Changed structure of project and renamed binary

1 files changed, 585 insertions, 0 deletions

diff --git a/graph-checker/src/main.rs b/graph-checker/src/main.rs
new file mode 100644
index 0000000..e09d15f
--- /dev/null
+++ b/graph-checker/src/main.rs
@@ -0,0 +1,585 @@
+use std::fmt;
+use std::io::{self, BufRead};
+use std::time::Instant;
+
+struct Graph {
+    size: usize,
+    matrix: Vec<Vec<i32>>,
+}
+
+struct Cutset {
+    cardinality: usize,
+    vertices: Vec<i32>,
+    graph: Graph,
+}
+
+impl Clone for Graph {
+    fn clone(&self) -> Self {
+        let mut matrix = vec![vec![0; self.size]; self.size];
+        for row in 0..self.size {
+            for col in 0..self.size {
+                matrix[row][col] = self.matrix[row][col];
+            }
+        }
+        return Graph {
+            size: self.size,
+            matrix,
+        };
+    }
+}
+
+impl fmt::Display for Graph {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        for row in 0..self.size {
+            for col in 0..self.size {
+                write!(f, "{}", self.matrix[row][col])?;
+                if col < self.size - 1 {
+                    write!(f, " ")?;
+                }
+            }
+            if row < self.size - 1 {
+                write!(f, "\n")?;
+            }
+        }
+        return Ok(());
+    }
+}
+
+fn iterate(n: usize) -> Vec<Vec<i32>> {
+    let mut components = Vec::new();
+
+    let mut v: Vec<i32> = vec![0; n];
+    loop {
+        let mut sum: usize = 0;
+        for i in &v {
+            sum += *i as usize;
+        }
+
+        if sum == v.len() {
+            break;
+        }
+
+        let mut k = 0;
+        for i in 0..v.len() {
+            if v[i] == 1 {
+                v[i] = 0;
+            } else {
+                k = i;
+                break;
+            }
+        }
+        v[k] = 1;
+        components.push(v.clone());
+    }
+
+    return components;
+}
+
+impl Graph {
+    fn from_g6(line: &String) -> Graph {
+        let mut chars: Vec<u8> = Vec::new();
+        for character in line.chars() {
+            chars.push((character as i32 - 63) as u8);
+        }
+        // TODO: spec allows multi-byte vector size
+        let size = chars[0] as usize;
+        let bytes = &chars[1..];
+
+        let mut matrix: Vec<Vec<i32>> = vec![vec![0; size]; size];
+        let mut i = 0;
+        for col in 1..size {
+            for row in 0..col {
+                let bit: i32 = (bytes[i / 6] >> (5 - i % 6) & 1) as i32;
+                matrix[row][col] = bit;
+                matrix[col][row] = bit;
+                i += 1;
+            }
+        }
+        return Graph { size, matrix };
+    }
+
+    fn degree(&self, vertex: usize) -> usize {
+        let mut sum: usize = 0;
+        for i in &self.matrix[vertex] {
+            sum += if *i == 0 { 0 } else { 1 } as usize;
+        }
+        return sum;
+    }
+
+    fn min_degree(&self) -> usize {
+        let mut min = self.size + 1;
+        for i in 0..self.size {
+            let d = self.degree(i);
+            if d < min {
+                min = d;
+            }
+        }
+        return min;
+    }
+
+    fn get_closure_traced(&self, trace_steps: bool) -> Graph {
+        let mut step = if trace_steps { 2 } else { 1 };
+
+        let mut closure = self.clone();
+        for _ in 0..(closure.size * closure.size) {
+            let mut changed = false;
+            for row in 0..closure.size {
+                for col in 0..closure.size {
+                    if row == col || closure.matrix[row][col] != 0 {
+                        continue;
+                    }
+                    let sum = closure.degree(row) + closure.degree(col);
+                    if sum >= closure.size {
+                        closure.matrix[row][col] = step;
+                        if trace_steps {
+                            step += 1;
+                        }
+                        changed = true;
+                    }
+                }
+            }
+            if !changed {
+                break;
+            }
+        }
+        return closure;
+    }
+
+    fn get_hamiltonian_cycle(&self) -> Vec<usize> {
+        let closure = self.get_closure_traced(true);
+
+        let mut cycle = Vec::new();
+        for i in 0..self.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..self.size - 1 {
+                cycle[new_cycle[i]] = new_cycle[i + 1];
+            }
+            cycle[new_cycle[self.size - 1]] = new_cycle[0];
+        }
+
+        return cycle;
+    }
+
