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Given a set S of integers, we say that S can be partitioned if it can...
9. (20) Given a set of integers, we say that can be partitioned if it can be split into two sets U and V so that considering all u EU and all v € V, Eu = Ev. Let PARTITION = {<s> S can be partitioned }. a. (5) Show that PARTITION € NP by writing either a verifier or an NDTM. b. (15) Show that PARTITION is NP-complete by reduction from SUBSET-SUM.
Given a set S of integers, we say that S can be partitioned if it can be split into two sets U and V so that considering all u U and all v V, u = v. Let PARTITION = { | S can be partitioned }. a. (5) Show that PARTITION NP by writing either a verifier or an NDTM. b. (15) Show that PARTITION is NP-complete by reduction from SUBSET-SUM.
Given a set S of integers, we say that S can be partitioned if it can be split into two sets U and V so that considering all u ∈ U and all v ∈ V, Σu = Σ v. Let PARTITION = { <S>| S can be partitioned }. a. (5) Show that PARTITION ∈ NP by writing either a verifier or an NDTM b. (15) Show that PARTITION is NP-complete by reduction from SUBSET-SUM.
Show that PARTITION NP by writing either a verifier or an NDTM. Given a set of integers, we say that can be partitioned if it can be split into two sets U and V so that considering all u EU and all v € V, Eu = Ev. Let PARTITION = {<s> S can be partitioned ). a. (5) Show that PARTITION E NP by writing either a verifier or an NDTM.
Given a set S of integers, we say that S can be partitioned if it can be split into two sets U and V so that considering all u Î U and all v Î V, Su = Sv. Let PARTITION = { | S can be partitioned }. Show that PARTITION is NP-complete by reduction from SUBSET-SUM
Show that PARTITION is NP-complete by reduction from SUBSET-SUM. Given a set of integers, we say that can be partitioned if it can be split into two sets U and V so that considering all u EU and all v € V, Eu = Ev. Let PARTITION = { <S> S can be partitioned ). Show that PARTITION IS NP-complete by reduction from SUBSET-SUM.
* SUBSET-SUM-kS, t> I S -[xi Xk] and for some lyı yn)cIxi.... xk) the sum of the yi's equals t. For example, <S-2, 3, 5, 7, 11, 14], t-21> is in SUBSET-SUM because 3+7 11-21. xk) can be partitioned into two parts A and -A where -A * SET-PARTITION <S> S-Ixi S-A and the sum of the elements in A is equal to the sum of the elements in A. For example, 〈 S-12, 3, 4, 7, 8/> works because...
Problem 2. In the Subset-Sum problem the input consists of a set of positive integers X = {x1, . . . , xn}, and some integer k. The answer is YES if and only if there exists some subset of X that sums to k. In the Bipartition problem the input consists of a set of positive integers Y = {y1, . . . , yn}. The answer is YES if and only if there exists some subset of X...
Let U be the set of all integers. Consider the following sets: S is the set of all even integers; T is the set of integers obtained by tripling any one integer and adding 1; V is the set of integers that are multiples of 2 and 3. a) Use set builder notation to describe S, T and V symbolically. b) Compute s n T, s n V and T V. Describe these sets using set builder notation
5. Dynamic Programming (a) Given a set of four matrices for the following dimensions: We need to compute Al* A2 A3 A4 Al=2X3; A2=3X5; A3=5X2: A4=2X4 Find the order in which the matrix pairs should be multiplied to produce the optimum number of operations. Show all your steps (10) (b) For the problems given below, determine whether it is more efficient to use a divide and conquer strategy or a dynamic programming strategy. Give the reasons for your choice (5*3=15)...