You are given a sequence of n integers and an integer k such that 1< k< n. The goal is to partition the sequence into k contiguous subsequences such that the largest sum of the numbers in any subsequence is minimized. Design a dynamic programming algorithm to find this minimum sum value as well as the partition that produces this minimum value. An example is given below. 1. Consider your 7 digit UH ID as a sequence of 7 integers. For example, if your UH ID is 3255967, then the sequence is 3, 2, 5, 5, 9, 6, 7. Let the given value of k be 3. Then, the best way to partition this particular sequence into 3 subsequences so that the largest subsequence sum is minimized is: {3,2, 5}{5,9}{6, 7} Note that the largest sum value is 5 + 9 = 14, attained by the second subsequence. Any other partition will increase the largest subsequence sum. What is the best way to partition your 7 digit UH ID sequence assuming k = 3? 2. Define the subproblems for your DP solution on a general instance of the problem where the sequence is of length n. Note that k is a fixed integer given as part of the input. 3. Give a recursive formulation, including the base cases, to solve this problem. 4. What is the running time of your solution? 5. Write a DP algorithm (give pseudocode) that outputs the minimum sum value. 6. Describe an algorithm to output the partition that corresponds to the minimum value.
You are given a sequence of n integers and an integer k such that 1< k< n. The goal is to partition the sequence into k contiguous subsequences such that the largest sum of the numbers in any subsequence is minimized. Design a dynamic programming algorithm to find this minimum sum value as well as the partition that produces this minimum value. An example is given below. 1. Consider your 7 digit UH ID as a sequence of 7 integers. For example, if your UH ID is 3255967, then the sequence is 3, 2, 5, 5, 9, 6, 7. Let the given value of k be 3. Then, the best way to partition this particular sequence into 3 subsequences so that the largest subsequence sum is minimized is: {3,2, 5}{5,9}{6, 7} Note that the largest sum value is 5 + 9 = 14, attained by the second subsequence. Any other partition will increase the largest subsequence sum. What is the best way to partition your 7 digit UH ID sequence assuming k = 3? 2. Define the subproblems for your DP solution on a general instance of the problem where the sequence is of length n. Note that k is a fixed integer given as part of the input. 3. Give a recursive formulation, including the base cases, to solve this problem. 4. What is the running time of your solution? 5. Write a DP algorithm (give pseudocode) that outputs the minimum sum value. 6. Describe an algorithm to output the partition that corresponds to the minimum value.
Programming Logic & Design Comprehensive
9th Edition
ISBN:9781337669405
Author:FARRELL
Publisher:FARRELL
Chapter8: Advanced Data Handling Concepts
Section: Chapter Questions
Problem 1PE
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assuming ID is 1542553
Transcribed Image Text:UH ID:
You are given a sequence of n integers and an integer k such that 1< k<n. The goal
is to partition the sequence into k contiguous subsequences such that the largest sum of
the numbers in any subsequence is minimized. Design a dynamic programming algorithm
to find this minimum sum value as well as the partition that produces this minimum
value. An example is given below.
1. Consider your 7 digit UH ID as a sequence of 7 integers. For example, if your UH
ID is 3255967, then the sequence is 3, 2, 5, 5, 9, 6, 7. Let the given value of k be 3.
Then, the best way to partition this particular sequence into 3 subsequences so that
the largest subsequence sum is minimized is:
{3,2, 5}{5,9}{6, 7}
Note that the largest sum value is 5+ 9 = 14, attained by the second subsequence.
Any other partition will increase the largest subsequence sum.
What is the best way to partition your 7 digit UH ID sequence assuming k = 3?
2. Define the subproblems for your DP solution on a general instance of the problem
where the sequence is of length n. Note that k is a fixed integer given as part of the
input.
3. Give a recursive formulation, including the base cases, to solve this problem.
4. What is the running time of your solution?
5. Write a DP algorithm (give pseudocode) that outputs the minimum sum value.
6. Describe an algorithm to output the partition that corresponds to the minimum
value.
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