+    fn cutsets(&self) -> Vec<Cutset> {
+        let mut cs = Vec::new();
+        for vertices in iterate(self.size) {
+            let mut g = self.clone();
+            for vertex in 0..g.size {
+                for i in 0..g.size {
+                    if vertices[vertex] == 0 {
+                        g.matrix[vertex as usize][i as usize] = 0;
+                        g.matrix[i as usize][vertex as usize] = 0;
+                    }
+                }
+            }
+            let cardinality = vertices.iter().sum::<i32>() as usize;
+            cs.push(Cutset {
+                cardinality,
+                vertices: vertices.clone(),
+                graph: g,
+            });
+        }
+        return cs;
+    }
+
+    fn max_independent_cutset(&self) -> Cutset {
+        let mut max_cutset = None;
+        for cutset in self.cutsets() {
+            if cutset.graph.is_independent() {
+                match &max_cutset {
+                    None => max_cutset = Some(cutset),
+                    Some(m_cutset) => {
+                        if cutset.cardinality > m_cutset.cardinality {
+                            max_cutset = Some(cutset);
+                        }
+                    }
+                };
+            }
+        }
+        return max_cutset.unwrap();
+    }
+
+    fn dfs(&self, vertex: &usize, visited: &mut Vec<usize>) {
+        visited[*vertex] = 1;
+        for i in 0..self.size {
+            if visited[i] == 0 && self.matrix[*vertex][i] != 0 {
+                self.dfs(&i, visited);
+            }
+        }
+    }
+
+    fn count_components_partial(&self, included_vertices: &Vec<i32>) -> usize {
+        let mut visited = vec![0; self.size];
+        for i in 0..included_vertices.len() {
+            if included_vertices[i] == 0 {
+                visited[i] = 1;
+            }
+        }
+        let mut count = 0;
+        while visited.iter().sum::<usize>() != visited.len() {
+            let mut next = 0;
+            for i in 0..self.size {
+                if visited[i] == 0 {
+                    next = i;
+                    break;
+                }
+            }
+            self.dfs(&next, &mut visited);
+            count += 1;
+        }
+        return count;
+    }
+
+    fn count_components(&self) -> usize {
+        self.count_components_partial(&vec![1; self.size])
+    }
+
+    fn get_closure(&self) -> Graph {
+        self.get_closure_traced(false)
+    }
+
+    fn check_toughness(&self, t: f64) -> bool {
+        for cutset in self.cutsets() {
+            let components_count = cutset.graph.count_components_partial(&cutset.vertices) as f64;
+            let cut_cardinality = (self.size - cutset.cardinality) as f64;
+            if components_count > 1.0 && cut_cardinality < t * components_count {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    fn get_toughness(&self) -> f64 {
+        let mut left: f64 = 0.0;
+        let mut right: f64 = 1024.0; // Reasonable limit
+        let eps: f64 = 1e-9;
+
+        while (right - left).abs() > eps {
+            let mid = (left + right) / 2.0;
+
+            if self.check_toughness(mid) == false {
+                right = mid;
+            } else {
+                left = mid;
+            }
+        }
+
+        return (left * 1e7).round() / 1e7;
+    }
+
+    fn is_complete(&self) -> bool {
+        for row in 0..self.size {
+            for col in 0..self.size {
+                if row != col && self.matrix[row][col] == 0 {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+
+    fn is_independent(&self) -> bool {
+        for row in 0..self.size {
+            for col in 0..self.size {
+                if row != col && self.matrix[row][col] != 0 {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+}
+
+struct Counters {
+    graphs: i32,
+    tough_1: i32,
+    tough_2: i32,
+    bch_hamiltonian: i32,
+    t15_hamiltonian: i32,
+    t25_hamiltonian: i32,
+    dirac_hamiltonian: i32,
+    ore_hamiltonian: i32,
+    posa_hamiltonian: i32,
+}
+
+impl Counters {
+    fn new() -> Counters {
+        return Counters {
+            graphs: 0,
+            tough_1: 0,
+            tough_2: 0,
+            bch_hamiltonian: 0,
+            t15_hamiltonian: 0,
+            t25_hamiltonian: 0,
+            dirac_hamiltonian: 0,
+            ore_hamiltonian: 0,
+            posa_hamiltonian: 0,
+        };
+    }
+}
+
+fn theorem15(g: &Graph, toughness: f64, min_degree: f64) -> bool {
+    let max_ind_cutset_size = g.max_independent_cutset().cardinality as f64;
