Find the Shortest Superstring - Solution & Explanation

This approach uses dynamic programming with bitmasking to explore all subsets of the strings. The dynamic programming state dp[mask][i] is the shortest superstring for the subset of words represented by the bitmask 'mask' ending with the 'i-th' string. By iterating through all possible states and updating them based on the previously computed states, we determine the shortest superstring that includes all words. The final superstring is constructed by backtracking through the computed states.

The Python solution calculates the maximum overlap for every pair of strings and uses dynamic programming to find the shortest superstring that can be constructed. Overlaps are computed once and stored in a 2D list "overlaps". The dp table keeps track of the optimal solution for every subset of strings represented by a bitmask, and backtracking on this table gives the final superstring.

This approach translates the problem into a variant of the Travelling Salesman Problem (TSP) where the cities correspond to the strings and the distances between them are the inverse of the overlap size. The solution can use heuristics to find a short path that visits all the 'cities' once, effectively creating the shortest superstring. Since exact TSP is NP-hard, approximation algorithms or heuristics can speed up finding a good solution.

This C++ solution uses a dynamical approach similar to TSP by using bitmasks to represent subsets of words. The overlap between strings is used to define "distances", and the algorithm tries to maximize the overlap, effectively minimizing the path length, or the resulting superstring length. The "cost" or path length is maximized by summing up the overlaps between consecutive elements in permutations.

This approach involves generating all permutations of the words and computing the shortest superstring by calculating overlaps greedily. We concatenate each pair of words in the permutation, reducing the length by maximizing the overlap between consecutive strings. This brute force method is feasible with a small number of words due to its factorial time complexity but ensures the optimal solution is found.

This C program defines a function shortestSuperstring that uses permutation and greedy approach to find the shortest superstring for the given array of words. The auxiliary function findOverlap calculates maximum overlap between two strings and constructs a new string by overlapping. The permute function generates permutations and keeps track of the shortest constructed superstring.

This approach models the problem using dynamic programming with a bitmask and Traveling Salesman Problem (TSP) style optimization. By representing used words as a bitmask, we systematically build the shortest superstring by adding each word while maximizing overlaps, applying dynamic programming to store and reuse results of subproblems.

This C solution applies dynamic programming and bitmasking to calculate the shortest superstring. The method constructs a graph where nodes represent words, and edges express overlaps. By treating the problem as a TSP, the dp array is used to store minimum path lengths, leveraging overlap calculations to optimize transitions.