377. Combination Sum IV

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377. Combination Sum IV

Description

Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up totarget.

The test cases are generated so that the answer can fit in a 32-bit integer.

Example 1:

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Input: nums = [1,2,3], target = 4
Output: 7
Explanation:
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.

Example 2:

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Input: nums = [9], target = 3
Output: 0

Constraints:

  • 1 <= nums.length <= 200
  • 1 <= nums[i] <= 1000
  • All the elements of nums are unique .
  • 1 <= target <= 1000

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?

Hints/Notes

Solution

Language: C++

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class Solution {
public:
    vector<int> dp;

    int combinationSum4(vector<int>& nums, int target) {
        ranges::sort(nums);
        int n = nums.size();
        dp.resize(target + 1, -1);
        int res = dfs(target, nums);
        return res;
    }

    int dfs(int target, vector<int>& nums) {
        if (target == 0) {
            return 1;
        }
        if (dp[target] != -1) {
            return dp[target];
        }
        int res = 0;
        for (int i = 0; i < nums.size(); i++) {
            if (target >= nums[i]) {
                res += dfs(target - nums[i], nums);
            }
        }
        dp[target] = res;
        return res;
    }
};