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* Assignment: Longest increasing subsequence  *  * Sequences are a natural source of computational problems. One such  * family of problems involves finding subsequences with specified  * properties in a given sequence. This exercise asks you to write  * a program that, given a sequence  *  *   s(0), s(1), ..., s(n-1)  *  * of integers as input, finds a ___longest increasing subsequence___  * of the sequence s.  *  * For example, suppose we are given as input the sequence  *  *    72, 16, 51, 17, 6, 21, 92, 59, 54, 78, 41, 33, 94,  *        85, 83, 56, 2, 46, 57, 44, 73, 6, 47, 47, 0.  *  * In this sequence, a longest increasing subsequence has length 7.  * One example of such an increasing subsequence is  *  *    16 < 17 < 21 < 54 < 56 < 57 < 73.  *  * More generally, your program must be such that  * given a sequence  *  *   s(0), s(1), ..., s(n-1)  *  * of integers as input, the program returns a subsequence  *  *   s(i_1), s(i_2), ..., s(i_k)  *  * that meets all of the following three properties:  *  *   1. The positions that define the subsequence are increasing:  *  *        0 <= i_1 < i_2 < ... < i_k <= n-1  *  *   2. The subsequence is increasing:  *  *        s(i_1) < s(i_2) < ... < s(i_k)  *  *   3. The length k of the subsequence is as large as possible.       package longestIncreasingSubsequence   /** Returns a longest increasing subsequence in the sequence s.    *  If there are multiple such subsequences, any subsequence will do. */   def longestIncreasingSubsequence(s: Seq[Int]): Seq[Int] =     require(s.length > 0)     ???   end longestIncreasingSubsequence

* Assignment: Longest increasing subsequence  *  * Sequences are a natural source of computational problems. One such  * family of problems involves finding subsequences with specified  * properties in a given sequence. This exercise asks you to write  * a program that, given a sequence  *  *   s(0), s(1), ..., s(n-1)  *  * of integers as input, finds a ___longest increasing subsequence___  * of the sequence s.  *  * For example, suppose we are given as input the sequence  *  *    72, 16, 51, 17, 6, 21, 92, 59, 54, 78, 41, 33, 94,  *        85, 83, 56, 2, 46, 57, 44, 73, 6, 47, 47, 0.  *  * In this sequence, a longest increasing subsequence has length 7.  * One example of such an increasing subsequence is  *  *    16 < 17 < 21 < 54 < 56 < 57 < 73.  *  * More generally, your program must be such that  * given a sequence  *  *   s(0), s(1), ..., s(n-1)  *  * of integers as input, the program returns a subsequence  *  *   s(i_1), s(i_2), ..., s(i_k)  *  * that meets all of the following three properties:  *  *   1. The positions that define the subsequence are increasing:  *  *        0 <= i_1 < i_2 < ... < i_k <= n-1  *  *   2. The subsequence is increasing:  *  *        s(i_1) < s(i_2) < ... < s(i_k)  *  *   3. The length k of the subsequence is as large as possible.       package longestIncreasingSubsequence   /** Returns a longest increasing subsequence in the sequence s.    *  If there are multiple such subsequences, any subsequence will do. */   def longestIncreasingSubsequence(s: Seq[Int]): Seq[Int] =     require(s.length > 0)     ???   end longestIncreasingSubsequence

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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 * Assignment: Longest increasing subsequence
 *
 * Sequences are a natural source of computational problems. One such
 * family of problems involves finding subsequences with specified
 * properties in a given sequence. This exercise asks you to write
 * a program that, given a sequence
 *
 *   s(0), s(1), ..., s(n-1)
 *
 * of integers as input, finds a ___longest increasing subsequence___
 * of the sequence s.
 *
 * For example, suppose we are given as input the sequence
 *
 *    72, 16, 51, 17, 6, 21, 92, 59, 54, 78, 41, 33, 94,
 *        85, 83, 56, 2, 46, 57, 44, 73, 6, 47, 47, 0.
 *
 * In this sequence, a longest increasing subsequence has length 7.
 * One example of such an increasing subsequence is
 *
 *    16 < 17 < 21 < 54 < 56 < 57 < 73.
 *
 * More generally, your program must be such that
 * given a sequence
 *
 *   s(0), s(1), ..., s(n-1)
 *
 * of integers as input, the program returns a subsequence
 *
 *   s(i_1), s(i_2), ..., s(i_k)
 *
 * that meets all of the following three properties:
 *
 *   1. The positions that define the subsequence are increasing:
 *
 *        0 <= i_1 < i_2 < ... < i_k <= n-1
 *
 *   2. The subsequence is increasing:
 *
 *        s(i_1) < s(i_2) < ... < s(i_k)
 *
 *   3. The length k of the subsequence is as large as possible.
 
