# Leetcode: Combination Sum IV

Combination Sum IV

Similar Problems:

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?

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

```// Blog link: https://code.dennyzhang.com/combination-sum-iv
// Basic Ideas: dynamic programming
// [1, 2, 3], 4
// 1, 2, 3
// 1 1, 2 1, 3 1, 1 2, 2 2, 1 3
//   2:1, 3:2, 4:3
// 1 1 1, 1 1 2, 1 1 3, 2 1 1....
//   3:1, 4:3
//
// Complexity: Time ?, Space O(n)
func combinationSum4(nums []int, target int) int {
res := 0
m := map[int]int{}
for _, num := range nums {
if num > target { continue }
m[num] = 1
}
should_continue := true
for should_continue {
m2 := map[int]int{}
for _, num := range nums {
for p := range m {
if p+num<=target {
m2[p+num] += m[p]
}
}
}
if len(m2) == 0 {
should_continue = false
} else {
res += m[target]
m = map[int]int{}
for num := range m2 {
m[num] = m2[num]
}
}
}
return res + m[target]
}
```

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