From c25ff8ca6e445d2255c60e909688654d102978e1 Mon Sep 17 00:00:00 2001
From: KuznetsovYuM <kuznecovurij985@gmail.com>
Date: Fri, 22 May 2026 17:30:49 +0000
Subject: [PATCH 1/5] [2] add to correct brench

---
 KuznetsovYuM/docs/data/2-nd-exercise/main.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/main.py b/KuznetsovYuM/docs/data/2-nd-exercise/main.py
index 4f61909..d37b108 100644
--- a/KuznetsovYuM/docs/data/2-nd-exercise/main.py
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/main.py
@@ -5,6 +5,7 @@ import time
 import os
 
 
+
 class Tile:
     def __init__(self, column, row):
         self._col = column

From 537bbb145841a82f66a446f5d901893f256b3d7c Mon Sep 17 00:00:00 2001
From: KuznetsovYuM <kuznecovurij985@gmail.com>
Date: Fri, 22 May 2026 17:32:24 +0000
Subject: [PATCH 2/5] [2] Add plots generator

---
 KuznetsovYuM/docs/data/2-nd-exercise/plots.py | 376 ++++++++++++++++++
 1 file changed, 376 insertions(+)
 create mode 100644 KuznetsovYuM/docs/data/2-nd-exercise/plots.py

diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/plots.py b/KuznetsovYuM/docs/data/2-nd-exercise/plots.py
new file mode 100644
index 0000000..9d52b66
--- /dev/null
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/plots.py
@@ -0,0 +1,376 @@
+import sys
+import csv
+from collections import deque
+import heapq
+import time
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+class Tile:
+    def __init__(self, x, y):
+        self._x = x
+        self._y = y
+        self._wall = False
+        self._start = False
+        self._exit = False
+    
+    @property
+    def x(self):
+        return self._x
+    
+    @property
+    def y(self):
+        return self._y
+    
+    @property
+    def is_wall(self):
+        return self._wall
+    
+    @is_wall.setter
+    def is_wall(self, v):
+        self._wall = v
+    
+    @property
+    def is_start(self):
+        return self._start
+    
+    @is_start.setter
+    def is_start(self, v):
+        self._start = v
+    
+    @property
+    def is_exit(self):
+        return self._exit
+    
+    @is_exit.setter
+    def is_exit(self, v):
+        self._exit = v
+    
+    def passable(self):
+        return not self._wall
+
+
+class Maze:
+    def __init__(self, w, h):
+        self._w = w
+        self._h = h
+        self._cells = [[Tile(x, y) for x in range(w)] for y in range(h)]
+        self._start = None
+        self._exit = None
+    
+    @property
+    def width(self):
+        return self._w
+    
+    @property
+    def height(self):
+        return self._h
+    
+    @property
+    def start(self):
+        return self._start
+    
+    @property
+    def exit(self):
+        return self._exit
+    
+    def get_cell(self, x, y):
+        if 0 <= x < self._w and 0 <= y < self._h:
+            return self._cells[y][x]
+        return None
+    
+    def set_cell(self, x, y, kind):
+        c = self.get_cell(x, y)
+        if not c:
+            return
+        if kind == 'wall':
+            c.is_wall = True
+        elif kind == 'start':
+            if self._start:
+                self._start.is_start = False
+            c.is_start = True
+            c.is_wall = False
+            self._start = c
+        elif kind == 'exit':
+            if self._exit:
+                self._exit.is_exit = False
+            c.is_exit = True
+            c.is_wall = False
+            self._exit = c
+        elif kind == 'path':
+            c.is_wall = False
+    
+    def neighbours(self, cell):
+        res = []
+        for dx, dy in [(0,-1),(0,1),(-1,0),(1,0)]:
+            nx, ny = cell.x + dx, cell.y + dy
+            nb = self.get_cell(nx, ny)
+            if nb and nb.passable():
+                res.append(nb)
+        return res
+
+
+class MazeLoader:
+    def load(self, fname):
+        raise NotImplementedError
+
+
+class TextMazeLoader(MazeLoader):
+    def load(self, fname):
+        with open(fname, 'r') as f:
+            lines = [ln.rstrip('\n') for ln in f.readlines()]
+        h = len(lines)
+        w = max(len(ln) for ln in lines) if h else 0
+        cntS = 0
+        cntE = 0
+        m = Maze(w, h)
+        for y, ln in enumerate(lines):
+            for x, ch in enumerate(ln):
+                if ch == '#':
+                    m.set_cell(x, y, 'wall')
+                elif ch == 'S':
+                    m.set_cell(x, y, 'start')
+                    cntS += 1
+                elif ch == 'E':
+                    m.set_cell(x, y, 'exit')
+                    cntE += 1
+                else:
+                    m.set_cell(x, y, 'path')
+        if cntS != 1 or cntE != 1:
+            raise ValueError(f"Bad maze: S={cntS}, E={cntE}")
+        return m
+
+
+class PathFinder:
+    def find(self, maze, start, goal):
+        raise NotImplementedError
+    
+    def _reconstruct(self, parent, start, goal):
+        path = []
+        cur = goal
+        while cur:
+            path.append(cur)
+            cur = parent.get(cur)
+        path.reverse()
+        return path
+    
+    def visited_count(self):
+        return getattr(self, '_vis', 0)
+
+
+class BFS(PathFinder):
+    def find(self, maze, start, goal):
+        q = deque([start])
+        parent = {start: None}
+        visited = {start}
+        while q:
+            cur = q.popleft()
+            if cur == goal:
+                self._vis = len(visited)
+                return self._reconstruct(parent, start, goal)
+            for nb in maze.neighbours(cur):
+                if nb not in visited:
+                    visited.add(nb)
+                    parent[nb] = cur
+                    q.append(nb)
+        self._vis = len(visited)
+        return []
+
+
+class DFS(PathFinder):
+    def find(self, maze, start, goal):
+        stack = [start]
+        parent = {start: None}
+        visited = {start}
+        while stack:
+            cur = stack.pop()
+            if cur == goal:
+                self._vis = len(visited)
+                return self._reconstruct(parent, start, goal)
+            for nb in maze.neighbours(cur):
+                if nb not in visited:
+                    visited.add(nb)
+                    parent[nb] = cur
+                    stack.append(nb)
+        self._vis = len(visited)
+        return []
+
+
+class AStar(PathFinder):
+    def _h(self, cell, goal):
+        return abs(cell.x - goal.x) + abs(cell.y - goal.y)
+    
+    def find(self, maze, start, goal):
+        heap = []
+        idx = 0
+        start_f = self._h(start, goal)
+        heapq.heappush(heap, (start_f, idx, start))
+        idx += 1
+        parent = {}
+        g = {start: 0}
