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Commit 218b095

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ArcSpec::apply() takes a size parameter for convenience
1 parent 468c0b0 commit 218b095

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5 files changed

+48
-40
lines changed

5 files changed

+48
-40
lines changed

‎src/range_query/dynamic_arq.rs

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -31,7 +31,7 @@ impl<T: ArqSpec> Default for DynamicArqNode<T> {
3131

3232
impl<T: ArqSpec> DynamicArqNode<T> {
3333
fn apply(&mut self, f: &T::F, size: i64) {
34-
self.val = T::apply(f, &self.val);
34+
self.val = T::apply(f, &self.val, size);
3535
if size > 1 {
3636
let h = match self.app {
3737
Some(ref g) => T::compose(f, g),
@@ -107,7 +107,7 @@ impl<T: ArqSpec> DynamicArq<T> {
107107
((lp, ls), (rp, s - ls))
108108
}
109109

110-
fn pull(&mut self, p: usize) {
110+
pubfn pull(&mut self, p: usize) {
111111
let (lp, rp) = self.nodes[p].down;
112112
let left_val = &self.nodes[lp].val;
113113
let right_val = &self.nodes[rp].val;

‎src/range_query/mod.rs

Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -69,29 +69,29 @@ mod test {
6969

7070
#[test]
7171
fn test_range_sum() {
72-
let mut arq = StaticArq::<AssignSum>::new(&[(0,1); 10]);
72+
let mut arq = StaticArq::<AssignSum>::new(&[0; 10]);
7373

74-
assert_eq!(arq.query(0, 9), (0,10));
74+
assert_eq!(arq.query(0, 9), 0);
7575

7676
arq.update(1, 3, &10);
7777
arq.update(3, 5, &1);
7878

79-
assert_eq!(arq.query(0, 9), (23,10));
80-
assert_eq!(arq.query(10, 4), (0,0));
79+
assert_eq!(arq.query(0, 9), 23);
80+
assert_eq!(arq.query(10, 4), 0);
8181
}
8282

8383
#[test]
8484
fn test_dynamic_range_sum() {
8585
let mut arq = DynamicArq::<AssignSum>::new(false);
86-
let view = arq.build_from_slice(&[(0,1); 10]);
86+
let view = arq.build_from_slice(&[0; 10]);
8787

88-
assert_eq!(arq.query(view, 0, 9), (0,10));
88+
assert_eq!(arq.query(view, 0, 9), 0);
8989

9090
arq.update(view, 1, 3, &10);
9191
arq.update(view, 3, 5, &1);
9292

93-
assert_eq!(arq.query(view, 0, 9), (23,10));
94-
assert_eq!(arq.query(view, 10, 4), (0,0));
93+
assert_eq!(arq.query(view, 0, 9), 23);
94+
assert_eq!(arq.query(view, 10, 4), 0);
9595
}
9696

9797
#[test]

‎src/range_query/specs.rs

Lines changed: 23 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -9,16 +9,21 @@ pub trait ArqSpec {
99
// their parts. This representation is more efficient.
1010
type F: Clone;
1111

12-
/// Require for all a,b,c: op(a, op(b, c)) = op(op(a, b), c)
12+
/// Must satisfy the Associative Law:
13+
/// For all a,b,c, op(a, op(b, c)) = op(op(a, b), c)
1314
fn op(a: &Self::S, b: &Self::S) -> Self::S;
14-
/// Require for all a: op(a, identity()) = op(identity(), a) = a
15+
/// Must satisfy the Identity Law:
16+
/// For all a, op(a, identity()) = op(identity(), a) = a
1517
fn identity() -> Self::S;
16-
/// For eager updates, compose() can be unimplemented!(). For lazy updates:
17-
/// Require for all f,g,a: apply(compose(f, g), a) = apply(f, apply(g, a))
18+
/// For point query / eager updates, compose() can be unimplemented!()
19+
/// For range query / lazy updates, it must satisfy the Composition Law:
20+
/// For all f,g,a, apply(compose(f, g), a) = apply(f, apply(g, a))
1821
fn compose(f: &Self::F, g: &Self::F) -> Self::F;
19-
/// For eager updates, apply() can assume to act on a leaf. For lazy updates:
20-
/// Require for all f,a,b: apply(f, op(a, b)) = op(apply(f, a), apply(f, b))
21-
fn apply(f: &Self::F, a: &Self::S) -> Self::S;
22+
/// For point query / eager updates, apply() can assume it acts on a leaf.
23+
/// For range query / lazy updates, it must satisfy the Distributive Law:
24+
/// For all f,a,b, apply(f, op(a, b)) = op(apply(f, a), apply(f, b))
25+
/// The `size` parameter makes this law easier to satisfy in certain cases.
26+
fn apply(f: &Self::F, a: &Self::S, size: i64) -> Self::S;
2227
}
2328

