Please help me with the following practice question that has to do with recursion : In project 0, we saw that we can check if a solution is valid to summation puzzles. In this assignment, we're going to solve summation puzzles. In a summation puzzle, you are given three strings of the form POT + PAN = BIB. Typically each is a word, often with a theme to the three chosen. Your goal is to assign a distinct digit to each letter in the equation in order to make the resulting true. For example, if the puzzle is POT + PAN = BIB, the mapping P:2, O:3, T:1, A:7, N:4, B:5, I:0 will solve this, as 231 + 274 = 505

You are required to implement the function puzzleSolver in proj1.cpp. This function should return true if, and only if, the puzzle is solvable: that is, if there is a mapping of the letters that appear in the three strings to distinct digits such that the sum of the first two is the third. No string will have a value larger than 4,294,967,295 in its correct substitution, nor will the addition have any integer-overflow to check for. If you do not know what integer overflow is, you do not need to check during this assignment (although it's worth knowing in general). For this project, you have a few requirements: You must implement the function puzzleSolver in proj1.cpp. You may assume it is called with three valid non-empty strings as parameters and with an otherwise empty map. The strings will always consist only of all-capital letters. The puzzle solution may have a leading zero for a string. For example, in the provided test cases, we see that "UCI + ALEX = MIKE" has a solution. This corresponds to 572 + 8631 = 9203. The puzzle "KUCI + ALEX = MIKE" also has a solution with the same mapping. Your solution must explicitly use recursion in a meaningful way towards solving the problem. You may not solve this by using a function like std::next_permutation (from ) to enumerate possibilities. The function puzzleSolver itself need not be recursive if you would prefer to have a helper function that is. The function must return a boolean indicating whether or not the puzzle has a solution. If the puzzle does not have a solution, your function should return false. If the puzzle does have a solution your function should return true and have the unordered_map parameter contain said solution. That is, the four parameters to the puzzleSolver function need to be such that a correct solution to project 0 would return true with those parameters. If there are multiple solutions, returning any of them is fine. You can think of my grading code as this: I know if the test case has or hasn't a solution. I check that you return the right bool value. If it has a solution, I also run a (correct) solution to proj0 on the three strings + the map's status at the end of your function. If the previous point means you need to modify the given gtest code, feel free to do so -- my real grading code will run a verifier instead of checking for an explicitly expected mapping. For writing test cases, you may make use of the gradeYesAnswer function (whose code is provided as pre-compiled). You may not use this function when writing the app portions of your code. Your program must run in under three minutes on a reasonably modern computer. Test cases that take longer than this to run may be deemed to be incorrect. Note that this means you will need to think a little about efficiency in your program. You aren't expected to be an expert on efficiency at this point in your career. Many students in previous quarters were able to get theirs to run in under 90 seconds, even for the "difficult" (large) test cases. You may use standard libraries as appropriate, unless there is one that makes solving this problem trivial. I am unaware of any such part of the library. You are explicitly permitted to use std::unordered_set, std::list, std::queue, and std::stack if you so choose. You are pretty much required to use std::unordered_map. You are welcome to ask anything you want about these libraries, or to look up material about them online. Information about how to use an explicitly-permitted library may always be shared among classmates, but refrain from telling one another how you solved a problem in the assignment with them. For example, answering "how do I check if an element is in a std::unordered_set?" is great and encouraged, while answering "what did you use std::unordered_set for in your project?" is not.

#include "proj1.hpp" #include  #include  bool puzzleSolver(std::string s1, std::string s2, std::string s3, std::unordered_map & mapping) { return true; // This is not the correct general solution. }