Problem Statement: Consider an input string PAL of letters ‘P’, ‘A’, and ‘L’. This string, which is given by the user, ends with ‘#’. It should be stored in a table (or array), called PAL_TAB. The number of each of these letters is unknown. We have a function, called SWAP(PAL, i, j), which places the ith letter in the jth entry of string PAL and the jth letter in the ith entry of PAL. Note that SWAP(PAL, i, j) is defined for all integers i and j between 0 and length(PAL) – 1, where length(PAL) is the number of letters of PAL. 1. Using our algorithmic language, write an algorithm, called Sort_PAL, which sorts the letters in the array PAL_TAB in a way that all P’s appear first, followed by all A’s, and followed by all L’s. The algorithm Sort_PAL should have one parameter: The array PAL_TAB. Also, your solution is correct only if the four constraints below are satisfied: - Constraint 1: Each letter (‘A’, ‘L’, or ‘P’) is evaluated only once. - Constraint 2: The function SWAP(PAL, i, j) is used only when it is necessary. - Constraint 3: No extra space can be used by the algorithm Sort_PAL. In other words, only the array PAL_TAB can be used to sort the ‘A’, ‘L’, or ‘P’. - Constraint 4: You cannot count the number of each letter ‘A’, ‘L’, or ‘P’. 2. Show that the algorithm Sort_PAL is correct using an informal proof (i.e., discussion). 3. Give a program corresponding to Sort_PAL using your favorite programming language. Deliverables: Students may choose to work in team of up to two members. You should turn in a report explaining all the design decisions and your code should be commented appropriately for readability and understanding. More precisely, a report should include the problem statement, proposed approach/solution along with a detailed discussion, algorithm (high-level description of all the design parts along with some details when necessary), commented code, tests (input given by the user and output generated by your program execution), and lessons learned from such an implementation experience.

Problem Statement: Consider an input string PAL of letters ‘P’, ‘A’, and ‘L’. This string, which is given by the user, ends with ‘#’. It should be stored in a table (or array), called PAL_TAB. The number of each of these letters is unknown. We have a function, called SWAP(PAL, i, j), which places the ith letter in the jth entry of string PAL and the jth letter in the ith entry of PAL. Note that SWAP(PAL, i, j) is defined for all integers i and j between 0 and length(PAL) – 1, where length(PAL) is the number of letters of PAL. 1. Using our algorithmic language, write an algorithm, called Sort_PAL, which sorts the letters in the array PAL_TAB in a way that all P’s appear first, followed by all A’s, and followed by all L’s. The algorithm Sort_PAL should have one parameter: The array PAL_TAB. Also, your solution is correct only if the four constraints below are satisfied: - Constraint 1: Each letter (‘A’, ‘L’, or ‘P’) is evaluated only once. - Constraint 2: The function SWAP(PAL, i, j) is used only when it is necessary. - Constraint 3: No extra space can be used by the algorithm Sort_PAL. In other words, only the array PAL_TAB can be used to sort the ‘A’, ‘L’, or ‘P’. - Constraint 4: You cannot count the number of each letter ‘A’, ‘L’, or ‘P’. 2. Show that the algorithm Sort_PAL is correct using an informal proof (i.e., discussion). 3. Give a program corresponding to Sort_PAL using your favorite programming language. Deliverables: Students may choose to work in team of up to two members. You should turn in a report explaining all the design decisions and your code should be commented appropriately for readability and understanding. More precisely, a report should include the problem statement, proposed approach/solution along with a detailed discussion, algorithm (high-level description of all the design parts along with some details when necessary), commented code, tests (input given by the user and output generated by your program execution), and lessons learned from such an implementation experience.

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