LeetCode 筆記 - 329. Longest Increasing Path in a Matrix

題目在此 329. Longest Increasing Path in a Matrix

image 24

給一個 matrix,請計算出最長遞增路徑的長度

解題思維

這題的基本思維是做 n x m 次的 Depth First Search
但其實在每一次的 Depth First Search 之間,我們是可以利用之前計算的結果來加速的

宣告一張表,裡面存放的資訊是,該點可以找到的最長遞增路徑
Depth First Search 的過程中當某一個點遇到附近已經有結果的點
那就不用對有結果的點遞迴下去,因為已經跑過了,直接把結果拿過來用就可以了

完成 ✅

程式碼

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class Solution:
def longestIncreasingPath(self, matrix: List[List[int]]) -> int:

def get_neighbors(y, x):
offset = [-1, 1]

result = []
for o in offset:
new_y = y + o
if not 0 <= new_y < length_y:
continue
if matrix[new_y][x] <= matrix[y][x]:
continue
result.append((new_y, x))

for o in offset:
new_x = x + o
if not 0 <= new_x < length_x:
continue
if matrix[y][new_x] <= matrix[y][x]:
continue
result.append((y, new_x))

return result

length_y = len(matrix)
length_x = len(matrix[0])

long_map = [[0 for _ in range(length_x)] for _ in range(length_y)]

def dfs(y, x):
if long_map[y][x] != 0:
return long_map[y][x]

neighbors = get_neighbors(y, x)
if not neighbors:
long_map[y][x] = 1
return 1

max_path_legnth = 0
for n_y, n_x in neighbors:
max_path_legnth = max(dfs(n_y, n_x), max_path_legnth)
long_map[y][x] = max_path_legnth + 1

return max_path_legnth + 1

result = 0
for y in range(length_y):
for x in range(length_x):
# 加速用
if long_map[y][x] != 0:
continue
result = max(result, dfs(y, x))

return result

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