From 52fb255f37f75e5bc518dff4d55e6a33bc3f7223 Mon Sep 17 00:00:00 2001 From: TORUS <42745810+TORUS0818@users.noreply.github.com> Date: Thu, 28 Nov 2024 19:57:19 +0900 Subject: [PATCH] Create answer.md --- medium/63/answer.md | 287 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 287 insertions(+) create mode 100644 medium/63/answer.md diff --git a/medium/63/answer.md b/medium/63/answer.md new file mode 100644 index 0000000..dd48d36 --- /dev/null +++ b/medium/63/answer.md @@ -0,0 +1,287 @@ +# Step1 + +かかった時間：9min + +計算量： +obstacleGrid.length = M +obstacleGrid[i].length = Nとして、 + +時間計算量：O(M*N) + +空間計算量：O(M*N) + +DP +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + m = len(obstacleGrid) + n = len(obstacleGrid[0]) + num_ways = [[0] * n for _ in range(m)] + + if obstacleGrid[0][0] == 1\ + or obstacleGrid[-1][-1] == 1: + return 0 + + num_ways[0][0] = 1 + for row in range(m): + for col in range(n): + if row == 0 and col == 0: + continue + if obstacleGrid[row][col] == 1: + continue + if row == 0: + num_ways[row][col] = num_ways[row][col - 1] + continue + if col == 0: + num_ways[row][col] = num_ways[row - 1][col] + continue + num_ways[row][col] = ( + num_ways[row][col - 1] + num_ways[row - 1][col] + ) + + return num_ways[-1][-1] +``` +思考ログ： +- 前回のUniquePathsIのやり方を継承しつつ、obstacleGridを参照しながら行けない場所を考慮できるようにする +- ばーっと書いてしまったが、for文の中の処理を切り出して見通しをよくしたい（初手これを書いたので一応載せている） + +上を少しまとめた +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + def _count_unique_paths(row: int, col: int) -> int: + # gridのセル(row, col)までのパス数を数える + if row == 0: + return num_ways[row][col - 1] + if col == 0: + return num_ways[row - 1][col] + + return num_ways[row][col - 1] + num_ways[row - 1][col] + + m = len(obstacleGrid) + n = len(obstacleGrid[0]) + num_ways = [[0] * n for _ in range(m)] + + if obstacleGrid[0][0] == 1\ + or obstacleGrid[-1][-1] == 1: + return 0 + + num_ways[0][0] = 1 + for row in range(m): + for col in range(n): + if row == 0 and col == 0: + continue + if obstacleGrid[row][col] == 1: + continue + num_ways[row][col] = _count_unique_paths(row, col) + + return num_ways[-1][-1] +``` +思考ログ： + +再帰 +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + @cache + def _count_unique_paths(row: int, col: int) -> int: + assert row >= 0 or col >= 0, 'row and col must be positive integer values.' + + if obstacleGrid[row][col] == 1: + return 0 + if row == 0 and col == 0: + return 1 + if row == 0: + return _count_unique_paths(row, col - 1) + if col == 0: + return _count_unique_paths(row - 1, col) + + return _count_unique_paths(row - 1, col)\ + + _count_unique_paths(row, col - 1) + + return _count_unique_paths( + len(obstacleGrid) - 1, + len(obstacleGrid[0]) - 1 +``` +思考ログ： + +1-DP +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + # 11:59 + def _check_if_valid_cell(row: int, col: int, is_transposed: bool) -> bool: + if is_transposed: + return obstacleGrid[col][row] == 0 + else: + return obstacleGrid[row][col] == 0 + + if obstacleGrid[0][0] == 1\ + or obstacleGrid[-1][-1] == 1: + return 0 + + m = len(obstacleGrid) + n = len(obstacleGrid[0]) + is_transposed = False + if m < n: + n, m = m, n + is_transposed = True + + num_ways = [0] * n + num_ways[0] = 1 + for row in range(m): + for col in range(n): + if _check_if_valid_cell(row, col, is_transposed): + if col == 0: + continue + num_ways[col] += num_ways[col - 1] + else: + num_ways[col] = 0 + + return