Question

Given two numbers n, k, find an algorithm that outputs all combinations of k numbers in [1...n]. Which technique could be used to solve this problem?

1) Backtracking
2) Dynamic Programming
3) Breadth-First Search
4) Depth-First Search

Answer 1

The problem can be solved using the backtracking technique, which involves systematically exploring all possible solutions by generating combinations and backtracking.

Step-by-step explanation:

The problem of finding all combinations of k numbers in the range [1...n] can be solved using the backtracking technique. Backtracking is a recursive algorithm that systematically explores all possible solutions by generating combinations and then backtracking to explore other possibilities.

Here is a step-by-step explanation of the backtracking algorithm to solve this problem:

1. Initialize an empty list to store the combinations.
2. Start with an empty combination.
3. For each number from 1 to n:
4. Add the number to the current combination.
5. If the size of the combination is equal to k, add the combination to the list of combinations.
6. Recursively generate combinations with the remaining numbers (excluding the current number).
7. Remove the current number from the combination.
8. Return the list of combinations.

Using this backtracking algorithm, you can find all combinations of k numbers in the range [1...n].