【leetcode】377. Combination Sum IV【M】

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.

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?

Credits:

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

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动态规划，应该算是比较经典的无限背包问题

从1到target，

dp[i] = ∑ dp[i-j] (j<=0 and j < i) 求和

最后dp[target] 就是结果

class Solution(object):
def combinationSum4(self, nums, target):

nums.sort()
#print nums

res = [0] * (target+1)
res[0] = 1

for i in xrange(1,target+1):
t = 0
#print res
for j in nums:
#print i,j
if j > i:
break
t += res[i-j]
res[i] = t
return res[-1]

"""
:type nums: List[int]
:type target: int
:rtype: int
"""