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#[derive(Clone, Debug)]
enum MidOrRange {
Mid(usize),
Range((usize, usize), usize),
}
pub fn tree_depth(size: usize) -> u32 {
(size + 1).next_power_of_two().trailing_zeros()
}
fn index_aux(
index_rev: usize,
mut start: usize,
mut end: usize,
rem_depth: u32,
mut i: usize,
mut sum: usize,
) -> MidOrRange {
use std::cmp::Ordering::*;
use MidOrRange::{Mid, Range};
for rem_depth in (1..=rem_depth).rev() {
let mid = (end - start) / 2 + start;
let d = (1 << rem_depth) - 1;
match index_rev.cmp(&mid) {
Equal => {
return Mid(i + d);
}
Less => {
end = mid;
}
Greater => {
i += d + 1;
sum += mid - start - d;
start = mid + 1;
}
}
}
let mid = (end - start) / 2 + start;
match index_rev.cmp(&mid) {
Equal => Mid(i),
Less => Range((start, mid), sum),
Greater => Range((mid + 1, end), sum + mid - start),
}
}
pub fn veb_index(i: usize, size: usize) -> usize {
use MidOrRange::{Mid, Range};
if i == size || size < 2 {
i
} else {
let depth = tree_depth(size);
let u_depth = depth / 2;
let u_len = (1 << u_depth) - 1;
match index_aux(i, 0, size, u_depth - 1, 0, u_len) {
Mid(x) => veb_index(x, (1 << u_depth) - 1),
Range((s, e), sum) => sum + veb_index(i - s, e - s),
}
}
}
fn index_upper(
index_rev: usize,
mut start: usize,
mut end: usize,
rem_depth: u32,
mut i: usize,
) -> usize {
use std::cmp::Ordering::*;
for rem_depth in (1..=rem_depth).rev() {
let mid = (end - start) / 2 + start;
let d = (1 << rem_depth) - 1;
match index_rev.cmp(&(i + d)) {
Equal => {
return mid;
}
Less => {
end = mid;
}
Greater => {
i += d + 1;
start = mid + 1;
}
}
}
(end - start) / 2 + start
}
fn index_lower(
index_rev: usize,
mut start: usize,
mut end: usize,
rem_depth: u32,
mut sum: usize,
) -> ((usize, usize), usize) {
for rem_depth in (1..=rem_depth).rev() {
let mid = (end - start) / 2 + start;
let d = (1 << rem_depth) - 1;
let nsum = sum + mid - start - d;
if index_rev < nsum {
end = mid;
} else {
start = mid + 1;
sum = nsum;
}
}
let mid = (end - start) / 2 + start;
let nsum = sum + mid - start;
if index_rev < nsum {
((start, mid), sum)
} else {
((mid + 1, end), nsum)
}
}
pub fn veb_index_rev(i: usize, size: usize) -> usize {
if i == size || size < 2 {
i
} else {
let depth = tree_depth(size);
let u_depth = depth / 2;
let u_len = (1 << u_depth) - 1;
if i < u_len {
index_upper(veb_index_rev(i, u_len), 0, size, u_depth - 1, 0)
} else {
let ((s, e), sum) = index_lower(i, 0, size, u_depth - 1, u_len);
veb_index_rev(i - sum, e - s) + s
}
}
}
pub fn binary_mid(n: usize) -> usize {
if n < 2 {
0
} else {
let d = tree_depth(n);
std::cmp::min((1 << (d - 1)) - 1, n - (1 << (d - 2)))
}
}
pub fn index(i: usize, size: usize) -> usize {
use std::cmp::Ordering::*;
if i == size || size < 2 {
i
} else {
let mut start = 0;
let mut end = size;
let mut sum = 0;
loop {
let mid = binary_mid(end - start) + start;
match i.cmp(&mid) {
Equal => return sum,
Less => {
end = mid;
sum = 2 * sum + 1;
}
Greater => {
start = mid + 1;
sum = 2 * sum + 2;
}
}
}
}
}
pub fn index_rev(i: usize, size: usize) -> usize {
if i == size || size < 2 {
i
} else {
let mut suml = 0;
let mut sumr = 0;
let mut depth = 0;
let p = loop {
if suml <= i && i <= sumr {
break i - suml;
}
suml = 2 * suml + 1;
sumr = 2 * sumr + 2;
depth += 1;
};
let mut start = 0;
let mut end = size;
let mut sum = 0;
for d in 0..depth {
let mid = binary_mid(end - start) + start;
if p >> (depth - d - 1) & 1 == 0 {
end = mid;
sum = 2 * sum + 1;
} else {
start = mid + 1;
sum = 2 * sum + 2;
}
}
binary_mid(end - start) + start
}
}