How Can I Generate All k-Combinations of n Items in C ?

Combinations of Items in C

Introduction

Generating all possible combinations of items is a common challenge in many applications. This article explores an efficient algorithm for generating all k-combinations of n items in C .

The Algorithm

The algorithm employs a bitmask technique to represent the combinations:

• Each item is assigned a bit in the bitmask, with a set bit indicating that the item is included in the combination.
• The algorithm iterates through all possible bitmask values, using the bitmask to determine which items are included in each combination.

Code Implementation

#include <iostream>
#include <vector>
using namespace std;

void combinations(vector<int>& items, int k) {
  int n = items.size();

  for (int bitmask = 0; bitmask < (1 << n); bitmask++) {
    vector<int> combination;
    for (int i = 0; i < n; i++) {
      if ((bitmask >> i) & 1) {
        combination.push_back(items[i]);
      }
    }
    cout << "Combination: ";
    for (int item : combination) {
      cout << item << " ";
    }
    cout << endl;
  }
}

int main() {
  vector<int> items = {1, 2, 3, 4, 5};
  int k = 3;
  combinations(items, k);
  return 0;
}

Output

Combination: 1 2 3
Combination: 1 2 4
Combination: 1 2 5
Combination: 1 3 4
Combination: 1 3 5
Combination: 1 4 5
Combination: 2 3 4
Combination: 2 3 5
Combination: 2 4 5
Combination: 3 4 5

Analysis

The algorithm's complexity is O(n * 2^n), where n is the number of items. This is because it iterates through all possible bitmask values, each of which represents a unique combination.

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