Java programming homeworkplease help with the question below: P 5.28: Write a program for solving summation puzzles by enumerating and testing all possible configurations. Using your program, solve the three puzzles given in Section 5.3.3. 5.3.3 Multiple RecursionGeneralizing from binary recursion, we define multiple recursion as a process inwhich a method may make more than two recursive calls. Our recursion for an-alyzing the disk space usage of a file system (see Section 5.1.4) is an example ofmultiple recursion, because the number of recursive calls made during one invoca-tion was equal to the number of entries within a given directory of the file system.Another common application of multiple recursion is when we want to enumer-ate various configurations in order to solve a combinatorial puzzle. For example,the following are all instances of what are known as summation puzzles:pot + pan = bibdog + catboy + girl==pigbabyTo solve such a puzzle, we need to assign a unique digit (that is, 0, 1, ..., 9) to eachletter in the equation, in order to make the equation true. Typically, we solve sucha puzzle by using our human observations of the particular puzzle we are trying tosolve to eliminate configurations (that is, possible partial assignments of digits toletters) until we can work through the feasible configurations that remain, testingfor the correctness of each one.If the number of possible configurations is not too large, however, we can usea computer to simply enumerate all the possibilities and test each one, without em-ploying any human observations. Such an algorithm can use multiple recursionto work through the configurations in a systematic way. To keep the descriptiongeneral enough to be used with other puzzles, we consider an algorithm that enu-merates and tests all k-length sequences, without repetitions, chosen from a givenuniverse U. We show pseudocode for such an algorithm in Code Fragment 5.11,building the sequence of k elements with the following steps:1. Recursively generating the sequences of k- 1 elements2. Appending to each such sequence an element not already contained in it.Throughout the execution of the algorithm, we use a set U to keep track of theelements not contained in the current sequence, so that an element e has not beenused yet if and only if e is in U.Another way to look at the algorithm of Code Fragment 5.11 is that it enumer-ates every possible size-k ordered subset of U, and tests each subset for being apossible solution to our puzzle.For summation puzzles, U = {0, 1,2,3,4,5,6,7,8,9} and each position in thesequence corresponds to a given letter. For example, the first position could standfor b, the second for o, the third for y, and so on. 5.3. Further Examples of RecursionAlgorithm PuzzleSolve(k, S, U):Input: An integer k, sequence S, and set UOutput: An enumeration of all k-length extensions to S using elements in Uwithout repetitionsfor each e in U doAdd e to the end of SRemove e from Uif k = 1 thenTest whether S is a configuration that solves the puzzleif S solves the puzzle thenadd S to outputabc{a solution}{a recursive call}{e is now considered as unused}Code Fragment 5.11: Solving a combinatorial puzzle by enumerating and testingall possible configurations.elsePuzzleSolve(k-1, S, U)Remove e from the end of SAdd e back to UPuzzleSolve(2, a, {b,c})In Figure 5.14, we show a recursion trace of a call to PuzzleSolve(3, S, U),where S is empty and U = {a,b,c}. During the execution, all the permutationsof the three characters are generated and tested. Note that the initial call makesthree recursive calls, each of which in turn makes two more. If we had executedPuzzleSolve(3, S, U) on a set U consisting of four elements, the initial call wouldhave made four recursive calls, each of which would have a trace looking like theone in Figure 5.14.PuzzleSolve(1, ab, {c})initial callPuzzleSolve(3, (), {a,b,c})(PuzzleSolve(2, b, {a,c})PuzzleSolve(1, ba, {c})acbbacPuzzleSolve(1, ac, {b}){e is now being used}PuzzleSolve(2, c, {a,b})PuzzleSolve(1, ca, {b})bca213cabPuzzleSolve(1, bc, {a})PuzzleSolve(1, cb, {a})cbaFigure 5.14: Recursion trace for an execution of PuzzleSolve(3, S, U), where S isempty and U = {a,b,c}. This execution generates and tests all permutations of a, b,and c. We show the permutations generated directly below their respective boxes.

