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/*
note:
1. Arrays.sort(candidates);         可以不用
2. res.add(new ArrayList<>(cur));   一定要重新创建一个
*/


class Solution {
    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        List<List<Integer>> res = new ArrayList<>();
        //Arrays.sort(candidates);
        backtrack(res, new ArrayList<>(), candidates, target, 0);
        return res;
    }
    
    public void backtrack(List<List<Integer>> res, List<Integer> cur, int[] candidates, int target, int start) {
        if(target == 0) {
            res.add(new ArrayList<>(cur));
            return;
        } else if(target < 0) {
            return;
        } else {
            for(int i = start; i < candidates.length; i++) {
                cur.add(candidates[i]);
                backtrack(res, cur, candidates, target - candidates[i], i);
                cur.remove(cur.size() - 1);
            }
        }
    }    
}

    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        // sort candidates to try them in asc order
        Arrays.sort(candidates); 
        // dp[t] stores all combinations that add up to t
        List<List<Integer>>[] dp = new ArrayList[target+1];
        
        
        // build up dp
        for(int t=0; t<=target; t++) {
            // initialize
            dp[t] = new ArrayList();
            // initialize
            List<List<Integer>> combList = new ArrayList();
            
            // for each t, find possible combinations
            for(int j=0; j<candidates.length && candidates[j] <= t; j++) {
                if(candidates[j] == t) {
                    combList.add(Arrays.asList(candidates[j])); // itself can form a list
                } else {
                    for(List<Integer> prevlist: dp[t-candidates[j]]) { // here use our dp definition
                        // i thought it makes more sense to compare with the last element
                        // only add to list when the candidates[j] >= the last element
                        // so the list remains ascending order, can prevent duplicate (ex. has [2 3 3], no [3 2 3])
                        // equal is needed since we can choose the same element many times   
                        if(candidates[j] >= prevlist.get(prevlist.size()-1)){
                            List temp = new ArrayList(prevlist); // temp is needed since 
                            temp.add(candidates[j]); // cannot edit prevlist inside 4eeach looop
                            combList.add(temp);
                        }
                    }
                }
            }
            dp[t] = combList;
        }
        return dp[target];
    }