我试图解决一个编程挑战问题,从某个网站,我不想在这里提及。在
问题如下:
There is an square board with N*N points. An insect starts out at a particular point (x1,y1). It can jump to any point (x2,y2) if |x1-x2|+|y1-y2| <= S. Also, some points contain water on which the insect cannot jump. How many different paths can it take in M jumps? Note that it can remain at the same point by jumping in place.
给出了整数N
、S
、M
以及初始板配置。在
我很确定我的解决方案是正确的,并且可以通过归纳法加以证明。我把棋盘转换成一个图(邻接列表),点之间有边,可以使昆虫跳跃。那么这只是一个迭代M次和更新路径计数的问题。在
我主要关心的是代码需要进行优化,使其能够在多个测试用例中工作,而不会分配/释放太多时间,这会降低运行时间。如果有人能在算法本身中提出优化建议,那就太好了。在
谢谢!在
import sys
#The board on which Jumping insect moves.
#The max size in any test case is 200 * 200
board = [['_']*200 for j in xrange(200)]
#Graph in the form of an adjancency list created from the board
G = [list() for i in xrange(200*200)]
def paths(N,M,S):
'''Calculates the total number of paths insect takes
The board size is N*N, Length of paths: M,
Insect can jusp from square u to square v if ||u-v|| <=S
Here ||u-v|| refers to the 1 norm'''
# Totals paths are modulo 1000000007
MOD = 1000000007
# Clearing adjacency list for this testcase
for i in xrange(N*N): del(G[i][:])
s = -1 #Starting point s
#Creating G adjacency list
# Point 'L' represents starting point
# Point 'P' cannot be accessed by the insect
for u in xrange(N*N):
x1, y1 = u/N, u%N
if board[x1][y1] == 'L': s = u
elif board[x1][y1] == 'P': continue
for j in xrange(S+1):
for k in xrange(S+1-j):
x2, y2 = x1+j, y1+k
if x2 < N and y2 < N and not board[x2][y2] == 'P':
v = x2*N+y2
G[u].append(v)
if not u == v: G[v].append(u)
if j > 0 and k > 0:
x2, y2 = x1+j, y1-k
if x2 < N and y2 >= 0 and not board[x2][y2] == 'P':
v = x2*N+y2
G[u].append(v)
G[v].append(u)
# P stores path counts
P = [[0 for i in xrange(N*N)] for j in xrange(2)]
# Setting count for starting position to 1
P[0][s] = 1
# Using shifter to toggle between prev and curr paths
shifter, prev, curr = 0, 0, 0
# Calculating paths
for i in xrange(M):
prev, curr = shifter %2, (shifter+1)%2
#Clearing Path counts on curr
for i in xrange(N*N): P[curr][i] = 0
for u in xrange(N*N):
if P[prev][u] == 0: continue
for v in G[u]:
P[curr][v] = (P[curr][v]+P[prev][u]) % MOD
shifter = (shifter+1)%2
return (sum(P[curr])%MOD)
#Number of testcases
num = int(sys.stdin.readline().split()[0])
results = []
# Reading in test cases
for i in xrange(num):
N, M, S = [int(j) for j in sys.stdin.readline().split()]
for j in xrange(N):
board[j][:N] = list(sys.stdin.readline().split()[0])
results.append(paths(N,M,S))
for result in results:
print result
这正是
numpy
的优点,尽管您可以通过使用array
和struct
模块来管理这个特定用例。在相关问题 更多 >
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