377. Combination Sum IV

Loading Question ...

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.


Seen this question in a real interview before?  
Yes
No
When did you encounter this question?  
last week
last month
last 3 month
last 6 month
more than 6 months
other
Which stage?  
Online Assessment
Phone Interview
On Campus Interview
Onsite Interview
Don't know
Which company?  
Adobe
Aetion
Airbnb
Alibaba
Amazon
Apple
Baidu
Bloomberg
Cloudera
Coursera
Cryptic Studios
Dropbox
eBay
Epic Systems
Expedia
Facebook
Fallible
Games
Gilt Groupe
GoDaddy
Goo
Google
Hedvig
Helix
Houzz
Hulu
Indeed
Intuit
IXL
LinkedIn
LiveRamp
Lyft
MAQ Software
Mathworks
Microsoft
NetEase
Netsuite
Palantir
Palantir Technologies
Pinterest
Pocket Gems
Poynt
Pure
Pure Storage
Rackspace
Radius
Riot
Riot Games
Samsung
Snapchat
Square
Storage
Tencent
TinyCo
Twitter
Two Sigma
Uber
Valve
WAP
Works Applications
Yahoo
Yahoo!
Yelp
Zappos
Zenefits