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:

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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?

Ref时讲的很详细, 转化公式为: comb[target] = sum(comb[target - nums[i]]), where 0 <= i < nums.length, and target >= nums[i]

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public int combinationSum4(int[] nums, int target) {
    int[] comb = new int[target + 1];
    comb[0] = 1;
    for (int i = 1; i < comb.length; i++) {
        for (int j = 0; j < nums.length; j++) {
            if (i - nums[j] >= 0) {
                comb[i] += comb[i - nums[j]];
            }
        }
    }
    return comb[target];
}

Ref: https://discuss.leetcode.com/topic/52302/1ms-java-dp-solution-with-detailed-explanation