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use crate::Graph;
pub fn dirac_theorem(g: &Graph) -> bool {
for vertex in 0..g.size {
if (g.degree(vertex) as f64) < g.size as f64 / 2.0 {
return false;
}
}
return true;
}
pub fn ore_theorem(g: &Graph) -> bool {
for v1 in 0..g.size {
for v2 in 0..g.size {
if v1 == v2 || g.matrix[v1][v2] != 0 {
continue;
}
let d1 = g.degree(v1);
let d2 = g.degree(v2);
if d1 + d2 < g.size {
return false;
}
}
}
return true;
}
pub fn posa_theorem(g: &Graph) -> bool {
let mut degrees = Vec::new();
for v in 0..g.size {
degrees.push(g.degree(v));
}
let end = if g.size % 2 == 0 {
g.size / 2
} else {
(g.size - 1) / 2
};
for k in 1..end {
let mut cnt = 0;
for d in °rees {
if *d <= k {
cnt += 1;
}
}
if cnt >= k {
return false;
}
}
if g.size % 2 != 0 {
let mut cnt = 0;
for d in °rees {
if *d <= end {
cnt += 1;
}
}
if cnt > end {
return false;
}
}
return true;
}
pub fn bondy_chvatal_hamiltonian_cycle(graph: &Graph) -> Vec<usize> {
let closure = graph.get_closure_traced(true);
let mut cycle = Vec::new();
for i in 0..graph.size - 1 {
cycle.push(i + 1);
}
cycle.push(0);
loop {
let mut start = 0;
let mut m = 0;
let mut end = start;
let mut new_start = start;
let mut current = start;
loop {
let next = cycle[current];
let val = closure.matrix[current][next];
// println!("{current} -> {next} = {val}");
if val > m {
m = val;
end = current;
new_start = next;
}
current = next;
if current == start {
break;
}
}
if m == 1 {
break;
}
// println!("New start: {new_start}, end: {end}, m = {m}");
start = new_start;
let mut s = start;
let mut current = cycle[start];
while current != end {
let next = cycle[current];
let u1 = closure.matrix[start][next];
let u2 = closure.matrix[end][current];
if u1 < m && u2 < m {
s = current;
break;
}
current = next;
}
// println!("s = {s}");
let mut new_cycle = Vec::new();
new_cycle.push(start);
let mut current = cycle[s];
while current != end {
new_cycle.push(current);
current = cycle[current];
}
new_cycle.push(end);
{
let mut tmp = Vec::new();
let mut current = cycle[start];
while current != s {
tmp.push(current);
current = cycle[current];
}
tmp.push(s);
tmp.reverse();
for i in tmp {
new_cycle.push(i);
}
}
for i in 0..graph.size - 1 {
cycle[new_cycle[i]] = new_cycle[i + 1];
}
cycle[new_cycle[graph.size - 1]] = new_cycle[0];
}
return cycle;
}
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