Minimum Moves in Snakes and Ladders Game in Python

Suppose we are playing a game of snakes and ladders. We have a condition that we can roll any number that we can like on a dice. We start from position 0 and our destination is position 100, and we roll the dice several times to reach the destination. We must find out the least number of dice rolls required to reach the destination if we are provided with the position of the snakes and ladders on the board.The arrays snakes and ladders represent the positions of snakes and ladders in the board and each entry in the arrays contains a start value and an end value of a snake or a ladder on the board.

So, if the input is like ladders = [(11, 40), (37,67),(47, 73),(15, 72)], snakes = [(90, 12), (98, 31), (85, 23), (75, 42), (70, 18), (49, 47)], then the output will be 8.

The minimum number of moves required is 8 to reach the 100th position on the board given the positions of snakes and ladders.

To solve this, we will follow these steps −

• append the array snakes to array ladders
• edges := a new map
• for each pair f,t in ladders, do
  • edges[f] := t
• u := a new set
• v := a new set
• add(1) to v
• m := 0
• while 100 is not present in v, do
  • m := m + 1
  • w := a new set
  • for each f in v, do
    • for i in range 1 to 6, do
      • n := f + i
      • if n is present in edges, then
        • n := edges[n]
      • if n is present in u, then
        • go for next iteration
      • add(n) to u
      • add(n) to w
  • v := w
• return m

Example

Let us see the following implementation to get better understanding −

def solve(ladders, snakes):
    ladders.extend(snakes)
    edges = {}
    for f,t in ladders:
        edges[f] = t
    u = set()
    v = set()
    v.add(1)
    m = 0
    while 100 not in v:
        m += 1
        w = set()
        for f in v:
            for i in range(1,7):
                n = f + i
                if n in edges:
                    n = edges[n]
                if n in u:
                    continue
                u.add(n)
                w.add(n)
        v = w
    return m
print(solve([(11, 40), (37,67),(47, 73),(15, 72)], [(90, 12), (98, 31), (85, 23), (75, 42), (70, 18), (49, 47)]))

Input

[(11, 40), (37,67),(47, 73),(15, 72)], [(90, 12), (98, 31), (85, 23), (75, 42), (70, 18), (49, 47)]

Output

8