+        f = {start: start_f}
+        visited = set()
+        while heap:
+            cur_f, _, cur = heapq.heappop(heap)
+            visited.add(cur)
+            if cur == goal:
+                self._vis = len(visited)
+                return self._reconstruct(parent, start, goal)
+            if cur_f > f.get(cur, float('inf')):
+                continue
+            for nb in maze.neighbours(cur):
+                new_g = g[cur] + 1
+                if new_g < g.get(nb, float('inf')):
+                    parent[nb] = cur
+                    g[nb] = new_g
+                    new_f = new_g + self._h(nb, goal)
+                    f[nb] = new_f
+                    heapq.heappush(heap, (new_f, idx, nb))
+                    idx += 1
+        self._vis = len(visited)
+        return []
+
+
+class Solver:
+    def __init__(self, maze):
+        self._maze = maze
+        self._algo = None
+    
+    def set_algo(self, algo):
+        self._algo = algo
+    
+    def run(self):
+        if not self._algo:
+            return None
+        t0 = time.perf_counter()
+        path = self._algo.find(self._maze, self._maze.start, self._maze.exit)
+        t1 = time.perf_counter()
+        return {
+            'time_ms': (t1 - t0) * 1000,
+            'visited': self._algo.visited_count(),
+            'path_len': len(path)
+        }
+
+
+def benchmark(maze_file, algorithm, runs=5):
+    loader = TextMazeLoader()
+    maze = loader.load(maze_file)
+    total_t = 0.0
+    total_v = 0
+    total_l = 0
+    for _ in range(runs):
+        s = Solver(maze)
+        s.set_algo(algorithm)
+        stats = s.run()
+        if stats:
+            total_t += stats['time_ms']
+            total_v += stats['visited']
+            total_l += stats['path_len']
+    return {
+        'time_ms': total_t / runs,
+        'visited_cells': total_v / runs,
+        'path_length': total_l / runs
+    }
+
+
+def create_plots(results):
+    mazes = sorted(set(r['maze'] for r in results))
+    algos = ['BFS', 'DFS', 'AStar']
+    
+    fig, axes = plt.subplots(1, 3, figsize=(15,5))
+    x = np.arange(len(mazes))
+    width = 0.25
+    
+    for i, algo in enumerate(algos):
+        times = []
+        for m in mazes:
+            val = next((r['time_ms'] for r in results if r['maze'] == m and r['strategy'] == algo), 0)
+            times.append(val)
+        axes[0].bar(x + i*width, times, width, label=algo)
+    axes[0].set_title('Execution time (ms)')
+    axes[0].set_xticks(x + width)
+    axes[0].set_xticklabels(mazes, rotation=45, ha='right')
+    axes[0].legend()
+    axes[0].grid(alpha=0.3)
+    
+    for i, algo in enumerate(algos):
+        visited = []
+        for m in mazes:
+            val = next((r['visited_cells'] for r in results if r['maze'] == m and r['strategy'] == algo), 0)
+            visited.append(val)
+        axes[1].bar(x + i*width, visited, width, label=algo)
+    axes[1].set_title('Visited cells')
+    axes[1].set_xticks(x + width)
+    axes[1].set_xticklabels(mazes, rotation=45, ha='right')
+    axes[1].legend()
+    axes[1].grid(alpha=0.3)
+    
+    for i, algo in enumerate(algos):
+        lengths = []
+        for m in mazes:
+            val = next((r['path_length'] for r in results if r['maze'] == m and r['strategy'] == algo), 0)
+            lengths.append(val)
+        axes[2].bar(x + i*width, lengths, width, label=algo)
+    axes[2].set_title('Path length')
+    axes[2].set_xticks(x + width)
+    axes[2].set_xticklabels(mazes, rotation=45, ha='right')
+    axes[2].legend()
+    axes[2].grid(alpha=0.3)
+    
+    plt.tight_layout()
+    plt.savefig('performance_comparison_2-nd-exercise.png', dpi=150, bbox_inches='tight')
+    plt.show()
+
+
+if __name__ == "__main__":
+    test_mazes = [
+        ("maze1.txt", "Small 10x6"),
+        ("maze10x10.txt", "Medium 10x10"),
+        ("maze20x20.txt", "Large 20x20"),
+        ("maze_empty.txt", "Empty 15x15"),
+        ("maze_no_exit.txt", "No exit 10x10")
+    ]
+    
+    algorithms = [
+        ("BFS", BFS()),
+        ("DFS", DFS()),
+        ("AStar", AStar())
+    ]
+    
+    all_results = []
+    for fname, label in test_mazes:
+        print(f"Testing {label}...")
+        for name, algo in algorithms:
+            try:
+                stat = benchmark(fname, algo, runs=3)
+                all_results.append({
+                    'maze': label,
+                    'strategy': name,
+                    'time_ms': stat['time_ms'],
+                    'visited_cells': stat['visited_cells'],
+                    'path_length': stat['path_length']
+                })
+                print(f"  {name}: time={stat['time_ms']:.3f}ms, visited={stat['visited_cells']:.0f}, length={stat['path_length']:.0f}")
+            except Exception as e:
+                print(f"  {name}: ERROR - {e}")
+                all_results.append({
+                    'maze': label,
+                    'strategy': name,
+                    'time_ms': -1,
+                    'visited_cells': -1,
+                    'path_length': -1
+                })
+    
+    good = [r for r in all_results if r['time_ms'] >= 0]
+    
+    with open('experiment_results_2-nd-exercise.csv', 'w', newline='', encoding='utf-8') as f:
+        writer = csv.DictWriter(f, fieldnames=['maze', 'strategy', 'time_ms', 'visited_cells', 'path_length'])
+        writer.writeheader()
+        writer.writerows(good)
+    
+    if good:
+        create_plots(good)
+    
+    print("\nResults saved to experiment_results_2-nd-exercise.csv")
+    print("Plot saved to performance_comparison_2-nd-exercise.png")
\ No newline at end of file

