How does python find out the number of combinations?

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Topic: combination summation

Given an array of positive integers with no duplicate numbers, find out the number of combinations of positive integers with a given target.

Example:

Nums = [1,2,3]

Target = 4

All possible combinations are:

(1, 1, 1, 1)

(1, 1, 2)

(1, 2, 1)

(1, 3)

(2, 1, 1)

(2, 2)

(3, 1)

Note that sequences with different orders are treated as different combinations.

So the output is 7.

Solve the problem:

1. Dp problem. Dp [I] = sum (DP [I-nums [j])), where nums [j]

< i。 代码 class Solution: def combinationSum4(self, nums: List[int], target: int) ->

Int:

Nums.sort ()

Dp = [0] * (target + 1)

For i in range (1, target + 1):

For n in nums:

If n > I:

Break

If n = = I:

Dp [I] + = 1

Else:

Dp [I] + = dp [I-n]

Return dp [- 1]

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