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Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target.
The answer is guaranteed to fit in a 32-bit integer.
Example 1:
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:
Input: nums = [9], target = 3 Output: 0
Constraints:
1 <= nums.length <= 2001 <= nums[i] <= 1000nums 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?
Dynamic programming.
dp[i] represents the number of element combinations whose sum is i.
class Solution:
def combinationSum4(self, nums: List[int], target: int) -> int:
dp = [0] * (target + 1)
dp[0] = 1
for i in range(1, target + 1):
for num in nums:
if i >= num:
dp[i] += dp[i - num]
return dp[-1]
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) {
if (i >= num) {
dp[i] += dp[i - num];
}
}
}
return dp[target];
}
}
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 (int num : nums) {
if (i >= num && dp[i - num] < INT_MAX - dp[i]) {
dp[i] += dp[i - num];
}
}
}
return dp[target];
}
};
func combinationSum4(nums []int, target int) int {
dp := make([]int, target+1)
dp[0] = 1
for i := 1; i <= target; i++ {
for _, num := range nums {
if i >= num {
dp[i] += dp[i-num]
}
}
}
return dp[target]
}
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