num_ways[-1] +``` +思考ログ： +- メモリ節約ver +- 今回は、n, mを入れ替えた時に参照するobstacleGridにも影響が及ぶ + - これも転置しちゃえば良いのだが、破壊的な変更をしたくないし、転置した情報を別に用意したらこれはこれで本末転倒なことに + - 転置フラグで管理するようにしたが、どうだろうか +- ```num_ways```の0番目の要素の扱いで少しハマった + - ```num_ways```がどんな要素を持つ配列なのか、それは意図したものなのか、確認がまだ甘い + - colのループの前で```col = 0```だけ処理してしまってもいいが、うーん + +# Step2 + +講師役目線でのセルフツッコミポイント： +- マジックナンバー（obstacle） + +参考にした過去ログなど： +- https://github.com/Ryotaro25/leetcode_first60/pull/40 +- https://github.com/seal-azarashi/leetcode/pull/32 +- https://github.com/Yoshiki-Iwasa/Arai60/pull/49 + - BFS +- https://github.com/nittoco/leetcode/pull/27 +- https://github.com/fhiyo/leetcode/pull/35 +- https://github.com/goto-untrapped/Arai60/pull/33 + - 以下の条件のまとめ方が頭になかった + - https://github.com/goto-untrapped/Arai60/pull/33/files#r1665011732 +- https://github.com/YukiMichishita/LeetCode/pull/15 +- https://github.com/sakupan102/arai60-practice/pull/35 + - シンプルな1DP +- https://github.com/SuperHotDogCat/coding-interview/pull/17 +- https://github.com/shining-ai/leetcode/pull/34 +- https://github.com/hayashi-ay/leetcode/pull/44 + - 値を受け取る、渡す + +DP +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + OBSTACLE = 1 + if obstacleGrid[0][0] == OBSTACLE \ + or obstacleGrid[-1][-1] == OBSTACLE: + return 0 + + m = len(obstacleGrid) + n = len(obstacleGrid[0]) + num_ways = [[0] * n for _ in range(m)] + num_ways[0][0] = 1 + for row in range(m): + for col in range(n): + if row == 0 and col == 0: + continue + if obstacleGrid[row][col] == OBSTACLE: + continue + if row > 0: + num_ways[row][col] += num_ways[row - 1][col] + if col > 0: + num_ways[row][col] += num_ways[row][col - 1] + + return num_ways[-1][-1] +``` +思考ログ： +- 少し処理の順序を変えた +- マジックナンバーの解消 +- DP受け取りの分岐を変更 + +DP、事前に初期化 +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + OBSTACLE = 1 + if obstacleGrid[0][0] == OBSTACLE \ + or obstacleGrid[-1][-1] == OBSTACLE: + return 0 + + m = len(obstacleGrid) + n = len(obstacleGrid[0]) + def initialize_num_ways() -> list[list[int]]: + num_ways = [[0] * n for _ in range(m)] + for row in range(m): + if obstacleGrid[row][0] == OBSTACLE: + break + num_ways[row][0] = 1 + for col in range(n): + if obstacleGrid[0][col] == OBSTACLE: + break + num_ways[0][col] = 1 + + return num_ways + + num_ways = initialize_num_ways() + for row in range(1, m): + for col in range(1, n): + if obstacleGrid[row][col] == OBSTACLE: + continue + num_ways[row][col] = num_ways[row - 1][col] + num_ways[row][col - 1] + + return num_ways[-1][-1] +``` +思考ログ： +- 後半がシンプルに書けて良い + +# Step3 + +かかった時間：6min + +```python +class Solution: + def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int: + OBSTACLE = 1 + if obstacleGrid[0][0] == OBSTACLE \ + or obstacleGrid[-1][-1] == OBSTACLE: + return 0 + + m = len(obstacleGrid) + n = len(obstacleGrid[0]) + def initialize_num_ways(): + num_ways = [[0] * n for _ in range(m)] + for row in range(m): + if obstacleGrid[row][0] == OBSTACLE: + break + num_ways[row][0] = 1 + for col in range(n): + if obstacleGrid[0][col] == OBSTACLE: + break + num_ways[0][col] = 1 + + return num_ways + + num_ways = initialize_num_ways() + for row in range(1, m): + for col in range(1, n): + if obstacleGrid[row][col] == OBSTACLE: + continue + num_ways[row][col] = num_ways[row - 1][col] + num_ways[row][col - 1] + + return num_ways[-1][-1] +``` +思考ログ： +- 個人的には後半の処理がすっきりするのが良かった +- 1DPは```min(n, m)```の最適化までやりたくなるが、コードが込み入ってくるので2DPでも良い気がする + +# Step4 + +```python +``` +思考ログ： +