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

To find all combinations of k numbers in the range 1 to n, you can use the Backtracking technique.

Step-by-step explanation:

To find all combinations of k numbers in the range 1 to n, you can use the Backtracking technique. Here is a step-by-step algorithm to solve this problem:

1. Start with an empty combination and an empty list to store the combinations.
2. For each number i from 1 to n:
   1. Add i to the current combination.
   2. If the size of the current combination is equal to k, add it to the list of combinations.
   3. Otherwise, recursively call the algorithm with the next number.
   4. Remove i from the current combination to backtrack and try other numbers.

The Backtracking technique is a suitable approach for this problem because it efficiently generates all possible combinations without duplicates. It explores all possible options and backtracks when necessary, ensuring that all valid combinations are found.