From 53f8c2034c8c3d5985651a83a40e474ca29393d6 Mon Sep 17 00:00:00 2001
From: hal8174 <henning.lindemann@pm.me>
Date: Thu, 14 Nov 2024 21:52:45 +0100
Subject: [PATCH 1/2] Fix bug and add reverse search for minimum

---
 vertex_cover/src/main.rs  | 17 +++++++++++++++++
 vertex_cover/src/owned.rs |  8 +++++++-
 2 files changed, 24 insertions(+), 1 deletion(-)

diff --git a/vertex_cover/src/main.rs b/vertex_cover/src/main.rs
index fc75d3c..42b2e7f 100644
--- a/vertex_cover/src/main.rs
+++ b/vertex_cover/src/main.rs
@@ -155,8 +155,11 @@ enum Method {
 #[derive(Debug, Parser)]
 struct Args {
     filename: PathBuf,
+    #[clap(default_value = "reduction2")]
     method: Method,
     k: Option<u16>,
+    #[clap(short, long)]
+    reverse: bool,
 }
 
 fn main() {
@@ -169,6 +172,20 @@ fn main() {
         let r = vertex_cover(&graph, k, args.method);
         eprintln!("{}: {:?}", k, start.elapsed());
         r
+    } else if args.reverse {
+        let mut k = graph.num_vertices();
+        let mut last_solution = None;
+        loop {
+            let start = std::time::Instant::now();
+            let r = vertex_cover(&graph, k, args.method);
+            eprintln!("{}: {:?}", k, start.elapsed());
+            if let Some(r) = r {
+                k = r.len() as u16 - 1;
+                last_solution = Some(r);
+            } else {
+                break last_solution;
+            };
+        }
     } else {
         let mut k = 0;
         loop {
diff --git a/vertex_cover/src/owned.rs b/vertex_cover/src/owned.rs
index 1171e0c..3dc3d31 100644
--- a/vertex_cover/src/owned.rs
+++ b/vertex_cover/src/owned.rs
@@ -237,6 +237,8 @@ pub fn reduction2(graph: &mut Graph, k: u16) -> Option<Vec<u16>> {
         let _ = graph.reinsert_vertices(1);
 
         r
+    } else if graph.is_empty() {
+        Some(Vec::new())
     } else if k == 0 {
         if graph.is_empty() {
             Some(Vec::new())
@@ -343,6 +345,10 @@ pub fn reduction2(graph: &mut Graph, k: u16) -> Option<Vec<u16>> {
             }
         }
     } else if let Some(vertex) = graph.get_vertex_with_degree_greater(3) {
+        if k < 1 {
+            return None;
+        }
+
         graph.remove_vertex(vertex);
 
         match reduction2(graph, k - 1) {
@@ -374,6 +380,6 @@ pub fn reduction2(graph: &mut Graph, k: u16) -> Option<Vec<u16>> {
             }
         }
     } else {
-        unreachable!()
+        unreachable!("{k}")
     }
 }

From 4d67a5480f6009c8d951a7277875f7f7eb0b2f25 Mon Sep 17 00:00:00 2001
From: hal8174 <henning.lindemann@pm.me>
Date: Thu, 14 Nov 2024 21:52:57 +0100
Subject: [PATCH 2/2] Add verzweigungsvectoren

---
 verzweigungsvectoren/main.py | 31 +++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100755 verzweigungsvectoren/main.py

diff --git a/verzweigungsvectoren/main.py b/verzweigungsvectoren/main.py
new file mode 100755
index 0000000..4c7a378
--- /dev/null
+++ b/verzweigungsvectoren/main.py
@@ -0,0 +1,31 @@
+#!/usr/bin/env python
+
+from numpy import roots,isreal
+from itertools import combinations_with_replacement
+
+
+solutions = []
+
+s = [1, 2, 3, 4, 5, 6, 7, 8, 9]
+
+for i in range(2, 7):
+
+    for j in combinations_with_replacement(s, i):
+
+        p = [-j.count(k) for k in range(max(j) + 1)]
+        p[0] = 1
+
+
+        r = [float(k) for k in roots(p) if isreal(k) and k > 0.0]
+        # print(j, max(j), p, r)
+
+        solutions.append((j, r[0]))
+
+
+
+solutions.sort(key=lambda e: e[1])
+
+for s in solutions:
+
+    print(f"{s[1]}\t{s[0]}")
+