mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
a936e94704
* Enable ruff ARG001 rule * Fix dynamic_programming/combination_sum_iv.py * Fix machine_learning/frequent_pattern_growth.py * Fix other/davis_putnam_logemann_loveland.py * Fix other/password.py * Fix * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix physics/n_body_simulation.py * Fix project_euler/problem_145/sol1.py * Fix project_euler/problem_174/sol1.py * Fix scheduling/highest_response_ratio_next.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix * Fix * Fix scheduling/job_sequencing_with_deadline.py * Fix scheduling/job_sequencing_with_deadline.py * Fix * Fix --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
102 lines
2.7 KiB
Python
102 lines
2.7 KiB
Python
"""
|
||
Question:
|
||
You are given an array of distinct integers and you have to tell how many
|
||
different ways of selecting the elements from the array are there such that
|
||
the sum of chosen elements is equal to the target number tar.
|
||
|
||
Example
|
||
|
||
Input:
|
||
N = 3
|
||
target = 5
|
||
array = [1, 2, 5]
|
||
|
||
Output:
|
||
9
|
||
|
||
Approach:
|
||
The basic idea is to go over recursively to find the way such that the sum
|
||
of chosen elements is “tar”. For every element, we have two choices
|
||
1. Include the element in our set of chosen elements.
|
||
2. Don’t include the element in our set of chosen elements.
|
||
"""
|
||
|
||
|
||
def combination_sum_iv(array: list[int], target: int) -> int:
|
||
"""
|
||
Function checks the all possible combinations, and returns the count
|
||
of possible combination in exponential Time Complexity.
|
||
|
||
>>> combination_sum_iv([1,2,5], 5)
|
||
9
|
||
"""
|
||
|
||
def count_of_possible_combinations(target: int) -> int:
|
||
if target < 0:
|
||
return 0
|
||
if target == 0:
|
||
return 1
|
||
return sum(count_of_possible_combinations(target - item) for item in array)
|
||
|
||
return count_of_possible_combinations(target)
|
||
|
||
|
||
def combination_sum_iv_dp_array(array: list[int], target: int) -> int:
|
||
"""
|
||
Function checks the all possible combinations, and returns the count
|
||
of possible combination in O(N^2) Time Complexity as we are using Dynamic
|
||
programming array here.
|
||
|
||
>>> combination_sum_iv_dp_array([1,2,5], 5)
|
||
9
|
||
"""
|
||
|
||
def count_of_possible_combinations_with_dp_array(
|
||
target: int, dp_array: list[int]
|
||
) -> int:
|
||
if target < 0:
|
||
return 0
|
||
if target == 0:
|
||
return 1
|
||
if dp_array[target] != -1:
|
||
return dp_array[target]
|
||
answer = sum(
|
||
count_of_possible_combinations_with_dp_array(target - item, dp_array)
|
||
for item in array
|
||
)
|
||
dp_array[target] = answer
|
||
return answer
|
||
|
||
dp_array = [-1] * (target + 1)
|
||
return count_of_possible_combinations_with_dp_array(target, dp_array)
|
||
|
||
|
||
def combination_sum_iv_bottom_up(n: int, array: list[int], target: int) -> int:
|
||
"""
|
||
Function checks the all possible combinations with using bottom up approach,
|
||
and returns the count of possible combination in O(N^2) Time Complexity
|
||
as we are using Dynamic programming array here.
|
||
|
||
>>> combination_sum_iv_bottom_up(3, [1,2,5], 5)
|
||
9
|
||
"""
|
||
|
||
dp_array = [0] * (target + 1)
|
||
dp_array[0] = 1
|
||
|
||
for i in range(1, target + 1):
|
||
for j in range(n):
|
||
if i - array[j] >= 0:
|
||
dp_array[i] += dp_array[i - array[j]]
|
||
|
||
return dp_array[target]
|
||
|
||
|
||
if __name__ == "__main__":
|
||
import doctest
|
||
|
||
doctest.testmod()
|
||
target = 5
|
||
array = [1, 2, 5]
|
||
print(combination_sum_iv(array, target))
|