Generating k Combinations of n Items Effectively in C
The task of generating all possible combinations of k individuals from a group of n involves employing a clever algorithm that leverages binary representations.
Implementation
The essence of the algorithm lies in creating a list of binary numbers where the first k bits are set to 1, with the remaining n - k bits being set to 0. This binary representation serves as an assignment list, where each bit indicates the inclusion or exclusion of a specific individual in the combination.
Algorithm
The key steps of the algorithm are as follows:
Example
Consider a scenario with n = 5 and k = 3. The algorithm would generate the following combinations:
0 1 2 0 1 3 0 1 4 0 2 3 0 2 4 0 3 4 1 2 3 1 2 4 1 3 4 2 3 4
Analysis
This algorithm effectively exploits binary representations to efficiently generate all possible combinations. The bitmask manipulation provides a straightforward and rapid method for determining the inclusion or exclusion of individuals in the combinations.
Optimization
To further enhance the efficiency, an optimization involves sorting the generated combinations. While not strictly necessary, it ensures a consistent order of combinations for the same input parameters.
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