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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.

Database System Concepts
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
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assuming ID is 1542553

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.
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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