+    let third_of_size = g.size as f64 / 3.0;
+    let tmp = if third_of_size > max_ind_cutset_size - 1.0 {
+        third_of_size
+    } else {
+        max_ind_cutset_size - 1.0
+    };
+
+    return toughness >= 1.0 && min_degree >= tmp;
+}
+
+fn theorem25(g: &Graph, toughness: f64, min_degree: f64) -> bool {
+    return min_degree > g.size as f64 / (toughness + 1.0) - 1.0;
+}
+
+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;
+}
+
+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;
+}
+
+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 &degrees {
+            if *d <= k {
+                cnt += 1;
+            }
+        }
+        if cnt >= k {
+            return false;
+        }
+    }
+    if g.size % 2 != 0 {
+        let mut cnt = 0;
+        for d in &degrees {
+            if *d <= end {
+                cnt += 1;
+            }
+        }
+        if cnt > end {
+            return false;
+        }
+    }
+    return true;
+}
+
+fn main() {
+    let stdin = io::stdin();
+
+    let mut time = 0;
+    let mut counters = Counters::new();
+
+    for line in stdin.lock().lines() {
+        let line = line.unwrap();
+
+        let g = Graph::from_g6(&line);
+        counters.graphs += 1;
+
+        let start = Instant::now();
+        let closure = g.get_closure();
+        let is_complete = closure.is_complete();
+
+        let toughness = if g.is_complete() {
+            f64::MAX
+        } else {
+            g.get_toughness()
+        };
+
+        if toughness >= 1.0 {
+            counters.tough_1 += 1;
+        }
+        if toughness >= 2.0 {
+            counters.tough_2 += 1;
+        }
+
+        let min_degree = g.min_degree() as f64;
+
+        if theorem15(&g, toughness, min_degree) {
+            counters.t15_hamiltonian += 1;
+            println!("g6:bigalke-jung:{}", line);
+        }
+
+        if theorem25(&g, toughness, min_degree) {
+            counters.t25_hamiltonian += 1;
+            println!("g6:bauer:{}", line);
+        }
+
+        if dirac_theorem(&g) {
+            counters.dirac_hamiltonian += 1;
+            println!("g6:dirac:{}", line);
+        }
+
+        if ore_theorem(&g) {
+            counters.ore_hamiltonian += 1;
+            println!("g6:ore:{}", line);
+        }
+
+        if posa_theorem(&g) {
+            counters.posa_hamiltonian += 1;
+            println!("g6:posa:{}", line);
+        }
+
+        if is_complete {
+            counters.bch_hamiltonian += 1;
+            println!("g6:bondy-chvatal:{}", line);
+        }
+
+        if is_complete && false {
+            println!("Graph: {line}\n{g}");
+
+            let components_count = g.count_components();
+            println!("Components count: {components_count}");
+            let min_degree = g.min_degree();
+            println!("Minimal degree: {min_degree}");
+
+            let cutset = g.max_independent_cutset();
+            println!("Maximal independent cutset:\n{}", cutset.graph);
+            println!("Included vertices: {:?}", cutset.vertices);
+            println!("Cutset cardinality: {}", cutset.cardinality);
+
+            let cycle = g.get_hamiltonian_cycle();
+            print!("Hamiltonian cycle: ");
+            let start = 0;
+            let mut current = start;
+            loop {
+                print!("{}", current + 1);
+                print!(" -> ");
+                current = cycle[current];
+                if current == start {
+                    println!("{}", current + 1);
+                    break;
+                }
+            }
+        }
+
+        let elapsed = start.elapsed();
+        time += elapsed.as_nanos();
+    }
+
+    println!("Total count of graphs: {}", counters.graphs);
+    println!("Count of 1-tough graphs: {}", counters.tough_1);
+    println!("Count of 2-tough graphs: {}", counters.tough_2);
+    println!(
+        "Count of Dirac's Hamiltonian graphs: {}",
+        counters.dirac_hamiltonian
+    );
+    println!(
+        "Count of Ore's Hamiltonian graphs: {}",
+        counters.ore_hamiltonian
+    );
+    println!(
+        "Count of Posa's Hamiltonian graphs: {}",
+        counters.posa_hamiltonian
+    );
+    println!(
+        "Count of Bondy-Chvatal Hamiltonian graphs: {}",
+        counters.bch_hamiltonian
+    );
+    println!(
+        "Count of Theorem 15 Hamiltonian graphs: {}",
+        counters.t15_hamiltonian
+    );
+    println!(
+        "Count of Theorem 25 Hamiltonian graphs: {}",
+        counters.t25_hamiltonian
+    );
+    println!("Time elapsed: {}s", time as f64 / 1e9);
+}