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Findroot #21

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Oct 6, 2023
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Findroot #21

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90 changes: 76 additions & 14 deletions src/lib.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@ impl LinkCutTree {
self.forest[v].weight = weight;
}

// Constructs a path from a node to the root of the tree.
/// Constructs a path from a node to the root of the tree.
pub fn access(&mut self, v: usize) {
splay(&mut self.forest, v);

Expand Down Expand Up @@ -50,7 +50,7 @@ impl LinkCutTree {
update_max(&mut self.forest, v);
}

/// Creates a link between two nodes in the forest (where w is the parent of v)
/// Creates a link between two nodes in the forest (where w is the parent of v).
pub fn link(&mut self, v: usize, w: usize) {
self.access(v);
self.access(w);
Expand All @@ -61,15 +61,15 @@ impl LinkCutTree {
self.forest[w].parent = Parent::Node(v);
}

// Checks if v and w are connected in the forest
/// Checks if v and w are connected in the forest.
pub fn connected(&mut self, v: usize, w: usize) -> bool {
self.access(v); // v is now the root of the tree
self.access(w);
// if access(w) messed with the root of the tree, then v and w are connected:
!matches!(self.forest[v].parent, Parent::Root) || v == w
}

// Cuts the link between v and its parent.
/// Cuts the link between v and its parent.
pub fn cut(&mut self, v: usize) {
self.access(v);
if let Some(left) = self.forest[v].left {
Expand All @@ -78,11 +78,21 @@ impl LinkCutTree {
}
}

// Finds the maximum weight in the path from v and its parent
/// Finds the maximum weight in the path from v and the root of the tree that v is in.
pub fn findmax(&mut self, v: usize) -> usize {
self.access(v);
self.forest[v].max_weight_idx
}

/// Finds the root of the tree that v is in.
pub fn findroot(&mut self, v: usize) -> usize {
self.access(v);
let mut root = v;
while let Some(left) = self.forest[root].left {
root = left;
}
root
}
}

#[cfg(test)]
Expand Down Expand Up @@ -306,13 +316,12 @@ mod tests {
// /
// 2
tree.link(2, 3);
// link(2, 3) should result in:
// link(2, 3) should now 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);
Expand All @@ -322,7 +331,7 @@ mod tests {
assert_eq!(tree.forest[3].right, None);
assert!(matches!(tree.forest[4].parent, Parent::Path(3)));

// we cut node 2 from its parent 3:
// We cut node 2 from its parent 3:
tree.cut(2);
assert!(!tree.connected(2, 3));
assert!(!tree.connected(2, 4));
Expand Down Expand Up @@ -351,17 +360,17 @@ mod tests {
lctree.link(8, 7);
lctree.link(9, 8);

// checking connectivity:
// Checking connectivity:
for i in 0..10 {
for j in 0..10 {
assert!(lctree.connected(i, j));
}
}

// we cut node 6 from its parent 0:
// We cut node 6 from its parent 0:
lctree.cut(6);

// the forest should now look like this:
// The forest should now look like this:
// 0
// /
// 1 6
Expand All @@ -372,7 +381,7 @@ mod tests {
// /
// 9

// we check connectivity again for the two trees:
// We check connectivity again for the two trees:
for i in 0..6 {
for j in 0..6 {
assert!(lctree.connected(i, j));
Expand Down Expand Up @@ -404,7 +413,8 @@ mod tests {
lctree.forest[8].weight = 1.0;
lctree.forest[9].weight = 8.0;

// we form the following structure:
// We form a link-cut tree from a rooted tree with the following structure
// (the numbers in parentheses are the weights of the nodes):
// 0(4)
// / \
// 1(2) 5(5)
Expand All @@ -424,7 +434,7 @@ mod tests {
lctree.link(8, 7);
lctree.link(9, 7);

// we check the node index with max weight in the path from each node to the root:
// We check the node index with max weight in the path from each node to the root:
assert_eq!(lctree.findmax(0), 0);
assert_eq!(lctree.findmax(5), 5);
assert_eq!(lctree.findmax(1), 0);
Expand All @@ -436,4 +446,56 @@ mod tests {
assert_eq!(lctree.findmax(3), 0);
assert_eq!(lctree.findmax(6), 5);
}

#[test]
pub fn findroot() {
// We form a link-cut tree from a rooted tree with the following structure:
// 0
// / \
// 1 6
// / \ \
// 2 3 7
// / \ \
// 4 5 8
// /
// 9
let mut lctree = super::LinkCutTree::new(10);
lctree.link(1, 0);
lctree.link(2, 1);
lctree.link(3, 1);
lctree.link(4, 3);
lctree.link(5, 3);
lctree.link(6, 0);
lctree.link(7, 6);
lctree.link(8, 7);
lctree.link(9, 8);

// Checking findroot:
for i in 0..10 {
assert_eq!(lctree.findroot(i), 0);
}

// We cut node 6 from its parent 0:
lctree.cut(6);

// the forest should now look like this:
// 0
// /
// 1 6
// / \ \
// 2 3 7
// / \ \
// 4 5 8
// /
// 9

// We check findroot again for the two trees:
for i in 0..6 {
assert_eq!(lctree.findroot(i), 0);
}

for i in 6..10 {
assert_eq!(lctree.findroot(i), 6);
}
}
}
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