Published in Algorithm

# Algorithm to Return All Combinations of k Elements from n

To generate all possible combinations of k elements from a given set of n elements, you can use a recursive algorithm. Combinations are distinct subsets of elements without regard to their order.

## Understanding Combinations

### What are Combinations?

Combinations are selections of elements from a set without considering the order of the elements. For example, given the set {1, 2, 3}, the combinations of 2 elements are {1, 2}, {1, 3}, and {2, 3}.

## Implementing the Combinations Algorithm

### Recursive Backtracking Algorithm for Combinations

To generate all combinations, you can use a recursive backtracking algorithm. The idea is to either include or exclude each element from the set in each recursive call, building all possible combinations along the way.

## Example in Python

``````def generate_combinations(nums, k, start=0, current=[], result=[]):
if len(current) == k:
result.append(current.copy())
return

for i in range(start, len(nums)):
current.append(nums[i])
generate_combinations(nums, k, i + 1, current, result)
current.pop()

# Example usage:
nums = [1, 2, 3, 4]
k = 2
combinations = []
generate_combinations(nums, k, result=combinations)
print(combinations)
``````

## Output

``````[[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
``````

In this Python example, the `generate_combinations` function generates all combinations of k elements from the list `nums`. The function uses recursion and backtracking to explore all possible combinations and stores the results in the `combinations` list.