2429
/// Range Minimum Query (RMQ), a classic application of ARQ.
@@ -42,7 +47,7 @@ impl ArqSpec for AssignMin {
4247
fn compose(&f: &Self::F, _: &Self::F) -> Self::F {
4348
f
4449
}
45-
fn apply(&f: &Self::F, _: &Self::S) -> Self::S {
50+
fn apply(&f: &Self::F, _: &Self::S, _:i64) -> Self::S {
4651
f
4752
}
4853
}
@@ -55,9 +60,9 @@ impl ArqSpec for AssignMin {
5560
///
5661
/// Associated functions will panic on overflow.
5762
//
58-
// Note that the apply() operation on raw entries is undefined: while leaf nodes
59-
// should simply be set to f, internal nodes must be set to f * size_of_subtree.
60-
// Thus, our monoid type S should store the pair (entry, size_of_subtree).
63+
// Note that while the `size` parameter seems necessary to satisfy the
64+
// Distributive Law, it is merely a convenience: in essence what we've done
65+
// is move to the product monoid of tuples (value, size_of_subtree).
6166
//
6267
// In mathematical jargon, we say that constant assignment f(a) = f is not an
6368
// endomorphism on (i64, +) because f(a+b) = f != 2*f = f(a) + f(b).
@@ -66,19 +71,19 @@ impl ArqSpec for AssignMin {
6671
// = (f*s, s) + (f*t, t) = f((a,s)) + f((b,t)).
6772
pub enum AssignSum {}
6873
impl ArqSpec for AssignSum {
69-
type S = (i64,i64);
74+
type S = i64;
7075
type F = i64;
71-
fn op(&(a, s): &Self::S, &(b, t): &Self::S) -> Self::S {
72-
(a + b, s + t)
76+
fn op(&a: &Self::S, &b: &Self::S) -> Self::S {
77+
a + b
7378
}
7479
fn identity() -> Self::S {
75-
(0,0)
80+
0
7681
}
7782
fn compose(&f: &Self::F, _: &Self::F) -> Self::F {
7883
f
7984
}
80-
fn apply(&f: &Self::F, &(_, s): &Self::S) -> Self::S {
81-
(f * s, s)
85+
fn apply(&f: &Self::F, _: &Self::S,size:i64) -> Self::S {
86+
f * size
8287
}
8388
}
8489

@@ -104,7 +109,7 @@ impl ArqSpec for SupplyDemand {
104109
fn compose(_: &Self::F, _: &Self::F) -> Self::F {
105110
unimplemented!()
106111
}
107-
fn apply(&(p_add, o_add): &Self::F, &(p, o, _): &Self::S) -> Self::S {
112+
fn apply(&(p_add, o_add): &Self::F, &(p, o, _): &Self::S, _:i64) -> Self::S {
108113
let p = p + p_add;
109114
let o = o + o_add;
110115
(p, o, p.min(o))

‎src/range_query/static_arq.rs

Lines changed: 11 additions & 9 deletions
Original file line numberDiff line numberDiff line change
@@ -37,8 +37,8 @@ impl<T: ArqSpec> StaticArq<T> {
3737
arq
3838
}
3939

40-
fn apply(&mut self, p: usize, f: &T::F) {
41-
self.val[p] = T::apply(f, &self.val[p]);
40+
fn apply(&mut self, p: usize, f: &T::F,s:i64) {
41+
self.val[p] = T::apply(f, &self.val[p], s);
4242
if let Some(lazy) = self.app.get_mut(p) {
4343
let h = match *lazy {
4444
Some(ref g) => T::compose(f, g),
@@ -50,8 +50,9 @@ impl<T: ArqSpec> StaticArq<T> {
5050

5151
fn push(&mut self, p: usize) {
5252
if let Some(ref f) = self.app[p].take() {
53-
self.apply(p << 1, f);
54-
self.apply(p << 1 | 1, f);
53+
let s = ((self.app.len() + p - 1) / p / 2).next_power_of_two() as i64;
54+
self.apply(p << 1, f, s);
55+
self.apply(p << 1 | 1, f, s);
5556
}
5657
}
5758

@@ -61,8 +62,8 @@ impl<T: ArqSpec> StaticArq<T> {
6162

6263
fn push_to(&mut self, p: usize) {
6364
let one_plus_floor_log_p = (p + 1).next_power_of_two().trailing_zeros();
64-
for s in (1..one_plus_floor_log_p).rev() {
65-
self.push(p >> s);
65+
for i in (1..one_plus_floor_log_p).rev() {
66+
self.push(p >> i);
6667
}
6768
}
6869

@@ -86,20 +87,21 @@ impl<T: ArqSpec> StaticArq<T> {
8687
self.push_to(l);
8788
}
8889
self.push_to(r);
89-
let (mut l0, mut r0) = (1, 1);
90+
let (mut l0, mut r0,mut s) = (1,1, 1);
9091
while l <= r {
9192
if l & 1 == 1 {
92-
self.apply(l, f);
93+
self.apply(l, f, s);
9394
l0 = l0.max(l);
9495
l += 1;
9596
}
9697
if r & 1 == 0 {
97-
self.apply(r, f);
98+
self.apply(r, f, s);
9899
r0 = r0.max(r);
99100
r -= 1;
100101
}
101102
l >>= 1;
102103
r >>= 1;
104+
s <<= 1;
103105
}
104106
self.pull_from(l0);
105107
self.pull_from(r0);

‎tests/codeforces343d.rs

Lines changed: 4 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -74,12 +74,13 @@ fn solve<R: io::BufRead, W: io::Write>(scan: &mut Scanner<R>, out: &mut W) {
7474
let mut p = vec![0; n];
7575
dfs(&tree, 0, &mut l, &mut r, &mut p, &mut 0);
7676

77-
let mut arq = StaticArq::<AssignSum>::new(&vec![(0,1); n + 1]);
77+
let mut arq = StaticArq::<AssignSum>::new(&vec![0; n + 1]);
7878
let q = scan.token::<usize>();
7979
for _ in 0..q {
8080
let c = scan.token::<usize>();
8181
let v = scan.token::<usize>() - 1;
82-
let (sum, len) = arq.query(l[v], r[v]);
82+
let len = (r[v] - l[v] + 1) as i64;
83+
let sum = arq.query(l[v], r[v]);
8384
if c == 1 {
8485
if sum != len {
8586
arq.update(p[v], p[v], &0);
@@ -101,4 +102,4 @@ fn main() {
101102
solve(&mut scan, &mut out);
102103

103104
assert_eq!(out, SAMPLE_OUTPUT);
104-
}
105+
}

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