[算法作业] 算法概论8.3

STINGY SAT is the following problem: given a set of clauses (each a disjunction of literals) and an interger k, find a satisfying assignment in which at most k variables are true, if such an assignment exists. Prove the STINGY is NP-complete.

答：

因为STINGY SAT的解是可在多项式时间内验证的，属于NP。而SAT可被归约到STINGY SAT（将k设为所有变量的总个数），因此STINGY SAT为NP完全问题。