use std::cmp::PartialOrd;
use std::fmt;
#[derive(Debug, PartialEq)]
pub struct RangeError;
impl fmt::Display for RangeError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "Invalid range")
}
}
pub struct RangeMinimumQuery<T: PartialOrd + Copy> {
array: Vec<T>,
sparse_table: Vec<Vec<usize>>,
}
impl<T: PartialOrd + Copy> RangeMinimumQuery<T> {
pub fn new(input: &[T]) -> RangeMinimumQuery<T> {
RangeMinimumQuery {
array: input.to_vec(),
sparse_table: build_sparse_table(input),
}
}
pub fn get_range_min(&self, start: usize, end: usize) -> Result<T, RangeError> {
if start >= end || start >= self.array.len() || end > self.array.len() {
return Err(RangeError);
}
let loglen = (end - start).ilog2() as usize;
let idx: usize = end - (1 << loglen);
let a = self.sparse_table[loglen][start];
let b = self.sparse_table[loglen][idx];
if self.array[a] < self.array[b] {
return Ok(self.array[a]);
}
Ok(self.array[b])
}
}
fn build_sparse_table<T: PartialOrd>(array: &[T]) -> Vec<Vec<usize>> {
let mut table: Vec<Vec<usize>> = vec![(0..array.len()).collect()];
let len = array.len();
for loglen in 1..=len.ilog2() {
let mut row = Vec::new();
for i in 0..=len - (1 << loglen) {
let a = table[table.len() - 1][i];
let b = table[table.len() - 1][i + (1 << (loglen - 1))];
if array[a] < array[b] {
row.push(a);
} else {
row.push(b);
}
}
table.push(row);
}
table
}
#[cfg(test)]
mod tests {
use super::build_sparse_table;
macro_rules! test_build_sparse_table {
($($name:ident: $inputs:expr,)*) => {
$(
#[test]
fn $name() {
let (array, expected) = $inputs;
assert_eq!(build_sparse_table(&array), expected);
}
)*
}
}
test_build_sparse_table! {
small: ([1, 6, 3], vec![vec![0, 1, 2], vec![0, 2]]),
tc_1: ([1, 3, 6, 123, 7, 235, 3, -4, 6, 2], vec![
vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
vec![0, 1, 2, 4, 4, 6, 7, 7, 9],
vec![0, 1, 2, 6, 7, 7, 7],
vec![7, 7, 7]
]),
tc_2: ([
20, 13, -13, 2, 3634, -2, 56, 3, 67, 8, 23, 0, -23, 1, 5, 85, 3, 24, 5, -10, 3, 4, 20,
], vec![
vec![
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22
],
vec![1, 2, 2, 3, 5, 5, 7, 7, 9, 9, 11, 12, 12, 13, 14, 16, 16, 18, 19, 19, 20, 21],
vec![2, 2, 2, 5, 5, 5, 7, 7, 11, 12, 12, 12, 12, 13, 16, 16, 19, 19, 19, 19],
vec![2, 2, 2, 5, 5, 12, 12, 12, 12, 12, 12, 12, 12, 19, 19, 19],
vec![12, 12, 12, 12, 12, 12, 12, 12]
]),
}
#[test]
fn simple_query_tests() {
let v1 = vec![1, 3, 6, 123, 7, 235, 3, -4, 6, 2];
let sparse_v1 = super::RangeMinimumQuery::new(&v1);
assert_eq!(Ok(3), sparse_v1.get_range_min(1, 6));
assert_eq!(Ok(-4), sparse_v1.get_range_min(0, 10));
assert_eq!(Ok(6), sparse_v1.get_range_min(8, 9));
assert!(sparse_v1.get_range_min(4, 3).is_err());
assert!(sparse_v1.get_range_min(0, 1000).is_err());
assert!(sparse_v1.get_range_min(1000, 1001).is_err());
}
#[test]
fn float_query_tests() {
let sparse_v1 = super::RangeMinimumQuery::new(&[0.4, -2.3, 0.0, 234.22, 12.2, -3.0]);
assert_eq!(Ok(-3.0), sparse_v1.get_range_min(0, 6));
assert_eq!(Ok(-2.3), sparse_v1.get_range_min(0, 4));
assert_eq!(Ok(12.2), sparse_v1.get_range_min(3, 5));
assert_eq!(Ok(0.0), sparse_v1.get_range_min(2, 3));
}
}