sort: simplify semantics of Search.

As discussed earlier.

R=gri
CC=golang-dev
https://golang.org/cl/3025042

src/pkg/sort/search.go

@@ -12,54 +12,54 @@ package sort
 // sorted.  It will often be passed as a closure.  For instance, given a slice
 // of integers, []data, sorted in ascending order, the function
 //
-//	func(i int) bool { return data[i] <= 23 }
+//	func(i int) bool { return data[i] < 23 }
 //
 // can be used to search for the value 23 in data.  The relationship expressed
-// by the function must be "less or equal" if the elements are sorted in ascending
-// order or "greater or equal" if they are sorted in descending order.
+// by the function must be "less" if the elements are sorted in ascending
+// order or "greater" if they are sorted in descending order.
 // The function f will be called with values of i in the range 0 to n-1.
 // 
 // For brevity, this discussion assumes ascending sort order. For descending
-// order, replace <= with >=, and swap 'smaller' with 'larger'.
+// order, replace < with >, and swap 'smaller' with 'larger'.
 //
-// If data[0] <= x and x <= data[n-1], Search returns the index i with:
+// Search returns the index i with:
 //
-//	data[i] <= x && x < data[i+1]    (0 <= i < n)
+//	data[i-1] < x && x <= data[i]
 //
-// where data[n] is assumed to be larger than any x.  Thus, i is the index of x
-// if it is present in the data.  It is the responsibility of the caller to
-// verify the actual presence by testing if data[i] == x.
-//
-// If n == 0 or if x is smaller than any element in data (f is always false),
-// the result is 0.  If x is larger than any element in data (f is always true),
-// the result is n-1.
+// where data[-1] is assumed to be smaller than any x and data[n] is
+// assumed to be larger than any x.  Thus 0 <= i <= n and i is the first
+// index of x if x is present in the data.  It is the responsibility of
+// the caller to verify the actual presence by testing if i < n and
+// data[i] == x.
 //
 // To complete the example above, the following code tries to find the element
 // elem in an integer slice data sorted in ascending order:
 //
 //	elem := 23
-//	i := sort.Search(len(data), func(i int) bool { return data[i] <= elem })
-//	if len(data) > 0 && data[i] == elem {
+//	i := sort.Search(len(data), func(i int) bool { return data[i] < elem })
+//	if i < len(data) && data[i] == elem {
 //		// elem is present at data[i]
 //	} else {
 //		// elem is not present in data
 //	}
-//
 func Search(n int, f func(int) bool) int {
-	// See "A Method of Programming", E.W. Dijkstra,
-	// for arguments on correctness and efficiency.
 	i, j := 0, n
 	for i+1 < j {
 		h := i + (j-i)/2 // avoid overflow when computing h
 		// i < h < j
 		if f(h) {
-			// data[h] <= x
-			i = h
+			// data[h] < x
+			i = h + 1
 		} else {
-			// x < data[h]
+			// x <= data[h]
 			j = h
 		}
 	}
+	// test the final element that the loop did not.
+	if i < j && f(i) {
+		i++
+	}
+
 	return i
 }
 
@@ -70,7 +70,7 @@ func Search(n int, f func(int) bool) int {
 // as specified by Search. The array must be sorted in ascending order.
 //
 func SearchInts(a []int, x int) int {
-	return Search(len(a), func(i int) bool { return a[i] <= x })
+	return Search(len(a), func(i int) bool { return a[i] < x })
 }
 
 
@@ -78,7 +78,7 @@ func SearchInts(a []int, x int) int {
 // as specified by Search. The array must be sorted in ascending order.
 // 
 func SearchFloats(a []float, x float) int {
-	return Search(len(a), func(i int) bool { return a[i] <= x })
+	return Search(len(a), func(i int) bool { return a[i] < x })
 }
 
