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n For n distinct elements a₁,..., an with positive weights w₁,..., wn s.t. -1 W₁ = 1, design a linear-time algorithm returning the element ak, which satisfies the following: Σ w₁ ≤ 1/2 and Σ wi ≤ 1/2. ai ak Assume that such an ak always exists. You should also justify the time complexity.

n For n distinct elements a₁,..., an with positive weights w₁,..., wn s.t. -1 W₁ = 1, design a linear-time algorithm returning the element ak, which satisfies the following: Σ w₁ ≤ 1/2 and Σ wi ≤ 1/2. ai ak Assume that such an ak always exists. You should also justify the time complexity.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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For \( n \) distinct elements \( a_1, \ldots, a_n \) with positive weights \( w_1, \ldots, w_n \) such that \( \sum_{i=1}^{n} w_i = 1 \), design a linear-time algorithm returning the element \( a_k \), which satisfies the following: \[ \sum_{a_i < a_k} w_i \leq 1/2 \quad \text{and} \quad \sum_{a_i > a_k} w_i \leq 1/2. \] Assume that such an \( a_k \) always exists. You should also justify the time complexity.
Transcribed Image Text:For \( n \) distinct elements \( a_1, \ldots, a_n \) with positive weights \( w_1, \ldots, w_n \) such that \( \sum_{i=1}^{n} w_i = 1 \), design a linear-time algorithm returning the element \( a_k \), which satisfies the following: \[ \sum_{a_i < a_k} w_i \leq 1/2 \quad \text{and} \quad \sum_{a_i > a_k} w_i \leq 1/2. \] Assume that such an \( a_k \) always exists. You should also justify the time complexity.
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