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Engineering
Data Structures and Algorithms
Suppose that you are given an n × n checkerboard and a checker. You must move the checker from the bottom edge of the board to the top edge of the board according to the following rule. At each step you may move the checker to one of three squares: 1. the square immediately above 2. the square that is one up and one to the left (but only if the checker if not already in the leftmost column) 3. the square that is one up and one to the right (but only if the checker is not already in the rightmost column). 1 Each time you move from square x to square y, you receive p(x, y) dollars. You are given p(x, y) for all pairs (x, y) for which a move from x to y is legal. Do not assume that p(x, y) is positive. design a recursive backtracking algorithm that determines the maximum amount of money you can recieve, when moving a checker frmo somewhere on the bottom row to somewhere on the top row.  your algorithm is free to pick any squrre along the bottom row as a starting point and any square along the top row as a destination in order to maximize the number of dollars gathered along the way.

Suppose that you are given an n × n checkerboard and a checker. You must move the checker from the bottom edge of the board to the top edge of the board according to the following rule. At each step you may move the checker to one of three squares: 1. the square immediately above 2. the square that is one up and one to the left (but only if the checker if not already in the leftmost column) 3. the square that is one up and one to the right (but only if the checker is not already in the rightmost column). 1 Each time you move from square x to square y, you receive p(x, y) dollars. You are given p(x, y) for all pairs (x, y) for which a move from x to y is legal. Do not assume that p(x, y) is positive. design a recursive backtracking algorithm that determines the maximum amount of money you can recieve, when moving a checker frmo somewhere on the bottom row to somewhere on the top row.  your algorithm is free to pick any squrre along the bottom row as a starting point and any square along the top row as a destination in order to maximize the number of dollars gathered along the way.

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Suppose that you are given an n × n checkerboard and a checker. You must move the checker from the bottom edge of the board to the top edge of the board according to the following rule. At each step you may move the checker to one of three squares: 1. the square immediately above 2. the square that is one up and one to the left (but only if the checker if not already in the leftmost column) 3. the square that is one up and one to the right (but only if the checker is not already in the rightmost column). 1 Each time you move from square x to square y, you receive p(x, y) dollars. You are given p(x, y) for all pairs (x, y) for which a move from x to y is legal. Do not assume that p(x, y) is positive. design a recursive backtracking algorithm that determines the maximum amount of money you can recieve, when moving a checker frmo somewhere on the bottom row to somewhere on the top row.  your algorithm is free to pick any squrre along the bottom row as a starting point and any square along the top row as a destination in order to maximize the number of dollars gathered along the way. 

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