_377.java

package com.fishercoder.solutions;

import com.fishercoder.common.utils.CommonUtils;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
/**Given an integer array with all positive numbers and no duplicates,
 * find the number of possible combinations that add up to a positive integer target.

 Example:

 nums = [1, 2, 3]
 target = 4

 The possible combination ways are:
 (1, 1, 1, 1)
 (1, 1, 2)
 (1, 2, 1)
 (1, 3)
 (2, 1, 1)
 (2, 2)
 (3, 1)

 Note that different sequences are counted as different combinations.

 Therefore the output is 7.

 Follow up:
 What if negative numbers are allowed in the given array?
 How does it change the problem?
 What limitation we need to add to the question to allow negative numbers?*/
public class _377 {
    /**since this question doesn't require to return all the combination result, instead, it just wants one number, we could use DP
    the idea is similar to Climbing Stairs.
    adopted this solution: https://discuss.leetcode.com/topic/52186/my-3ms-java-dp-solution*/
    public int combinationSum4(int[] nums, int target){
        Arrays.sort(nums);
        int[] result = new int[target+1];
        for(int i = 1; i < result.length; i++){
            for(int n : nums){
                if(n > target) break;
                else if(n == target) result[i] ++;
                else result[i] += result[i-n];
            }
        }
        return result[target];
    }
    
    //this normal backtracking recursive solution will end up in TLE.
    public List<List<Integer>> combinationSum4_printout(int[] nums, int target) {
        List<List<Integer>> result = new ArrayList();
        Arrays.sort(nums);
        backtracking(0, nums, target, new ArrayList(), result);
        return result;
    }

    private void backtracking(int start, int[] nums, int target, ArrayList temp,
            List<List<Integer>> result) {
        if(target == 0){
            List<Integer> newTemp = new ArrayList(temp);
            result.add(newTemp);
        } else if(target > 0){
            for(int i = start; i < nums.length; i++){
                temp.add(nums[i]);
                backtracking(i, nums, target-nums[i], temp, result);
                temp.remove(temp.size()-1);
            }
        }
    }
    
    public static void main(String...strings){
        _377 test = new _377();
        int[] nums = new int[]{1,2,3};
        int target = 4;
        CommonUtils.printListList(test.combinationSum4_printout(nums, target));
    }
}