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findmax
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@azizkayumov
azizkayumov committed Oct 3, 2023
1 parent 33fd7a1 commit 2c02cd5
Showing 1 changed file with 50 additions and 66 deletions.
116 changes: 50 additions & 66 deletions src/lib.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -42,30 +42,23 @@ impl LinkCutTree {
self.forest[path_idx].right = Some(v);
self.forest[v].parent = Parent::Node(path_idx);

// update aggregate information
update_max(&mut self.forest, path_idx);

splay(&mut self.forest, v);
}

// update aggregate information
update_max(&mut self.forest, v);
}

// Creates a link between two nodes in the forest (v becomes the parent of w)
/// Creates a link between two nodes in the forest (v becomes the parent of w)
/// # Panics if v has a left child (i.e. v is not a root node)
pub fn link(&mut self, v: usize, w: usize) {
self.access(v);
self.access(w);
if !matches!(self.forest[v].parent, Parent::Root) || v == w {
return; // already connected
}
assert!(matches!(self.forest[v].left, None));
self.forest[v].left = Some(w);
self.forest[w].parent = Parent::Node(v);

// update aggregate information
update_max(&mut self.forest, w);
update_max(&mut self.forest, v);
self.forest[w].right = Some(v);
self.forest[v].parent = Parent::Node(w);
}

// Checks if v and w are connected in the forest
Expand All @@ -83,9 +76,6 @@ impl LinkCutTree {
self.forest[left].parent = Parent::Root;
self.forest[v].left = None;
}

// update aggregate information
update_max(&mut self.forest, v);
}

// Finds the maximum weight in the path from v and its parent
Expand All @@ -110,7 +100,7 @@ mod tests {

#[test]
pub fn access_leaf() {
let mut tree = super::LinkCutTree::new(3);
let mut tree = super::LinkCutTree::new(4);
// '1' has a path pointer to '0', '1' has a right child '2'.
// after access(2), '2' should be the root of the tree:
// 0 0 0 2
Expand Down Expand Up @@ -211,31 +201,23 @@ mod tests {
// / \
// 1 2
// link(3, 1) should result in a single tree (| denotes a path pointer):
// 1 3 3
// | /
// 0 => 1
// \ |
// 2 0
// \
// 2
// 1 3 1
// | |\
// 0 => 0 3
// \ \
// 2 2
let mut tree = super::LinkCutTree::new(4);
tree.forest[0].left = Some(1);
tree.forest[0].right = Some(2);
tree.forest[1].parent = Parent::Node(0);
tree.forest[2].parent = Parent::Node(0);
tree.link(3, 1);
assert!(matches!(tree.forest[3].parent, Parent::Root));
assert_eq!(tree.forest[3].left, Some(1));
assert_eq!(tree.forest[3].right, None);
assert!(matches!(tree.forest[1].parent, Parent::Node(3)));
assert!(matches!(tree.forest[1].parent, Parent::Root));
assert_eq!(tree.forest[1].left, None);
assert_eq!(tree.forest[1].right, None);
assert_eq!(tree.forest[1].right, Some(3));
assert!(matches!(tree.forest[0].parent, Parent::Path(1)));
assert_eq!(tree.forest[0].left, None);
assert_eq!(tree.forest[0].right, Some(2));
assert!(matches!(tree.forest[2].parent, Parent::Node(0)));
assert_eq!(tree.forest[2].left, None);
assert_eq!(tree.forest[2].right, None);
}

#[test]
Expand Down Expand Up @@ -284,29 +266,26 @@ mod tests {
assert!(!tree.connected(0, 1)); // not connected yet

tree.link(0, 1);
// 0
// / <= link(0, 1)
// 1
assert!(matches!(tree.forest[0].parent, Parent::Root));
assert_eq!(tree.forest[0].right, None);
assert_eq!(tree.forest[0].left, Some(1));
assert!(matches!(tree.forest[1].parent, Parent::Node(0)));
// 1
// \ <= link(0, 1)
// 0
assert!(matches!(tree.forest[1].parent, Parent::Root));
assert_eq!(tree.forest[1].left, None);
assert_eq!(tree.forest[1].right, Some(0));
assert!(matches!(tree.forest[0].parent, Parent::Node(1)));

assert!(tree.connected(0, 1)); // now connected
assert!(matches!(tree.forest[1].parent, Parent::Root));
assert_eq!(tree.forest[1].right, None);
assert_eq!(tree.forest[1].left, None);
assert!(matches!(tree.forest[0].parent, Parent::Path(1)));
// 0 1
// / => |
// 1 0

tree.cut(0);
assert!(matches!(tree.forest[0].parent, Parent::Root));
assert_eq!(tree.forest[0].right, None);
// 0 0
// / =>
// 1 1
// 1 1
// \ =>
// 0 0
assert!(!tree.connected(0, 1)); // now disconnected
}

