在给定整数数组的情况下查找所有增长最长的子序列 - 动态编程

Question

I'm studying dynamic programing & I came across this question in which I have to print out all the longest subsequences. There could be more than one longest subsequence given an array. The program that I tried would give me only one longest subsequence but not all the longest subsequence. How do I get all longest subsequences?

//Initially I create two arrays of the length of the given input array 

public static void LIS(int[] input) {

    String paths[] = new String[input.length];
    int[] size = new int[input.length];

    for(int i=0;i<input.length; i++) {
       paths[i] = input[i];
       size[i] = 1;
    }

    for(i=1; i<input.length ; i++) {

        for(j=i; j< i ; j++) {
            if(input[i] > input[j] && size[i] < size[j] + 1) {
                size[i] =  size[j] +1;
                paths[i] =  paths[j] + input[i] + ""

                if (maxlength < size[i]) {
                    maxlength = size[i];
                }
            }
        }
    }
}

My example input[] = 1,8,10,3,7,12,15

with the above algorithm I get the longest subsequence as 1,8,10,12,15

I should also get 1,3,7,12,15

How can I modify the code to get this?

Answer 1

If you want to modify this code you may store all possible predecessors for any element; from your code:

for(i=1; i<input.length ; i++) {

    for(j=i; j< i ; j++) {
        //if(input[i] > input[j] && size[i] < size[j] + 1) {
        if(input[i] > input[j] && size[i] <= size[j] + 1) {
            size[i] =  size[j] +1;
            //paths[i] =  paths[j] + input[i] + ""
            if (size[i] < size[j] + 1 )
               //empty p[i]
            p[i].push(j);

            if (maxlength < size[i]) {
                maxlength = size[i];
            }
        }
    }
}

and then you will need to restore all possible subsequences