Getting Robo to Safety

We need to follow an algorithm which avoids stepping onto any of the red tiles throughout the entire duration of the execution of the algorithm.

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Algorithm 1 fails because the robot steps on one red tile in the top row while performing "walk 4 squares left" part.

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Algorithm 2 successfully avoids the robot stepping on any of the red tiles throughout the entire algorithm and can also be observed to be the most efficient algorithm (with only 8 steps) if only horizontal and vertical movements are allowed.

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Algorithm 3 is the worst algorithm among the given four since it makes the robot step onto the red tile in the bottom row while performing "walk 2 square left" part, step onto the red tile in the 4th row while performing "walk 4 squares up" part and also step onto the red tile in the top row while performing "walk 2 squares left" part.

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Algorithm 4 is as bad as Algorithm 1 since it makes the robot step onto the red tile in the bottom row while performing the "walk 4 squares left" part.

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Note: Here, while explaining Algorithm 2 , we considered that the robot doesn't vaporize when it first steps on a red tile and hence we show that that algorithm has the potential to damage the robot 3 times. In reality, Algorithm 2 causes the robot to vaporize just as it steps on the first red tile it encounters, i.e., halts on the second step.

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From the analysis, it's obvious that Algorithm 2 is the only algorithm among the given four that avoids stepping into any of the red tiles and is hence, the algorithm Betty could use.

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A follow-up question would be to find the shortest algorithm possible if diagonal movements are allowed too. In that case, we use the fact that the straight line distance between two points is the shortest distance and get the shortest algorithm as follows:

• Walk 2 squares northwest (diagonally).
• Walk 1 square left.
• Walk 1 square northwest again (diagonally).
• Walk 1 square up (reaching X).

This algorithm is of 5 steps and can easily be observed to be the shortest possible algorithm if we allow diagonal movements. If we only allow horizontal and vertical movements, it's quite obvious that Algorithm 2 is the shortest possible algorithm in that case.

Algorithm 1 - Blue line
Algorithm 2 - Green line
Algorithm 3 - Yellow line Algorithm 4 - Purple line

Clearly only algorithm 2 would work.

just think and solved the question

we need to analyse all the given four algorithm. So that we can easily identify the path the robot has to go.