 
 
package longestIncreasingSubsequence

  /** Returns a longest increasing subsequence in the sequence s.
   *  If there are multiple such subsequences, any subsequence will do. */

  def longestIncreasingSubsequence(s: Seq[Int]): Seq[Int] =
    require(s.length > 0)
    ???
  end longestIncreasingSubsequence
* * * Sequences are a natural source of computational problems. One such * family of problems involves finding subsequences with specified * properties in a given sequence. This exercise asks you to write * a program that, given a sequence * * s(0), s(1), ..., s(n-1) * of integers as input, finds a _longest increasing subsequence * of the sequence s. * * * For example, suppose we are given as input the sequence * * * Assignment: Longest increasing subsequence * In this sequence, a longest increasing subsequence has length 7. * One example of such an increasing subsequence is * * * * * More generally, your program must be such that * given a sequence 72, 16, 51, 17, 6, 21, 92, 59, 54, 78, 41, 33, 94, 85, 83, 56, 2, 46, 57, 44, 73, 6, 47, 47, 0. * * 16 < 17 < 21 < 54 < 56 < 57 < 73. s(0), s(1), * of integers as input, the program returns a subsequence s(i_1), s(i_2), ..., s(i_k) * that meets all of the following three properties: * 1. The positions that define the subsequence are increasing: ..., s(n-1) 0 <= i_1 < i_2 < ... < i_k <= n-1 2. The subsequence is increasing: s(i_1) < s(i_2) < ... < s(i_k) 3. The length k of the subsequence is as large as possible.
Transcribed Image Text:* * * Sequences are a natural source of computational problems. One such * family of problems involves finding subsequences with specified * properties in a given sequence. This exercise asks you to write * a program that, given a sequence * * s(0), s(1), ..., s(n-1) * of integers as input, finds a _longest increasing subsequence * of the sequence s. * * * For example, suppose we are given as input the sequence * * * Assignment: Longest increasing subsequence * In this sequence, a longest increasing subsequence has length 7. * One example of such an increasing subsequence is * * * * * More generally, your program must be such that * given a sequence 72, 16, 51, 17, 6, 21, 92, 59, 54, 78, 41, 33, 94, 85, 83, 56, 2, 46, 57, 44, 73, 6, 47, 47, 0. * * 16 < 17 < 21 < 54 < 56 < 57 < 73. s(0), s(1), * of integers as input, the program returns a subsequence s(i_1), s(i_2), ..., s(i_k) * that meets all of the following three properties: * 1. The positions that define the subsequence are increasing: ..., s(n-1) 0 <= i_1 < i_2 < ... < i_k <= n-1 2. The subsequence is increasing: s(i_1) < s(i_2) < ... < s(i_k) 3. The length k of the subsequence is as large as possible.
package longest /** Returns a longest increasing subsequence in the sequence s. * If there are multiple such subsequences, any subsequence will do. */ IncreasingSubsequence def longestIncreasingSubsequence (s: Seq[Int]): Seq[Int] = require(s.length > 0) ??? end longestIncreasingSubsequence
Transcribed Image Text:package longest /** Returns a longest increasing subsequence in the sequence s. * If there are multiple such subsequences, any subsequence will do. */ IncreasingSubsequence def longestIncreasingSubsequence (s: Seq[Int]): Seq[Int] = require(s.length > 0) ??? end longestIncreasingSubsequence
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