#12096The SetStack Computer
★★★★Background from Wikipedia: “Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. Initially controversial, set theory has come to play the role of a foundational theory in modern mathematics, in the sense of a theory invoked to justify assumptions made in mathematics concerning the existence of mathematical objects (such as numbers or functions) and their properties. Formal versions of set theory also have a foundational role to play as specifying a theoretical ideal of mathematical rigor in proofs.”
Given this importance of sets, being the basis of mathematics, a set of eccentric theorist set off to construct a supercomputer operating on sets instead of numbers. The initial SetStack Alpha is under construction, 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, the cardinality of the topmost set on the stack is output. The cardinality of a set S is denoted |S| and is the number 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.
範例輸入 1
2 9 PUSH DUP ADD PUSH ADD DUP ADD DUP UNION 5 PUSH PUSH ADD PUSH INTERSECT
範例輸出 1
0 0 1 0 1 1 2 2 2 *** 0 0 1 0 0 ***
Pro 專屬功能： 查看這題在歷屆 CPE 出現過幾次 — 升級以解鎖.