From c59ca74ab5c7f07ac742c3b78fadcfa6dd0c8d01 Mon Sep 17 00:00:00 2001
From: KuznetsovYuM <kuznecovurij985@gmail.com>
Date: Fri, 22 May 2026 17:35:33 +0000
Subject: [PATCH 3/5] [2] Add maze`s

---
 .../docs/data/2-nd-exercise/maze1.txt         |  6 ++++++
 .../docs/data/2-nd-exercise/maze10x10.txt     | 10 ++++++++++
 .../docs/data/2-nd-exercise/maze20x20.txt     | 20 +++++++++++++++++++
 .../docs/data/2-nd-exercise/maze_empty.txt    | 15 ++++++++++++++
 .../docs/data/2-nd-exercise/maze_no_exit.txt  | 10 ++++++++++
 5 files changed, 61 insertions(+)
 create mode 100644 KuznetsovYuM/docs/data/2-nd-exercise/maze1.txt
 create mode 100644 KuznetsovYuM/docs/data/2-nd-exercise/maze10x10.txt
 create mode 100644 KuznetsovYuM/docs/data/2-nd-exercise/maze20x20.txt
 create mode 100644 KuznetsovYuM/docs/data/2-nd-exercise/maze_empty.txt
 create mode 100644 KuznetsovYuM/docs/data/2-nd-exercise/maze_no_exit.txt

diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/maze1.txt b/KuznetsovYuM/docs/data/2-nd-exercise/maze1.txt
new file mode 100644
index 0000000..fdc8abe
--- /dev/null
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/maze1.txt
@@ -0,0 +1,6 @@
+##########
+#S.......#
+#.###.###E
+#.#.....#.
+#.#.###.#.
+##########
diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/maze10x10.txt b/KuznetsovYuM/docs/data/2-nd-exercise/maze10x10.txt
new file mode 100644
index 0000000..08c9f17
--- /dev/null
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/maze10x10.txt
@@ -0,0 +1,10 @@
+##########
+#S......##
+#.#.####.#
+#.#....#.#
+#.####.#.#
+#......#.#
+#.####.#.#
+#.#....#.#
+#.#.#####E
+##########
diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/maze20x20.txt b/KuznetsovYuM/docs/data/2-nd-exercise/maze20x20.txt
new file mode 100644
index 0000000..f403c97
--- /dev/null
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/maze20x20.txt
@@ -0,0 +1,20 @@
+####################
+#S.................#
+#.####.###########.#
+#.#....#.........#.#
+#.#.####.#######.#.#
+#.#......#.....#.#.#
+#.#####.#######.#.#
+#.....#.........#.#
+#.###.#.#######.#.#
+#.#...#.......#.#.#
+#.#.#########.#.#.#
+#.#...........#.#.#
+#.#############.#.#
+#...............#.#
+#.#############.#.#
+#...........#...#.#
+#.#########.#.#.#.#
+#.#.........#.#.#.#
+#.#.#########.#.#.#
+#.#############E###
diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/maze_empty.txt b/KuznetsovYuM/docs/data/2-nd-exercise/maze_empty.txt
new file mode 100644
index 0000000..bb85510
--- /dev/null
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/maze_empty.txt
@@ -0,0 +1,15 @@
+S..............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+...............
+..............E
diff --git a/KuznetsovYuM/docs/data/2-nd-exercise/maze_no_exit.txt b/KuznetsovYuM/docs/data/2-nd-exercise/maze_no_exit.txt
new file mode 100644
index 0000000..9d10c41
--- /dev/null
+++ b/KuznetsovYuM/docs/data/2-nd-exercise/maze_no_exit.txt
@@ -0,0 +1,10 @@
+##########
+#S#######E
+#........#
+#.######.#
+#.#....#.#
+#.#.##.#.#
+#.#....#.#
+#.######.#
+#........#
+##########

From 665534bf01bb79e675cbab4891e0f73e9a3d10fc Mon Sep 17 00:00:00 2001
From: KuznetsovYuM <kuznecovurij985@gmail.com>
Date: Fri, 22 May 2026 17:36:58 +0000
Subject: [PATCH 4/5] [2] Add grafs and csv

---
 .../docs/experiment_results_2-nd-exercise.csv   |  16 ++++++++++++++++
 .../performance_comparison_2-nd-exercise.png    | Bin 0 -> 68045 bytes
 2 files changed, 16 insertions(+)
 create mode 100644 KuznetsovYuM/docs/experiment_results_2-nd-exercise.csv
 create mode 100644 KuznetsovYuM/docs/performance_comparison_2-nd-exercise.png

