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Problem 3. For n = N, let b = b₁b2 ….. b₂ be a binary string with b₁ + b2 + +bn ≥ 1 (that is, b₁ = 1 for at least one index i), and let v = (C1, C2, ..., Cn) be a value vector with entries in N. An improvement operation on the value vector v with respect to the binary string b consists of the following two steps. 1. Choose an index i from the set {1, 2,...,n} with probability Сі c1+c2++Cn' == 1. 2. For a chosen index i, replace ci by ci - 1 if bi = 0 and replace ci by ci +1 if bi Design an efficient algorithm that computes the expected value of each entry of the vector value v after m improvement operations, and explain the worst time complexity of your algorithm in terms of m and n.

Problem 3. For n = N, let b = b₁b2 ….. b₂ be a binary string with b₁ + b2 + +bn ≥ 1 (that is, b₁ = 1 for at least one index i), and let v = (C1, C2, ..., Cn) be a value vector with entries in N. An improvement operation on the value vector v with respect to the binary string b consists of the following two steps. 1. Choose an index i from the set {1, 2,...,n} with probability Сі c1+c2++Cn' == 1. 2. For a chosen index i, replace ci by ci - 1 if bi = 0 and replace ci by ci +1 if bi Design an efficient algorithm that computes the expected value of each entry of the vector value v after m improvement operations, and explain the worst time complexity of your algorithm in terms of m and n.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 40E
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Problem 3. For n = N, let b = b₁b2 ….. b₂ be a binary string with b₁ + b2 + +bn ≥ 1 (that is, b₁ = 1 for at least one index i), and let v = (C1, C2, ..., Cn) be a value vector with entries in N. An improvement operation on the value vector v with respect to the binary string b consists of the following two steps. 1. Choose an index i from the set {1, 2,...,n} with probability Сі c1+c2++Cn' == 1. 2. For a chosen index i, replace ci by ci - 1 if bi = 0 and replace ci by ci +1 if bi Design an efficient algorithm that computes the expected value of each entry of the vector value v after m improvement operations, and explain the worst time complexity of your algorithm in terms of m and n.
Transcribed Image Text:Problem 3. For n = N, let b = b₁b2 ….. b₂ be a binary string with b₁ + b2 + +bn ≥ 1 (that is, b₁ = 1 for at least one index i), and let v = (C1, C2, ..., Cn) be a value vector with entries in N. An improvement operation on the value vector v with respect to the binary string b consists of the following two steps. 1. Choose an index i from the set {1, 2,...,n} with probability Сі c1+c2++Cn' == 1. 2. For a chosen index i, replace ci by ci - 1 if bi = 0 and replace ci by ci +1 if bi Design an efficient algorithm that computes the expected value of each entry of the vector value v after m improvement operations, and explain the worst time complexity of your algorithm in terms of m and n.
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