1. Design and write, in pseudocode, a recursive backtracking algorithm that solves the following problem (3-D MATCHING) Input. A base set X and a set of triples S C {(x, y, z) | x, y, z x} Output: Is there some S, S such that every element of X occurs in exactly one triple of S'? 2. (a) Design and write, in pseudocode, a recursive backtracking algorithm that, given a graph G V E) and an integer k, determines if there is a set of k vertices of G such that no two vertices in this set have an edge between them (b) Design and write, in pseudocode, a recursive branch-and-bound algorithm that, given a graph G- (V, E), will find the size of the largest set of vertices V' CV such that no two vertices in V have an edge between them. 1. Design and write, in pseudocode, a recursive backtracking algorithm that solves the following problem (3-D MATCHING) Input. A base set X and a set of triples S C {(x, y, z) | x, y, z x} Output: Is there some S, S such that every element of X occurs in exactly one triple of S'? 2. (a) Design and write, in pseudocode, a recursive backtracking algorithm that, given a graph G V E) and an integer k, determines if there is a set of k vertices of G such that no two vertices in this set have an edge between them (b) Design and write, in pseudocode, a recursive branch-and-bound algorithm that, given a graph G- (V, E), will find the size of the largest set of vertices V' CV such that no two vertices in V have an edge between them