377. Combination Sum IV.md

377. Combination Sum IV

Question

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?

Solution:

• Method 1: Search dfs TLE

  class Solution {
      private int res = 0;
      public int combinationSum4(int[] nums, int target) {
          dfs(nums, target, 0);
          return res;
      }
      private void dfs(int[] nums, int target, int temp){
          if(temp == target) res++;
          else if(temp < target){
              for(int i = 0; i < nums.length; i++){
                  dfs(nums, target, temp + nums[i]);
              }
          }
      }
  }

• Method 1:DP AC 87.93%

  class Solution {
      public int combinationSum4(int[] nums, int target) {
          int[] dp = new int[target + 1];
          dp[0] = 1;
          for(int i = 1; i <= target; i++){
              for(int num : nums){
                  dp[i] += i - num >= 0 ? dp[i - num]: 0;
              }
          }
          return dp[target];
      }
  }