Create City Tour Problem

Author: satty08

Mathematics/City Tour Problem

@@ -0,0 +1,86 @@
+'''
+There are A cities numbered from 1 to A. You have already visited M cities, the indices of which are given in an array B of M integers.
+
+If a city with index i is visited, you can visit either the city with index i-1 (i >= 2) or the city with index i+1 (i < A) if they are not already visited.
+Eg: if N = 5 and array M consists of [3, 4], then in the first level of moves, you can either visit 2 or 5.
+
+You keep visiting cities in this fashion until all the cities are not visited.
+Find the number of ways in which you can visit all the cities modulo 10^9+7.
+
+Input Format
+
+The 1st argument given is an integer A, i.e total number of cities.
+The 2nd argument given is an integer array B, where B[i] denotes ith city you already visited.
+Output Format
+
+Return an Integer X % (1e9 + 7), number of ways in which you can visit all the cities.
+Constraints
+
+1 <= A <= 1000
+1 <= M <= A
+1 <= B[i] <= A
+For Example
+
+Input:
+ A = 5
+ B = [2, 5]
+Output:
+ 6
+ 
+Explanation:
+ All possible ways to visit remaining cities are :
+ 1. 1 -> 3 -> 4
+ 2. 1 -> 4 -> 3
+ 3. 3 -> 1 -> 4
+ 4. 3 -> 4 -> 1
+ 5. 4 -> 1 -> 3
+ 6. 4 -> 3 -> 1
+'''
+
+Solution:
+
+class Solution:
+ # @param A : integer
+ # @param B : list of integers
+ # @return an integer
+ def solve(self, A, B):
+ v = []
+ old = 0
+ for i in B:
+ v.append(i-old-1)
+ old = i
+ 
+ v.append(A-old)
+ 
+ 
+ t = 0
+ for i in v:
+ if i>0:
+ t+=i
+ 
+ res = 1
+ for i in range(t):
+ res = (res*(i+1))%1000000007
+ 
+ 
+ s = 0
+ for i in v[1:-1]:
+ if i>0:
+ s+=(i-1)
+ 
+ for i in range(s):
+ res = (res*2)%1000000007
+ 
+ tp = 1
+ for i in v:
+ if i>1:
+ for j in range(i):
+ tp = (tp*(j+1))%1000000007
+ i = 1000000005
+ while i:
+ if i%2==1:
+ res = (res*tp)%1000000007
+ tp = (tp*tp)%1000000007
+ i = int(i/2)
+ return res
+