Problem 2. Suppose we have n persons with their heights given in an array P[1: n] and n skis with heights. given in an array S[1: n]. Design and analyze a greedy algorithm that in O(n log n) time assign a ski to each person so that the average difference between the height of a person and their assigned ski is minimized. The algorithm should output a permutation o of {1,...,n} with the meaning that person i is assigned the ski o (i) such that P[i] - S[o(i)] is minimized. 1 72 Example: If P = [3,2,5, 1] and B = [5, 7,2, 9], we can output o = [2, 1,4,3] with value ·Σ|P{i}]— B[o (6)|| = ¦ ¦· (|P|{1}]— B|2||+|P|2|—B|1||+|P|3}—B|4||+|P|4|— B3|3||) = ¦· (4+3+4+1)=3, which you can also check is the minimum value.
Problem 2. Suppose we have n persons with their heights given in an array P[1: n] and n skis with heights. given in an array S[1: n]. Design and analyze a greedy algorithm that in O(n log n) time assign a ski to each person so that the average difference between the height of a person and their assigned ski is minimized. The algorithm should output a permutation o of {1,...,n} with the meaning that person i is assigned the ski o (i) such that P[i] - S[o(i)] is minimized. 1 72 Example: If P = [3,2,5, 1] and B = [5, 7,2, 9], we can output o = [2, 1,4,3] with value ·Σ|P{i}]— B[o (6)|| = ¦ ¦· (|P|{1}]— B|2||+|P|2|—B|1||+|P|3}—B|4||+|P|4|— B3|3||) = ¦· (4+3+4+1)=3, which you can also check is the minimum value.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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I need the answer in a specific format like this:
Proof of Correctness
Runtime Analysis
As stated in the question the algorithm should have a runtime of O(n log n)
![Problem 2. Suppose we have n persons with their heights given in an array P[1: n] and n skis with heights
given in an array S[1: n]. Design and analyze a greedy algorithm that in O(n log n) time assign a ski to each
person so that the average difference between the height of a person and their assigned ski is minimized.
The algorithm should output a permutation o of {1,...,n} with the meaning that person i is assigned the
ski o(i) such that
is minimized.
=
22
72
i=1
P[i] - S[o(i)]]
Example: If P = [3, 2, 5, 1] and B = [5, 7, 2, 9], we can output o = [2, 1, 4,3] with value
·Ĺ|P{i}– B[o (i)|| = ¦ ¦· (|P[1]— B|2||+|P|2|— B[1]|+|P|3]—B|4||+|P|4]— B[3]|) = } -(4+
4
i=1
which you can also check is the minimum value.
-(4+3+4+1) = 3,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98182d17-9434-4dd7-9261-6c7c628c58da%2Ffda0f019-ae9e-4cb1-9117-c0c30cde3c5f%2Fmyog82g_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2. Suppose we have n persons with their heights given in an array P[1: n] and n skis with heights
given in an array S[1: n]. Design and analyze a greedy algorithm that in O(n log n) time assign a ski to each
person so that the average difference between the height of a person and their assigned ski is minimized.
The algorithm should output a permutation o of {1,...,n} with the meaning that person i is assigned the
ski o(i) such that
is minimized.
=
22
72
i=1
P[i] - S[o(i)]]
Example: If P = [3, 2, 5, 1] and B = [5, 7, 2, 9], we can output o = [2, 1, 4,3] with value
·Ĺ|P{i}– B[o (i)|| = ¦ ¦· (|P[1]— B|2||+|P|2|— B[1]|+|P|3]—B|4||+|P|4]— B[3]|) = } -(4+
4
i=1
which you can also check is the minimum value.
-(4+3+4+1) = 3,
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