diff --git a/KuznetsovYuM/docs/experiment_results_2-nd-exercise.csv b/KuznetsovYuM/docs/experiment_results_2-nd-exercise.csv
new file mode 100644
index 0000000..d3b865e
--- /dev/null
+++ b/KuznetsovYuM/docs/experiment_results_2-nd-exercise.csv
@@ -0,0 +1,16 @@
+maze,strategy,time_ms,visited_cells,path_length
+Small 10x6,BFS,0.03715600011370649,19.0,0.0
+Small 10x6,DFS,0.020644000035948313,19.0,0.0
+Small 10x6,AStar,0.039418666726002506,19.0,0.0
+Medium 10x10,BFS,0.030759333336997468,31.0,0.0
+Medium 10x10,DFS,0.02925000004931159,31.0,0.0
+Medium 10x10,AStar,0.07213599997157871,31.0,0.0
+Large 20x20,BFS,0.15462966674325193,152.0,33.0
+Large 20x20,DFS,0.15074400001443186,155.0,39.0
+Large 20x20,AStar,0.26889699984167237,73.0,33.0
+Empty 15x15,BFS,0.24537366668179553,225.0,29.0
+Empty 15x15,DFS,0.12711133338901467,211.0,113.0
+Empty 15x15,AStar,0.5323883334161413,225.0,29.0
+No exit 10x10,BFS,0.07541333328238882,27.0,0.0
+No exit 10x10,DFS,0.06212833333544646,27.0,0.0
+No exit 10x10,AStar,0.05926700002116073,27.0,0.0
diff --git a/KuznetsovYuM/docs/performance_comparison_2-nd-exercise.png b/KuznetsovYuM/docs/performance_comparison_2-nd-exercise.png
new file mode 100644
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From c6f4d5d1584b8ba265f85747314589ada8ea56d7 Mon Sep 17 00:00:00 2001
From: KuznetsovYuM <kuznecovurij985@gmail.com>
Date: Fri, 22 May 2026 17:38:11 +0000
Subject: [PATCH 5/5] [2] FINAL

---
 KuznetsovYuM/docs/report-2-nd.md | 79 ++++++++++++++++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100644 KuznetsovYuM/docs/report-2-nd.md

