Teaching Kids Programming – Recursive Backtracking Algorithm to Compute the Combinations

Teaching Kids Programming: Videos on Data Structures and Algorithms

Given two integers n and k, return all possible combinations of k numbers out of 1 … n. You may return the answer in any order.

Example 1:
Input: n = 4, k = 2
Output:

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

Example 2:
Input: n = 1, k = 1
Output: [[1]]

Compute the Combinations via Recursive Backtracking (Depth First Search)

There are number of the combinations when you pick k items out of n. Therefore, the solution time complexity is . We can backtracking with Depth First Search so that for each round, we can pick an item and DFS to next pick until we have k items.

This is similar to Permutations where each result can have K! different sequences: Teaching Kids Programming – Recursive Permutation Algorithm

class Solution:
    def combine(self, n: int, k: int) -> List[List[int]]:
        def dfs(left, cur):
            if len(cur) == k:   # finish k items
                output.append(cur[:])
                return
            for i in range(left, n + 1):
                cur.append(i)   # pick i
                dfs(i + 1, cur) # pick next from i+1
                cur.pop()       # reset for next iteration
        output = []
        dfs(1, [])
        return output            

Permutations and Combinations

• Using Bitmasking Algorithm to Compute the Combinations of an Array
• Teaching Kids Programming – Recursive Backtracking Algorithm to Compute the Combinations
• Teaching Kids Programming – Recursive Permutation Algorithm
• Teaching Kids Programming – Introduction to Permutation and Combination
• Teaching Kids Programming – Three Algorithms to Compute the Combination Number
• A Recursive Full Permutation Algorithm in Python
• The Permutation Iterator in Python
• GoLang: Full Permutation Command Line Tool
• The Permutation Algorithm for Arrays using Recursion
• Full Permutation Algorithm Implementation in BASH

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