algorithms/dp/combination_sum.py at master · AbeyK/algorithms · GitHub

History

66 lines (50 loc) · 1.39 KB

Raw

"""

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?

"""

dp = None

def helper_topdown(nums, target):

global dp

if dp[target] != -1:

return dp[target]

res = 0

for i in range(0, len(nums)):

if target >= nums[i]:

res += helper_topdown(nums, target - nums[i])

dp[target] = res

return res

def combination_sum_topdown(nums, target):

global dp

dp = [-1] * (target + 1)

dp[0] = 1

return helper_topdown(nums, target)

# EDIT: The above solution is top-down. How about a bottom-up one?

def combination_sum_bottom_up(nums, target):

comb = [0] * (target + 1)

comb[0] = 1

for i in range(0, len(comb)):

for j in range(len(nums)):

if i - nums[j] >= 0:

comb[i] += comb[i - nums[j]]

return comb[target]

combination_sum_topdown([1, 2, 3], 4)

print dp[4]

print combination_sum_bottom_up([1, 2, 3], 4)

algorithms/dp/combination_sum.py at master · AbeyK/algorithms · GitHub

Expand file tree

Breadcrumbs

combination_sum.py

Latest commit

History

Breadcrumbs

combination_sum.py

File metadata and controls