Dynamic Programming Longest Increasing Subsequence

Question

I need help understanding this. How are the elements in the parent list given - like which list of the previous element in the sequence is it referring to? I've tried testing for each list and I'm still getting a different parent list. Sorry in advance if this is a silly question.

The parent list is the list of index of the parent. parent of a[0] is -1 because it has no parent, parent of a[1] is 0 (meaning a[0]) because a[1] is in the increasing subssequence starting with a a[0] etc — Julien Rousé, Nov 03 '18 at 01:16

score -1 · Answer 1 · answered Nov 03 '18 at 02:07

Look at this Java code to understand the solution

/* A Naive Java Program for LIS Implementation */
class LIS 
{ 
   static int max_ref; // stores the LIS 
  
   /* To make use of recursive calls, this function must return 
   two things: 
   1) Length of LIS ending with element arr[n-1]. We use 
      max_ending_here for this purpose 
   2) Overall maximum as the LIS may end with an element 
      before arr[n-1] max_ref is used this purpose. 
   The value of LIS of full array of size n is stored in 
   *max_ref which is our final result */
   static int _lis(int arr[], int n) 
   { 
       // base case 
       if (n == 1) 
           return 1; 
  
       // 'max_ending_here' is length of LIS ending with arr[n-1] 
       int res, max_ending_here = 1; 
  
        /* Recursively get all LIS ending with arr[0], arr[1] ... 
           arr[n-2]. If   arr[i-1] is smaller than arr[n-1], and 
           max ending with arr[n-1] needs to be updated, then 
           update it */
        for (int i = 1; i < n; i++) 
        { 
            res = _lis(arr, i); 
            if (arr[i-1] < arr[n-1] && res + 1 > max_ending_here) 
                max_ending_here = res + 1; 
        } 
  
        // Compare max_ending_here with the overall max. And 
        // update the overall max if needed 
        if (max_ref < max_ending_here) 
           max_ref = max_ending_here; 
  
        // Return length of LIS ending with arr[n-1] 
        return max_ending_here; 
   } 
  
    // The wrapper function for _lis() 
    static int lis(int arr[], int n) 
    { 
        // The max variable holds the result 
         max_ref = 1; 
  
        // The function _lis() stores its result in max 
        _lis( arr, n); 
  
        // returns max 
        return max_ref; 
    } 
  
    // driver program to test above functions 
    public static void main(String args[]) 
    { 
        int arr[] = { 10, 22, 9, 33, 21, 50, 41, 60 }; 
        int n = arr.length; 
        System.out.println("Length of lis is "
                           + lis(arr, n) + "n"); 
    } 
 }

Dynamic Programming Longest Increasing Subsequence

1 Answers1