Syntax error Program to check we can cross river by stones or not in Python

Program to check we can cross river by stones or not in Python

Suppose we have a list of sorted numbers called stones and this is representing the positions of stones on a river that we are trying to cross. To cross the river, we must finish at the last stone. Now in each step, we can jump (k - 1, k, or k + 1) steps ahead where k is the distance of the last jump. We have to check whether we can cross the river or not.

So, if the input is like stones = [0, 1, 3, 4, 5, 6, 8, 9, 13], then the output will be True, as we can start from 0, then jump 1 unit to go stone 1, then 2 units to go 3, after that 2 units to 5, then 3 units to go 8, and finally 5 units to go 13, and this is the final place.

To solve this, we will follow these steps −

  • start := A[0], end := last element of A
  • A := a set of all unique elements of A
  • Define a function check() . This will take pos:= start, prev:= 0
  • if pos is same as end, then
    • return True
  • for each jump in [prev - 1, prev, prev + 1], do
    • if jump >= 1, then
      • next_pos := jump + pos
      • if next_pos is in A and check(next_pos, jump) is true, then
        • return True
  • return False
  • From the main method call check() and return result

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

class Solution:
   def solve(self, A):
      start, end = A[0], A[-1]
      A = set(A)
      def check(pos=start, prev=0):
         if pos == end:
            return True
         for jump in [prev - 1, prev, prev + 1]:
            if jump >= 1:
               next_pos = jump + pos
               if next_pos in A and check(next_pos, jump):
                  return True
         return False
      return check()
ob = Solution()
stones = [0, 1, 3, 4, 5, 6, 8, 9, 13]
print(ob.solve(stones))

Input

[0, 1, 3, 4, 5, 6, 8, 9, 13]

Output

True
Updated on: 2020-12-12T09:29:42+05:30

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