Add tree_isomorphism alg

top_order/top_order.cpp

@@ -13,13 +13,8 @@ int main() {
     int size = 10;
     Digraph G(size);
     G.add_edge(3,4);
-    // G.add_edge(4,3);
-    // G.add_edge(5,6);
     G.add_edge(6,7);
     G.add_edge(7,5);
-    // G.add_edge(7,3);
-    // G.add_edge(0,3);
-    // G.add_edge(3,0);
 
     // keeps track of vertices with zero indegree, these can be put at the beginning
     std::stack<int> zero_indegree;

tree_isomorphism/CMakeLists.txt

@@ -0,0 +1,4 @@
+cmake_minimum_required(VERSION 3.10)
+project(tree_isomorphism)
+add_executable(tree_isomorphism
+	tree_isomorphism.cpp)

tree_isomorphism/tree_isomorphism.cpp

@@ -0,0 +1,175 @@
+//  Algorithm deciding if two rooted trees are isomorphic
+//  Authors: Georǵi Kocharyan
+
+#include <iostream>
+#include <cstdio>
+#include <vector>
+#include <list>
+#include <queue>
+#include <algorithm>
+#include <string>
+
+// Node has to store parent to make naming possible in linear time
+
+struct TreeNode {
+    std::vector<TreeNode*> children;
+    std::string name;
+    TreeNode* parent;
+    TreeNode() = default;
+    TreeNode(TreeNode* node) : parent(node) {}
+    void add_child()
+    {
+        children.push_back(new TreeNode(this));
+    }
+};
+
+// outputs a vector of lists of each depth of the tree
+
+std::vector<std::list<TreeNode*>> tree_levels(TreeNode* root) {
+   if (!root) return {};
+
+    std::vector<std::list<TreeNode*>> result;
+    std::queue<std::pair<TreeNode*, int>> q;
+    q.push(std::make_pair(root, 0));
+
+    while (!q.empty())
+    {
+        TreeNode* node = q.front().first;
+        int depth = q.front().second;
+        q.pop();
+
+        // If this is a new depth, add a new list to the result
+        if (depth >= result.size()) {
+            result.push_back(std::list<TreeNode*>());
+        }
+
+        // Add the current node's value to the appropriate depth list
+        result[depth].push_back(node);
+
+        // Enqueue children with their depth
+        for (const auto& child : node->children) {
+            q.push(std::make_pair(child, depth + 1));
+        }
+    }
+    return result;
+}
+    
+bool lexicographicOrder(TreeNode* a,TreeNode* b) {
+    return (a->name)<(b->name);
+}
+
+// to do: actually implement linear bucket sort
+void bucketSort(std::list<TreeNode*>& nodes) {
+    if (nodes.empty()) return;
+    nodes.sort(lexicographicOrder);
+}
+
+int main() {
+
+    // initialise tree 1
+    TreeNode* root = new TreeNode();
+    root->add_child();
+    root->add_child();
+    root->add_child();
+    root->children[1]->add_child();
+    root->children[1]->add_child();
+    root->children[2]->add_child();
+    root->children[1]->children[1]->add_child();
+    root->children[2]->children[0]->add_child();
+    root->children[2]->children[0]->add_child();
+
+    // initialise tree 2
+    TreeNode* root2 = new TreeNode();
+    root2->add_child();
+    root2->add_child();
+    root2->add_child();
+    root2->children[0]->add_child();
+    root2->children[2]->add_child();
+    root2->children[2]->add_child();
+    root2->children[0]->children[0]->add_child();
+    root2->children[2]->children[1]->add_child();
+    root2->children[2]->children[1]->add_child();
+
+    // store all nodes by their depth
+    std::vector<std::list<TreeNode*>> levels1 = tree_levels(root);
+    std::vector<std::list<TreeNode*>> levels2 = tree_levels(root2);
+
+    int height = levels1.size()-1;
+
+    // if heights are different trees cannot be isomorphic
+    if (!(height == levels2.size()-1)) 
+    {
+        std::cout << "Trees are not isomorphic. Their heights are different." << std::endl;
+        return 0;
+    }
+
+    // the name of all leaves is 1
+    std::string s("1");
+
+    for (auto leaf : levels1[height])
+    {
+        leaf->name = s;
+    }
+    for (auto leaf : levels2[height])
+    {
+        leaf->name = s;
+    }
+
+    for (int i = height-1; i >= 0; i--)
+    {
+        int amount = levels1[i].size();
+        if (!(amount == levels2[i].size()))
+        {
+            std::cout << "Trees are not isomorphic, they have a different number of nodes in depth " << i << "." << std::endl;
+            return 0;
+        }
+
+        // name all nodes of current height by iterating through all (sorted) children
+
+        for (const auto& node : levels1[i+1])
+        {
+            node->parent->name = node->parent->name + node->name;
+        }
+
+        for (const auto& node : levels2[i+1])
+        {
+            node->parent->name = node->parent->name + node->name;
+        }
+
+        // sort nodes of current height by name
+        bucketSort(levels1[i]);
+        bucketSort(levels2[i]);
+
+        // check if both trees have the same names in the current level
+        std::list<TreeNode*>::iterator itr1 = levels1[i].begin();
+        std::list<TreeNode*>::iterator itr2 = levels2[i].begin();
+
+        for (auto _ = amount; _--;)
+        {
+            if (!(((*itr1)->name) == ((*itr2)->name)))
+            {
+                std::cout << "Trees are not isomorphic!" << std::endl;
+                return 0;
+            }
+            itr1++;
+            itr2++;
+        }
+
+        // rename words according to index in sorted vector
+        int count = 0;
+        for (auto& node : levels1[i])
+        {
+            node->name = std::to_string(count);
+            count++;
+        }
+        count = 0;
+        for (auto& node : levels2[i])
+        {
+            node->name = std::to_string(count);
+            count++;
+        }
+    }
+        
+    std::cout << "Trees are isomorphic." << std::endl;
+    return 0;
+}