Shortest-path counting A chess rook can move horizontally or vertically to any square in the same row or in the same column of a chessboard. Find the number of shortest paths by which a rook can move form one corner of a chessboard to the diagonally opposite corner. The length of a path is measured by the number of squares it passes through, including the first and the last squares.
a) Formulate a dynamic programming algorithm for solving the above problem. Provide a description in words and pseudocode.
b) State and prove the time and space efficiencies of your algorithm in terms of order notation (e. g., Big-Oh).
c) Solve the problem using elementary combinatorics.

Solution: the categorization of functional and non-functional requirement are as follows: some of the more typical functional requirements include: • business rules• transaction corrections, adjustments and cancellations• administrative functions• authentication• authorization levels• audit tracking• external interfaces• certification requirements• reporting requirements• historical data• legal or regulatory requirementswhile,some typical non-functional requirements are: • performance – for example response time, throughput, utilization, static volumetric• scalability• capacity• availability• reliability• recoverability• maintainability• serviceability• security• regulatory• manageability• environmental• data integrity• usability• interoperability

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