 
@@ -86,7 +86,7 @@ func SearchFloats(a []float, x float) int {
 // as specified by Search. The array must be sorted in ascending order.
 // 
 func SearchStrings(a []string, x string) int {
-	return Search(len(a), func(i int) bool { return a[i] <= x })
+	return Search(len(a), func(i int) bool { return a[i] < x })
 }
 
 

src/pkg/sort/search_test.go

@@ -9,7 +9,7 @@ import "testing"
 
 func f(a []int, x int) func(int) bool {
 	return func(i int) bool {
-		return a[i] <= x
+		return a[i] < x
 	}
 }
 
@@ -23,25 +23,26 @@ var tests = []struct {
 	i    int
 }{
 	{"empty", 0, nil, 0},
-	{"1 1", 1, func(i int) bool { return i <= 1 }, 0},
+	{"1 1", 1, func(i int) bool { return i < 1 }, 1},
 	{"1 false", 1, func(i int) bool { return false }, 0},
-	{"1 true", 1, func(i int) bool { return true }, 0},
-	{"1e9 991", 1e9, func(i int) bool { return i <= 991 }, 991},
+	{"1 true", 1, func(i int) bool { return true }, 1},
+	{"1e9 991", 1e9, func(i int) bool { return i < 991 }, 991},
 	{"1e9 false", 1e9, func(i int) bool { return false }, 0},
-	{"1e9 true", 1e9, func(i int) bool { return true }, 1e9 - 1},
+	{"1e9 true", 1e9, func(i int) bool { return true }, 1e9},
 	{"data -20", len(data), f(data, -20), 0},
 	{"data -10", len(data), f(data, -10), 0},
-	{"data -9", len(data), f(data, -9), 0},
-	{"data -6", len(data), f(data, -6), 0},
+	{"data -9", len(data), f(data, -9), 1},
+	{"data -6", len(data), f(data, -6), 1},
 	{"data -5", len(data), f(data, -5), 1},
 	{"data 3", len(data), f(data, 3), 5},
-	{"data 99", len(data), f(data, 99), 8},
-	{"data 100", len(data), f(data, 100), 11},
-	{"data 101", len(data), f(data, 101), 11},
+	{"data 11", len(data), f(data, 11), 8},
+	{"data 99", len(data), f(data, 99), 9},
+	{"data 100", len(data), f(data, 100), 9},
+	{"data 101", len(data), f(data, 101), 12},
 	{"data 10000", len(data), f(data, 10000), 13},
-	{"data 10001", len(data), f(data, 10001), 13},
-	{"descending a", 7, func(i int) bool { return []int{99, 99, 59, 42, 7, 0, -1, -1}[i] >= 7 }, 4},
-	{"descending 7", 1e9, func(i int) bool { return 1e9-i >= 7 }, 1e9 - 7},
+	{"data 10001", len(data), f(data, 10001), 14},
+	{"descending a", 7, func(i int) bool { return []int{99, 99, 59, 42, 7, 0, -1, -1}[i] > 7 }, 4},
+	{"descending 7", 1e9, func(i int) bool { return 1e9-i > 7 }, 1e9 - 7},
 }
 
 
@@ -78,7 +79,7 @@ func TestSearchEfficiency(t *testing.T) {
 		max := log2(n)
 		for x := 0; x < n; x += step {
 			count := 0
-			i := Search(n, func(i int) bool { count++; return i <= x })
+			i := Search(n, func(i int) bool { count++; return i < x })
 			if i != x {
 				t.Errorf("n = %d: expected index %d; got %d", n, x, i)
 			}
@@ -103,7 +104,7 @@ var wrappertests = []struct {
 	i      int
 }{
 	{"SearchInts", SearchInts(data, 11), 8},
-	{"SearchFloats", SearchFloats(fdata, 2.1), 3},
+	{"SearchFloats", SearchFloats(fdata, 2.1), 4},
 	{"SearchStrings", SearchStrings(sdata, ""), 0},
 	{"IntArray.Search", IntArray(data).Search(0), 2},
 	{"FloatArray.Search", FloatArray(fdata).Search(2.0), 3},