# 377. Combination Sum IV

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**_.
``````

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?

Credits:
Special thanks to @pbrother for adding this problem and creating all test cases.

``````class Solution {
public:
int combinationSum4(vector<int>& nums, int target) {
vector<int> dp(target + 1);
dp[0] = 1;
for (int i = 1; i <= target; ++i) {
for (auto a : nums) {
if (i >= a) dp[i] += dp[i - a];
}
}
return dp.back();
}
};
``````

``````class Solution {
public:
int combinationSum4(vector<int>& nums, int target) {
vector<int> dp(target + 1);
dp[0] = 1;
sort(nums.begin(), nums.end());
for (int i = 1; i <= target; ++i) {
for (auto a : nums) {
if (i < a) break;
dp[i] += dp[i - a];
}
}
return dp.back();
}
};
``````

``````class Solution {
public:
int combinationSum4(vector<int>& nums, int target) {
unordered_map<int, int> memo;
return helper(nums, target, memo);
}
int helper(vector<int>& nums, int target, unordered_map<int, int>& memo) {
if (target < 0) return 0;
if (target == 0) return 1;
if (memo.count(target)) return memo[target];
int res = 0, n = nums.size();
for (int i = 0; i < n; ++i) {
res += helper(nums, target - nums[i], memo);
}
return memo[target] = res;
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/377

Combination Sum

Combination Sum II

Combination Sum III

https://leetcode.com/problems/combination-sum-iv/

https://leetcode.com/problems/combination-sum-iv/discuss/85079/My-3ms-Java-DP-solution

https://leetcode.com/problems/combination-sum-iv/discuss/85036/1ms-Java-DP-Solution-with-Detailed-Explanation

https://leetcode.com/problems/combination-sum-iv/discuss/85120/C%2B%2B-template-for-ALL-Combination-Problem-Set

LeetCode All in One 题目讲解汇总(持续更新中…)

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