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Explain why the algorithm works

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You are inebriated on an island and want to go swimming, but you can't walk straight. Write algorithm to calculate the probability that you reach the water before you fall asleep.

The island is a square D-by-D grid. You start at a given grid cell x, y (1-indexed), and each "step" you take is a random step up, right, down, or left (uniformly distributed with probability 0.25 in each direction). Diagonal steps are not allowed. If you step outside the D-by-D square you have made it to the "water". After N steps, you fall asleep. What is the probability that you make it into the water before falling asleep?

Provide an efficient algorithm that solves the problem for arbitrary integers D and N.

Explain why the algorithm works.

What is the time complexity of your algorithm?

What is the space complexity of your algorithm?

Reference no: EM133294912

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