }
+///
+/// `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), key: @TypeOf(key), lhs: T) bool,
+    comptime lessThan: fn (context: @TypeOf(context), lhs: @TypeOf(key), rhs: T) bool,
-    comptime greaterThan: fn (context: @TypeOf(context), key: @TypeOf(key), rhs: T) bool,
 ) struct { usize, usize } {
     return .{
         lowerBound(T, key, items, context, lessThan),
-        upperBound(T, key, items, context, greaterThan),
+        upperBound(T, key, items, context, lessThan),
     };
 }
 test "equalRange" {
     const S = struct {
-        fn lower_i32(context: void, key: i32, lhs: i32) bool {
+        fn lower_u32(context: void, lhs: u32, rhs: u32) bool {
-            _ = context;
-            return lhs < key;
-        }
-        fn upper_i32(context: void, key: i32, rhs: i32) bool {
-            _ = context;
-            return key >= rhs;
-        }
-        fn lower_u32(context: void, key: u32, lhs: u32) bool {
-            _ = context;
-            return lhs < key;
-        }
-        fn upper_u32(context: void, key: u32, rhs: u32) bool {
             _ = context;
-            return key >= rhs;
+            return lhs < rhs;
         }
-        fn lower_f32(context: void, key: f32, lhs: f32) bool {
+        fn lower_i32(context: void, lhs: i32, rhs: i32) bool {
             _ = context;
-            return lhs < key;
+            return lhs < rhs;
         }
-        fn upper_f32(context: void, key: f32, rhs: f32) bool {
+        fn lower_f32(context: void, lhs: f32, rhs: f32) bool {
             _ = context;
-            return key >= rhs;
+            return lhs < rhs;
         }
     };
-    // i32
-    // test no data
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 0, 0 }),
-        equalRange(i32, @as(i32, 0), &[_]i32{}, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 0), &[_]i32{}, {}, S.lower_i32),
     );
-    // test below the first element
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 0, 0 }),
-        equalRange(i32, @as(i32, 0), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 0), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // test equal to the first element
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 0, 1 }),
-        equalRange(i32, @as(i32, 2), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 2), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // test between two numbers
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 2, 2 }),
-        equalRange(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 5), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // test equal to a number not at the ends
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 2, 3 }),
-        equalRange(i32, @as(i32, 8), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 8), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // test equal to the last element
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 5, 6 }),
-        equalRange(i32, @as(i32, 64), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 64), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // test above the last element
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 6, 6 }),
-        equalRange(i32, @as(i32, 100), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32, S.upper_i32),
+        equalRange(i32, @as(i32, 100), &[_]i32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_i32),
     );
-    // test many of the same element
     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, S.upper_i32),
+        equalRange(i32, @as(i32, 8), &[_]i32{ 2, 4, 8, 8, 8, 8, 15, 22 }, {}, S.lower_i32),
     );
-    // u32
     try testing.expectEqual(
         @as(struct { usize, usize }, .{ 2, 2 }),
-        equalRange(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32, S.upper_u32),
+        equalRange(u32, @as(u32, 5), &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.lower_u32),
     );
-    // f32
     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, S.upper_f32),
+        equalRange(f32, @as(f32, -33.4), &[_]f32{ -54.2, -26.7, 0.0, 56.55, 100.1, 322.0 }, {}, S.lower_f32),
     );
 }