Expand All @@ -327,19 +306,22 @@ mod tests {
// 2
tree.link(2, 3);
// link(2, 3) should result in:
// 2
// / |
// 3 1
// | \
// 4 0
assert!(matches!(tree.forest[2].parent, Parent::Root));
assert_eq!(tree.forest[2].left, Some(3));
assert_eq!(tree.forest[2].right, None);
assert!(matches!(tree.forest[3].parent, Parent::Node(2)));
assert!(matches!(tree.forest[1].parent, Parent::Path(2)));
// 3
// | \
// 4 2
// |
// 1
// \
// 0
assert!(matches!(tree.forest[3].parent, Parent::Root));
assert_eq!(tree.forest[3].left, None);
assert_eq!(tree.forest[3].right, None);
assert_eq!(tree.forest[3].right, Some(2));
assert!(matches!(tree.forest[4].parent, Parent::Path(3)));
assert!(matches!(tree.forest[2].parent, Parent::Node(3)));
assert_eq!(tree.forest[2].left, None);
assert_eq!(tree.forest[2].right, None);
assert!(matches!(tree.forest[1].parent, Parent::Path(2)));
assert_eq!(tree.forest[1].left, None);
assert_eq!(tree.forest[1].right, Some(0));
assert!(matches!(tree.forest[0].parent, Parent::Node(1)));
assert!(tree.connected(2, 3));
Expand Down Expand Up @@ -450,11 +432,20 @@ mod tests {
assert_eq!(lctree.findmax(3), 2);
assert_eq!(lctree.findmax(1), 0);
assert_eq!(lctree.findmax(4), 2);

// we cut node 3 from its parent 2:
lctree.cut(3);
assert_eq!(lctree.findmax(5), 4);
assert_eq!(lctree.findmax(6), 3);
assert_eq!(lctree.findmax(4), 4);
assert_eq!(lctree.findmax(3), 3);
assert_eq!(lctree.findmax(2), 2);
assert_eq!(lctree.findmax(1), 0);
assert_eq!(lctree.findmax(0), 0);
}

// creates a random tree with n nodes
fn create_random_tree(n: usize, state: u64) -> (Vec<(usize, usize)>, Vec<f64>, Vec<usize>) {
let mut rng = rand::rngs::StdRng::seed_from_u64(state);
fn create_random_tree(n: usize, seed: u64) -> (Vec<(usize, usize)>, Vec<f64>, Vec<usize>) {
let mut rng = rand::rngs::StdRng::seed_from_u64(seed);

let mut edges = Vec::new();
let mut weights: Vec<f64> = (0..n).map(|i| i as f64).collect();
Expand All @@ -467,13 +458,11 @@ mod tests {
let parent = in_tree[parent_idx];
edges.push((i, parent));

let max_idx = if weights[i] >= weights[ground_truth[parent]] {
ground_truth[i] = if weights[i] > weights[ground_truth[parent]] {
i
} else {
ground_truth[parent]
};
ground_truth[i] = max_idx;

in_tree.push(i);
}

Expand All @@ -484,22 +473,17 @@ mod tests {
pub fn findmax_random() {
let n = 100;
let seed = rand::thread_rng().gen();
println!("seed = {}", seed);
let (edges, weights, ground_truth) = create_random_tree(n, seed);
let mut lctree = super::LinkCutTree::new(n);
for i in 0..n {
lctree.forest[i].weight = weights[i];
}

println!("weights: {:?}", weights);
println!("edges: {:?}", edges);
println!("ground truth: {:?}", ground_truth);

for (v, w) in edges {
lctree.link(v, w);
}

for _ in 0..n * 10 {
for _ in 0..n * 100 {
let v = rand::thread_rng().gen_range(0..n);
assert_eq!(lctree.findmax(v), ground_truth[v]);
}
Expand Down

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