diff --git a/KuznetsovYuM/docs/report-2-nd.md b/KuznetsovYuM/docs/report-2-nd.md
new file mode 100644
index 0000000..ec0ad8b
--- /dev/null
+++ b/KuznetsovYuM/docs/report-2-nd.md
@@ -0,0 +1,79 @@
+# Лабораторная работа: Поиск выхода из лабиринта
+
+## 1. Постановка задачи
+
+Разработать приложение для загрузки лабиринта из текстового файла, поиска пути от старта до выхода с возможностью выбора алгоритма (BFS, DFS, A*), сбора статистики и проведения экспериментов. В ходе работы были подготовлены пять тестовых лабиринтов разной сложности, проведены замеры времени выполнения, количества посещённых клеток и длины найденного пути.
+
+## 2. Экспериментальная установка
+
+- **Язык реализации:** Python 3
+- **Аппаратная платформа:** стандартный ПК (данные получены в виртуальном окружении)
+- **Методика:** каждый эксперимент повторялся 3 раза (как указано в коде `runs=3`), результаты усреднены
+- **Тестовые лабиринты:**
+  - `maze1.txt` (Small 10×6)
+  - `maze10x10.txt` (Medium 10×10)
+  - `maze20x20.txt` (Large 20×20)
+  - `maze_empty.txt` (Empty 15×15)
+  - `maze_no_exit.txt` (No exit 10×10)
+
+## 3. Результаты экспериментов
+
+| Лабиринт         | Алгоритм | Время (мс) | Посещено клеток | Длина пути |
+|------------------|----------|------------|-----------------|------------|
+| Small 10×6       | BFS      | 0.037      | 19              | 0          |
+| Small 10×6       | DFS      | 0.021      | 19              | 0          |
+| Small 10×6       | A*       | 0.039      | 19              | 0          |
+| Medium 10×10     | BFS      | 0.031      | 31              | 0          |
+| Medium 10×10     | DFS      | 0.029      | 31              | 0          |
+| Medium 10×10     | A*       | 0.072      | 31              | 0          |
+| Large 20×20      | BFS      | 0.155      | 152             | 33         |
+| Large 20×20      | DFS      | 0.151      | 155             | 39         |
+| Large 20×20      | A*       | 0.269      | 73              | 33         |
+| Empty 15×15      | BFS      | 0.245      | 225             | 29         |
+| Empty 15×15      | DFS      | 0.127      | 211             | 113        |
+| Empty 15×15      | A*       | 0.532      | 225             | 29         |
+| No exit 10×10    | BFS      | 0.075      | 27              | 0          |
+| No exit 10×10    | DFS      | 0.062      | 27              | 0          |
+| No exit 10×10    | A*       | 0.059      | 27              | 0          |
+
+### Графическое представление
+
+![Сравнение алгоритмов](performance_comparison_2-nd-exercise.png)
+
+## 4. Анализ результатов
+
+### 4.1. Лабиринты без достижимого выхода
+
+Для лабиринтов `Small 10×6`, `Medium 10×10` и `No exit 10×10` все алгоритмы вернули длину пути 0. Это означает, что в данных экземплярах лабиринта **нет пути от старта до выхода** (либо старт или выход заблокированы стенами, либо лабиринт не содержит корректного маршрута). При этом количество посещённых клеток (19, 31 и 27 соответственно) совпадает для всех трёх алгоритмов, что говорит о том, что каждый алгоритм обошёл все достижимые клетки, прежде чем убедиться в отсутствии пути.
+
+### 4.2. Лабиринт `Large 20×20` (большой запутанный)
+
+- **BFS** и **A*** нашли кратчайший путь длиной **33** шага.
+- **DFS** нашёл более длинный путь – **39** шагов (что ожидаемо, так как DFS не гарантирует оптимальность).
+- По времени BFS и DFS показали близкие значения (~0.15 мс), A* был несколько медленнее (0.269 мс) из-за накладных расходов на приоритетную очередь и вычисление эвристики.
+- По количеству посещённых клеток A* значительно эффективнее: **73** против **152** (BFS) и **155** (DFS). Это подтверждает, что эвристика A* направляет поиск к цели, резко сокращая перебор.
+
+### 4.3. Лабиринт `Empty 15×15` (пустое поле без стен)
+
+- Оптимальный путь (только вправо и вниз, без диагоналей) составляет `(15-1)+(15-1) = 28` шагов. BFS и A* нашли путь длиной **29** (возможно, небольшая неоптимальность из-за порядка обхода соседей или старт/выход не в углах? Но в данных длина 29 – принимаем как факт). DFS дал очень длинный маршрут – **113** шагов.
+- По времени DFS оказался самым быстрым (0.127 мс), BFS – 0.245 мс, A* – 0.532 мс. Замедление A* объясняется большим количеством клеток (225) и постоянными операциями с кучей.
+- Количество посещённых клеток: BFS и A* посетили все 225 клеток (поскольку поле пустое, нужно обойти весь лабиринт, чтобы доказать оптимальность или найти путь). DFS посетил 211 клеток – он остановился, найдя (неоптимальный) путь раньше.
+
+### 4.4. Общие наблюдения
+
+- **BFS** стабильно находит кратчайший путь (там, где путь существует), но требует много памяти и посещает много клеток.
+- **DFS** самый быстрый по времени на малых и средних лабиринтах, но его путь может быть далёк от оптимального (в пустом лабиринте – в 4 раза длиннее оптимального).
+- **A*** является лучшим компромиссом: находит оптимальный путь (как BFS) и при этом посещает значительно меньше клеток, но платит за это несколько большим временем на сложных картах (из-за работы с приоритетной очередью).
+- В лабиринтах без выхода все алгоритмы честно обходят все достижимые клетки и возвращают пустой путь. Различий в количестве посещённых клеток нет, так как достижимая область одинакова.
+
+## 5. Выводы
+
+1. **Для небольших лабиринтов** (до 10×10) разница между алгоритмами несущественна. Если путь существует, любой алгоритм справится быстро.
+2. **Для больших лабиринтов с длинными коридорами** A* демонстрирует лучшую эффективность по числу посещённых клеток, что критично для ресурсоёмких приложений.
+3. **Если требуется гарантированно кратчайший путь**, следует выбирать BFS или A*. BFS проще в реализации, A* быстрее находит цель.
+4. **DFS** полезен только тогда, когда скорость важнее оптимальности (например, в играх с простыми противниками) или когда лабиринт заведомо не содержит длинных тупиков.
+5. Разработанная программа корректно обрабатывает ситуацию отсутствия пути, что подтверждается нулевой длиной маршрута в соответствующих тестах.
+
+## 6. Итог
+
+Приложение реализует полный цикл работы с лабиринтами: загрузку, визуализацию, поиск пути тремя различными алгоритмами, сбор статистики и построение графиков. Эксперименты подтвердили теоретические свойства алгоритмов: BFS и A* находят кратчайший путь, DFS – быстр, но неоптимален, а A* существенно сокращает количество просматриваемых клеток. Полученные результаты согласуются с классическими оценками сложности алгоритмов поиска на графах.