Question

Java programming homeworkplease help with the question below: P 5.28: Write a program for solving summation puzzles by enumerating and testing all possible configurations. Using your program, solve the three puzzles given in Section 5.3.3. 5.3.3 Multiple RecursionGeneralizing from binary recursion, we define multiple recursion as a process inwhich a method may make more than two recursive calls. Our recursion for an-alyzing the disk space usage of a file system (see Section 5.1.4) is an example ofmultiple recursion, because the number of recursive calls made during one invoca-tion was equal to the number of entries within a given directory of the file system.Another common application of multiple recursion is when we want to enumer-ate various configurations in order to solve a combinatorial puzzle. For example,the following are all instances of what are known as summation puzzles:pot + pan = bibdog + catboy + girl==pigbabyTo solve such a puzzle, we need to assign a unique digit (that is, 0, 1, ..., 9) to eachletter in the equation, in order to make the equation true. Typically, we solve sucha puzzle by using our human observations of the particular puzzle we are trying tosolve to eliminate configurations (that is, possible partial assignments of digits toletters) until we can work through the feasible configurations that remain, testingfor the correctness of each one.If the number of possible configurations is not too large, however, we can usea computer to simply enumerate all the possibilities and test each one, without em-ploying any human observations. Such an algorithm can use multiple recursionto work through the configurations in a systematic way. To keep the descriptiongeneral enough to be used with other puzzles, we consider an algorithm that enu-merates and tests all k-length sequences, without repetitions, chosen from a givenuniverse U. We show pseudocode for such an algorithm in Code Fragment 5.11,building the sequence of k elements with the following steps:1. Recursively generating the sequences of k- 1 elements2. Appending to each such sequence an element not already contained in it.Throughout the execution of the algorithm, we use a set U to keep track of theelements not contained in the current sequence, so that an element e has not beenused yet if and only if e is in U.Another way to look at the algorithm of Code Fragment 5.11 is that it enumer-ates every possible size-k ordered subset of U, and tests each subset for being apossible solution to our puzzle.For summation puzzles, U = {0, 1,2,3,4,5,6,7,8,9} and each position in thesequence corresponds to a given letter. For example, the first position could standfor b, the second for o, the third for y, and so on. 5.3. Further Examples of RecursionAlgorithm PuzzleSolve(k, S, U):Input: An integer k, sequence S, and set UOutput: An enumeration of all k-length extensions to S using elements in Uwithout repetitionsfor each e in U doAdd e to the end of SRemove e from Uif k = 1 thenTest whether S is a configuration that solves the puzzleif S solves the puzzle thenadd S to outputabc{a solution}{a recursive call}{e is now considered as unused}Code Fragment 5.11: Solving a combinatorial puzzle by enumerating and testingall possible configurations.elsePuzzleSolve(k-1, S, U)Remove e from the end of SAdd e back to UPuzzleSolve(2, a, {b,c})In Figure 5.14, we show a recursion trace of a call to PuzzleSolve(3, S, U),where S is empty and U = {a,b,c}. During the execution, all the permutationsof the three characters are generated and tested. Note that the initial call makesthree recursive calls, each of which in turn makes two more. If we had executedPuzzleSolve(3, S, U) on a set U consisting of four elements, the initial call wouldhave made four recursive calls, each of which would have a trace looking like theone in Figure 5.14.PuzzleSolve(1, ab, {c})initial callPuzzleSolve(3, (), {a,b,c})(PuzzleSolve(2, b, {a,c})PuzzleSolve(1, ba, {c})acbbacPuzzleSolve(1, ac, {b}){e is now being used}PuzzleSolve(2, c, {a,b})PuzzleSolve(1, ca, {b})bca213cabPuzzleSolve(1, bc, {a})PuzzleSolve(1, cb, {a})cbaFigure 5.14: Recursion trace for an execution of PuzzleSolve(3, S, U), where S isempty and U = {a,b,c}. This execution generates and tests all permutations of a, b,and c. We show the permutations generated directly below their respective boxes.

Accepted Answer

Make a PuzzleSolve class.
Determine the amount of unique letters in the equation in the…