def faster_all_pairs_shorted_paths(W):
n = len(W)
L = W
m = 1
print 'L({}) = '.format(m)
print_2D_array(L)
while m < n-1:
L = extend_shortest_paths(L, L)
m = 2*m
print 'L({}) = '.format(m)
print_2D_array(L)
return L
def floyd_warshall(W):
n = len(W)
D = W
PI = [[0 for _ in range(n)] for _ in range(n)]
for i in range(n):
for j in range(n):
if i == j or W[i][j] == float("inf"):
PI[i][j] = None
else:
PI[i][j] = i
for k in range(n):
print "k = {}".format(k+1)
D_new = [[0 for _ in range(n)] for _ in range(n)]
PI_new = [[0 for _ in range(n)] for _ in range(n)]
#calculate D
for i in range(n):
for j in range(n):
D_new[i][j] = min(D[i][j], D[i][k] + D[k][j])
print "D({k})[{i}, {j}] = min(D({k_1})[{i}, {j}], D({k_1})[{i}, {j}] + D({k_1})[{i}, {j}])".format(k = k+1, k_1 = k, i = i+1, j = j+1)
print "{} = min({}, {} + {})".format(D_new[i][j], D[i][j], D[i][k], D[k][j])
print ""
#calculate PI
for i in range(n):
for j in range(n):
if D[i][j] <= D[i][k] + D[k][j]:
PI_new[i][j] = PI[i][j]
else:
PI_new[i][j] = PI[k][j]
#update D
D = D_new
print "D({}) = ".format(k + 1)
print_2D_array(D_new)
print ""
#update PI
PI = PI_new
print "PI({k}) = ".format(k = k+1)
display_mat = [[0 for _ in range(n)] for _ in range(n)]
for i in range(n):
for j in range(n):
if PI[i][j] is not None:
display_mat[i][j] = PI[i][j] + 1
else:
display_mat[i][j] = PI[i][j]
print_2D_array(display_mat)# display index from 1
return D_new
'''
Created on Oct 15, 2015
@author: shuaipeng
'''
from test.DP_problem import print_2D_array
def solve_DP(n, p):
P = [[0 for _ in range(n+1)] for _ in range(n+1)]
for i in range(n+1):
P[i][0] = 0
for j in range(n+1):
P[0][j] = 1
for i in range(1, n+1):
for j in range(1, n+1):
P[i][j] = p*P[i - 1][j] + (1 - p)*P[i][j-1]
return P
if __name__ == '__main__':
print_2D_array(solve_DP(n = 7, p = 0.4))
c[0][j] = 0
for i in range(1, m + 1):
for j in range(1, n + 1):
if x[i] == y[j]:
c[i][j] = c[i - 1][j - 1] + 1
elif c[i - 1][j] > c[i][j - 1]:
c[i][j] = c[i - 1][j]
else:
c[i][j] = c[i][j - 1]
return c
def construct_LCS(c, m, n, x ,y):
i, j = m, n
LCS = []
while c[i][j] != 0:
if x[i] == y[j]:
LCS.append(x[i])
i, j = i - 1, j - 1
elif c[i - 1][j] == c[i][j]:
i = i - 1
else:
j = j - 1
LCS.reverse()
return LCS
if __name__ == '__main__':
x = [None, 1, 0, 0, 1, 0, 1, 0, 1]
y = [None, 0, 1, 0, 1, 1, 0, 1, 1, 0]
c = solve_LCS(x, y)
print_2D_array(c)
print construct_LCS(c, len(x) - 1, len(y) - 1, x ,y)
m = 1
print 'L({}) = '.format(m)
print_2D_array(L)
while m < n-1:
L = extend_shortest_paths(L, L)
m = 2*m
print 'L({}) = '.format(m)
print_2D_array(L)
return L
if __name__ == '__main__':
# W = [[0, -4, 3, float("inf"), float("inf")],
# [float("inf"), 0, 2, 1, float("inf")],
# [float("inf"), -1, 0, 7, 5],
# [float("inf"), float("inf"), float("inf"), 0, 10],
# [float("inf"), float("inf"), float("inf"), -8, 0]]
W = [[0, 2.7, 3.1, float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf")],
[2.7, 0, 1, float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf")],
[3.1, 1, 0, 2.3, float("inf"), 2.6, float("inf"), float("inf"), float("inf"), float("inf"), float("inf")],
[float("inf"), float("inf"), 2.3, 0, 0.95, float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf")],
[float("inf"), float("inf"), float("inf"), 0.95, 0, 1.7, 1.3, float("inf"), float("inf"), float("inf"), float("inf")],
[float("inf"), float("inf"), 2.6, float("inf"), 1.7, 0, 0.1, float("inf"), float("inf"), float("inf"), float("inf")],
[float("inf"), float("inf"), float("inf"), float("inf"), 1.3, 0.1, 0, 7.1, float("inf"), float("inf"), 1.5],
[float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), 7.1, 0, 3.5, float("inf"), float("inf")],
[float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), 3.5, 0, 0.5, float("inf")],
[float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), 0.5, 0, 1.1],
[float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), float("inf"), 1.5, float("inf"), float("inf"), 1.1, 0]]
res = faster_all_pairs_shorted_paths(W)
print "shortest path matrix is "
print_2D_array(res)