Increasing Subsequences

Problem

Given an integer array, your task is to find all the different possible increasing subsequences of the given array, and the length of an increasing subsequence should be at least 2 .

Example:

Input: [4, 6, 7, 7]
Output: [[4, 6], [4, 7], [4, 6, 7], [4, 6, 7, 7], [6, 7], [6, 7, 7], [7,7], [4,7,7]]

Note:

• The length of the given array will not exceed 15.
• The range of integer in the given array is [-100,100].
• The given array may contain duplicates, and two equal integers should also be considered as a special case of increasing sequence.

Solution

public class Solution {
    public List<List<Integer>> findSubsequences(int[] nums) {
        Set<List<Integer>> set = new HashSet<>();
        helper(set, new ArrayList<>(), 0, nums);
        return new ArrayList<>(set);
    } 

    private void helper(Set<List<Integer>> set, List<Integer> list, int start, int[] nums) {
        if(list.size() >= 2) set.add(new ArrayList<>(list));
        for(int i = start; i < nums.length; i++) {
            if(list.size() == 0 || list.get(list.size() - 1) <= nums[i]) {
                list.add(nums[i]);
                helper(set, list, i + 1, nums);
                list.remove(list.size() - 1);
            }
        }
    }
}

Analysis

Unlike the Permutations and Combinations problems we solved earlier, this problem is essentially to find a special sequence from a given array (can be considered as sequence too). Since the size of list in returning result cannot be less than 2, we use this qualification in our if statement. Notice that we don't return in if statement, cause the length can be 3, 4 or even more. Hence, we need to pass a Set in the params of helper() method, and convert it to list in main method. The idea is still about backtracking, just adding some limitations(qualifications).