Create count-all-possible-routes.py

Author: kamyu104

Python/count-all-possible-routes.py

@@ -0,0 +1,66 @@
+# Time:  O(nlogn + n * f)
+# Space: O(n * f)
+
+import bisect
+
+
+class Solution(object):
+    def countRoutes(self, locations, start, finish, fuel):
+        """
+        :type locations: List[int]
+        :type start: int
+        :type finish: int
+        :type fuel: int
+        :rtype: int
+        """
+        MOD = 10**9+7
+
+        s, f = locations[start], locations[finish];
+        locations.sort()
+        start, finish = bisect.bisect_left(locations, s), bisect.bisect_left(locations, f)
+
+        left = [[0]*(fuel+1) for _ in xrange(len(locations))]  # left[i][f], last move is toward left to location i by f fuel
+        right = [[0]*(fuel+1) for _ in xrange(len(locations))]  # right[i][f], last move is toward right to location i by f fuel
+        for f in xrange(1, fuel+1):
+            for j in xrange(len(locations)-1):
+                d = locations[j+1]-locations[j]
+                if f > d:
+                    left[j][f] = (right[j+1][f-d] + 2*left[j+1][f-d] % MOD) % MOD;
+                elif f == d:
+                    left[j][f] = int(j+1 == start)
+            for j in xrange(1, len(locations)):
+                d = locations[j]-locations[j-1]
+                if f > d:
+                    right[j][f] = (left[j-1][f-d] + 2*right[j-1][f-d] % MOD) % MOD
+                elif f == d:
+                    right[j][f] = int(j-1 == start)
+        result = int(start == finish)
+        for f in xrange(1, fuel+1):
+            result = ((result + left[finish][f]) % MOD + right[finish][f]) % MOD
+        return result
+
+
+# Time:  O(n^2 * f)
+# Space: O(n * f)
+class Solution2(object):
+    def countRoutes(self, locations, start, finish, fuel):
+        """
+        :type locations: List[int]
+        :type start: int
+        :type finish: int
+        :type fuel: int
+        :rtype: int
+        """
+        MOD = 10**9+7
+        dp = [[0]*(fuel+1) for _ in xrange(len(locations))]
+        dp[start][0] = 1
+        for f in xrange(fuel+1):
+            for i in xrange(len(locations)):
+                for j in xrange(len(locations)):
+                    if i == j:
+                        continue
+                    d = abs(locations[i]-locations[j])
+                    if f-d < 0:
+                        continue
+                    dp[i][f] = (dp[i][f]+dp[j][f-d])%MOD
+        return reduce(lambda x, y: (x+y)%MOD, dp[finish])