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This Java program utilizes dynamic programming with memoization to solve the problem of counting the number of distinct ways to climb a staircase, where each step involves choosing between climbing one or two steps.
Objectives: given a problem statement design, debug and test a Java program that efficiently solves the problem; write programs that effectively implement arrays, maps, linked lists, trees, and graphs; and evaluate the time and space complexity of iterative and recursive algorithms using empirical and mathematical analysis. Official course grade: A