// Construct new range-min query index.
//
// The data argument is stored on the index. Modifying its contents may
// invalidate the range-min index's results.
//
// Takes O(n log n) time where n = data.Len().
func New(data Interface) *Index {
// Sparse table DP algorithm from Bender et al.:
// https://www3.cs.stonybrook.edu/~bender/pub/JALG05-daglca.pdf (§2.3)
n := data.Len()
if n == 0 {
panic("data.Len() must be > 0")
}
logn := intmath.Log2(n)
t := newTable(n, logn)
// Base case: unit length ranges.
for i := 0; i < n; i++ {
t.set(i, 0, i)
}
for j := uint(1); (1 << j) <= n; j++ {
for i := 0; i+int(1<<j)-1 < n; i++ {
l := t.at(i, j-1)
r := t.at(i+int(1<<(j-1)), j-1)
if data.Less(l, r) {
t.set(i, j, l)
} else {
t.set(i, j, r)
}
}
}
return &Index{Data: data, n: n, table: t}
}
// Returns the index of the minimum of r.Data[i:j]. Takes constant time.
//
// The index is relative to the start of r.Data. Ties are broken in an
// arbitrary way.
//
// i >= j is a runtime error.
func (r *Index) Min(i, j int) int {
switch {
case i >= j:
panic("got i >= j in Index.Min")
case j > r.n:
panic("j > data.Len() in Index.Min")
case i+1 == j:
return i
}
k := uint(intmath.Log2(j - i))
a := r.at(i, k)
b := r.at(j-int(1<<k), k)
if r.Data.Less(a, b) {
return a
}
return b
}
// Strings sorts a slice of strings in increasing order (byte-wise
// lexicographically).
//
// This function is equivalent to sort.Strings, but faster than the
// implementation in Go 1.4.
func Strings(a []string) {
n := len(a)
radixQuicksort(a, 0, 0, n, 2*intmath.Log2(n+1))
}