diff --git a/src/pkg/sort/search.go b/src/pkg/sort/search.go index 774764d3d0..6b053c2b1d 100644 --- a/src/pkg/sort/search.go +++ b/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 }) } diff --git a/src/pkg/sort/search_test.go b/src/pkg/sort/search_test.go index 5f85748128..10dbd3a75a 100644 --- a/src/pkg/sort/search_test.go +++ b/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},