第五章 - The SetStack Computer - uva - 12096

Background from Wikipedia: “Set theory is abranch of mathematics created principally by theGerman mathematician Georg Cantor at the end ofthe 19th century. Initially controversial, set theoryhas come to play the role of a foundational theoryin modern mathematics, in the sense of a theoryinvoked to justify assumptions made in mathematicsconcerning the existence of mathematical objects(such as numbers or functions) and their properties.Formal versions of set theory also have a foundationalrole to play as specifying a theoretical idealof mathematical rigor in proofs.”Given this importance of sets, being the basis of mathematics, a set of eccentric theorist set off toconstruct a supercomputer operating on sets instead of numbers. The initial SetStack Alpha is underconstruction, and they need you to simulate it in order to verify the operation of the prototype.The computer operates on a single stack of sets, which is initially empty. After each operation, thecardinality of the topmost set on the stack is output. The cardinality of a set S is denoted |S| and is thenumber of elements in S. The instruction set of the SetStack Alpha is PUSH, DUP, UNION, INTERSECT,and ADD.• PUSH will push the empty set {} on the stack.• DUP will duplicate the topmost set (pop the stack, and then push that set on the stack twice).• UNION will pop the stack twice and then push the union of the two sets on the stack.• INTERSECT will pop the stack twice and then push the intersection of the two sets on the stack.• ADD will pop the stack twice, add the first set to the second one, and then push the resulting seton the stack.For illustration purposes, assume that the topmost element of the stack isA = {{}, {{}}}and that the next one isB = {{}, {{{}}}}For these sets, we have |A| = 2 and |B| = 2. Then:• UNION would result in the set {{}, {{}}, {{{}}}}. The output is 3.• INTERSECT would result in the set {{}}. The output is 1.• ADD would result in the set {{}, {{{}}}, {{},{{}}}}. The output is 3.InputAn integer 0 ≤ T ≤ 5 on the first line gives the cardinality of the set of test cases. The first line of eachtest case contains the number of operations 0 ≤ N ≤ 2000. Then follow N lines each containing one ofthe five commands. It is guaranteed that the SetStack computer can execute all the commands in thesequence without ever popping an empty stack.OutputFor each operation specified in the input, there will be one line of output consisting of a single integer.This integer is the cardinality of the topmost element of the stack after the corresponding commandhas executed. After each test case there will be a line with ‘***’ (three asterisks).Sample Input29PUSHDUPADDPUSHADDDUPADDDUPUNION5PUSHPUSHADDPUSHINTERSECTSample Output001011222***00100***

#include
#include
#include
#include
#include