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Snake Ladder Problem!


Problem Description

Rishabh takes out his Snakes and Ladders Game, stares the board and wonders: "If I can always roll the die to whatever number I want, what would be the least number of rolls to reach the destination?"

RULES:

  • The game is played with cubic dice of 6 faces numbered from 1 to A.
  • Starting from 1 , land on square 100 with the exact roll of the die. If moving the number rolled would place the player beyond square 100, no move is made.
  • If a player lands at the base of a ladder, the player must climb the ladder. Ladders go up only.
  • If a player lands at the mouth of a snake, the player must go down the snake and come out through the tail. Snakes go down only.

BOARD DESCRIPTION:

  • The board is always 10 x 10 with squares numbered from 1 to 100.
  • The board contains N ladders given in a form of 2D matrix A of size N * 2 where (A[i][0], A[i][1]) denotes a ladder that has its base on square A[i][0] and end at square A[i][1].
  • The board contains M snakes given in a form of 2D matrix B of size M * 2 where (B[i][0], B[i][1]) denotes a snake that has its mouth on square B[i][0] and tail at square B[i][1].



Problem Constraints

1 <= N, M <= 15

1 <= A[i][0], A[i][1], B[i][0], B[i][1] <= 100

A[i][0] < A[i][1] and B[i][0] > B[i][1]

Neither square 1 nor square 100 will be the starting point of a ladder or snake.

A square will have at most one endpoint from either a snake or a ladder.



Input Format

First argument is a 2D matrix A of size N * 2 where (A[i][0], A[i][1]) denotes a ladder that has its base on square A[i][0] and end at square A[i][1].

Second argument is a 2D matrix B of size M * 2 where (B[i][0], B[i][1]) denotes a snake that has its mouth on square B[i][0] and tail at square B[i][1].



Output Format

Return the least number of rolls to move from start to finish on a separate line. If there is no solution, return -1.



Example Input

Input 1:

 A = [  [32, 62]
        [42, 68]
        [12, 98]
     ]
 B = [  [95, 13]
        [97, 25]
        [93, 37]
        [79, 27]
        [75, 19]
        [49, 47]
        [67, 17]

Input 2:

 A = [  [8, 52]
        [6, 80]
        [26, 42]
        [2, 72]
     ]
 B = [  [51, 19]
        [39, 11]
        [37, 29]
        [81, 3]
        [59, 5]
        [79, 23]
        [53, 7]
        [43, 33]
        [77, 21] 



Example Output

Output 1:

 3

Output 2:

 5



Example Explanation

Explanation 1:

 The player can roll a 5 and a 6 to land at square 12. There is a ladder to square 98. A roll of 2 ends the traverse in 3 rolls.

Explanation 2:

 The player first rolls 5 and climbs the ladder to square 80. Three rolls of 6 get to square 98.
 A final roll of 2 lands on the target square in 5 total rolls.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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