Add tasks 15 materials

Author: TeogopK

Seminars/sem_15/README.md

@@ -57,12 +57,9 @@
 - Хамилтоновият цикъл е път, който минава всеки един **връх** на даден на даден граф само по един път, като свършва във върха, от който е тръгнал.
 - Проблемът за намирането на минимален Хамилтонов цикъл е известен като *The Traveling Salesman Problem* (*NP hard problem*).
 
-Пример:
-
 ![Hamiltonian path and cycle example](media/hamiltonian_path_and_cycle.png)
 
-- Хамилтонов път - *ABCED*
-- Хамилтонов цикъл - *ABDECA*
+Пример за Хамилтонов път - *ABCED*, за Хамилтонов цикъл - *ABDECA*.
 
 ## P, NP, NP complete, NP hard проблеми
 
@@ -101,7 +98,8 @@
 
 ## Задачи за упражнение
 
+- [Permutations](https://leetcode.com/problems/permutations)
+- [All Paths From Source to Target](https://leetcode.com/problems/all-paths-from-source-to-target)
 - [Reconstruct Itinerary](https://leetcode.com/problems/reconstruct-itinerary)
 
-
 Решения на задачите: [тук](/Tasks/tasks_15)

Tasks/tasks_15/README.md

@@ -0,0 +1,5 @@
+## Условия:
+
+- [Permutations](https://leetcode.com/problems/permutations)
+- [All Paths From Source to Target](https://leetcode.com/problems/all-paths-from-source-to-target)
+- [Reconstruct Itinerary](https://leetcode.com/problems/reconstruct-itinerary)

Tasks/tasks_15/all_paths_from_source_to_target/solution_backtracking.py

@@ -0,0 +1,30 @@
+class Solution:
+    def dfs(self, current_node, end_node, path, visited, all_paths, graph):
+        for neigh in graph[current_node]:
+            if neigh in visited:
+                continue
+            
+            if neigh == end_node:
+                all_paths.append(path + [end_node])
+                continue
+
+            path.append(neigh)
+            visited.add(neigh)
+
+            self.dfs(neigh, end_node, path, visited, all_paths, graph)
+            path.pop()
+            visited.remove(neigh)
+        
+        return all_paths
+
+    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
+        N = len(graph)
+
+        start_node = 0
+        end_node =  N - 1
+
+        all_paths = []
+        path = [start_node]
+        visited = set([start_node])
+
+        return self.dfs(start_node, end_node, path, visited, all_paths, graph)

Tasks/tasks_15/permutations/solution_backtracking.py

@@ -0,0 +1,25 @@
+class Solution:
+    def dfs(self, path, all_paths, nums, used):
+        if len(path) == len(nums):
+            all_paths.append(path.copy())
+            return all_paths
+
+        for num in nums:
+            if num in used:
+                continue
+            path.append(num)
+            used.add(num)
+
+            self.dfs(path, all_paths, nums, used)
+        
+            path.pop()
+            used.remove(num)
+
+        return all_paths
+
+    def permute(self, nums: List[int]) -> List[List[int]]:
+        all_paths = []
+        path = []
+        used = set()
+
+        return self.dfs(path, all_paths, nums, used)

Tasks/tasks_15/permutations/solution_itertools.py

@@ -0,0 +1,5 @@
+from itertools import permutations
+
+class Solution:
+    def permute(self, nums: List[int]) -> List[List[int]]:
+        return permutations(nums)