Question

Give a polynomial time reduction of the subset sum problem to the partition problem.

Answer #1

Consider the following two decision problems.
Problem: Subset Sum
Input Instance: Set of of non-negative numbers S and an integer
k > 0.
Decision: Is there a subset S′ of S such that sum of numbers in
S′ equals k.
Problem: Walking Tourist
Input Instance: A weighted graph G(with non-zero, non-negative
weights on edges), a special vertex s and an integer L.
Decision: Is there a tour that starts at s and ends at s such
that the total length...

2. There is a famous problem in computation called Subset Sum:
Given a set S of n integers S = {a1, a2, a3, · · · , an} and a
target value T, is it possible to find a subset of S that adds up
to T? Consider the following example: S = {−17, −11, 22, 59} and
the target is T = 65. (a) What are all the possible subsets I can
make with S = {−17, −11, 22,...

prove that f(x)= x^2 is integrable on [0,2] using
Reimann Sum
and what is the partition and Delta for this
proof?

(a) For a polynomial x2 + bx + c, give the
coefficients in terms of its roots: α1 and α2.
(b) For a monic, cubic polynomial, give the coefficients in
terms of its roots.
(c) Generalize these result to monic polynomials of higher
degree

What is a subset of pentagon D5 that is a subgroup?
Why?, then give an example of a cyclic subgroup of pentagon
D5

Give an example where X is not Hausdorff, and A is a compact
subset of X, but A is not closed. Justify your claims with
proof.

a)Give an example of a polynomial with integer coefficients of
degree at least 3 that has at least 3 terms that satisfies the
hypotheses of Eisenstein's Criterion, and is therefore
irreducible.
b)Give an example of a polynomial with degree 3 that has at
least 3 terms that does not satisfy the hypotheses of Eisenstein's
Criterion.

Give reasons why a Stock Market graph for one week does not
represent a true polynomial function
Give one real life example where a polynomial function can be
used and give reasons for your choice.

Give a polynomial of degree 3that has zeros of 18, 10i,
and ?10i, and has a value of ?3434 when x =1.
Write the polynomial in standard form
ax^n+bx^n?1+….

problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... +
anx^n: ai in Z[x],a0 = 5n}, that is, the set of all polynomials
where the constant coefficient is a multiple of 5. You can assume
that I is an ideal of Z[x]. a. What is the simplest form of an
element in the quotient ring z[x] / I? b. Explicitly give the
elements in Z[x] / I. c. Prove that I is not a...

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