太久沒有回來寫了。寒假的時候把題目都刷完，這次暑假剛剛開始就正好可以刷一刷。
這道題目是經典dp題目，記得poj上面就有。
Description:
Given an integer matrix, find the length of the longest increasing path.
From each cell, you can either move to four directions: left, right, up or down. You may NOT move diagonally or move outside of the boundary (i.e. wrap-around is not allowed).
大概就是說給一個矩陣，然後找一個最長連續上升或者下降序列。求這個序列的長度。連續的定義爲矩陣中有相鄰邊。
直接記憶化搜索，每次搜索相鄰邊，如果已有記憶則讀取記憶，否則相鄰邊+1與當前比，取大。
class Solution(object):
def Solution(self):
self.dir = [[1,0], [-1,0], [0,1], [0,-1]]
return
def longestIncreasingPath(self, matrix):
self.dir = [[1,0], [-1,0], [0,1], [0,-1]]
self.n = len(matrix)
self.m = len(matrix[0])
self.step = [ [-1 for j in range(self.m)] for i in range(self.n)]
self.matrix = matrix
max_step = 1
for i in range(self.n):
for j in range(self.m):
if self.step[i][j] == -1:
max_step = max(max_step, self.dfs(i,j))
return max_step
def dfs(self, cur_x, cur_y):
if self.step[cur_x][cur_y] > 0:
return self.step[cur_x][cur_y]
self.step[cur_x][cur_y] = 1
for i in range(4):
next_x = cur_x + self.dir[i][0]
next_y = cur_y + self.dir[i][1]
if not self.valid(next_x, next_y):
continue
if self.matrix[cur_x][cur_y] > self.matrix[next_x][next_y]:
self.step[cur_x][cur_y] = max(self.step[cur_x][cur_y], self.dfs(next_x, next_y) + 1)
return self.step[cur_x][cur_y]
def valid(self, x, y):
if x < 0 or x >= self.n:
return False
if y < 0 or y >= self.m:
return False
return True
