Detailed explanation of C++ function recursion: solving combination problems recursively

Recursion is a method used to solve combinatorial problems where a function calls itself. The algorithm steps include a baseline condition (returning an empty set when the number of elements to be selected is 0) and a recursive step (enumerating all possible combinations and appending the current element). In the actual case, a recursive function is used to solve all possible combinations of selecting 3 numbers from the number set to form a three-digit number.

Detailed explanation of C function recursion: recursively solving combination problems

Introduction

Recursion It is a process in which a function calls itself, and it can be used to solve a variety of problems. In this article, we will explore techniques for solving combinatorial problems using recursion.

Combination problem

Combination problem refers to selecting a specific number of elements from a set of elements, regardless of the order of the elements. For example, choose 3 letters from a set to form a word.

Recursive algorithm

We can use recursive functions to solve combinatorial problems. This function accepts two parameters:

• Element collection
• The number of elements to be selected

Algorithm steps:

1. Baseline condition: If the number of elements to be selected is 0, an empty set (that is, a set without any elements) is returned.

2. Recursive steps:

   • Remove any element from the element set.
   • Call the function recursively on the remaining element set and reduce the number of elements to be selected by 1.
   • Append the current element to the result of the recursive call.

Practical case:

Let us use a recursive function to solve a practical problem:

Question: Select 3 numbers from a set of numbers to form a three-digit number and find all possible combinations.

Solution:

#include <iostream>
#include <vector>

using namespace std;

void findCombinations(vector<int> numbers, int n, int k) {
    if (k == 0) {
        for (int i : numbers) {
            cout << i;
        }
        cout << endl;
    } else {
        for (int i = 0; i < n; i++) {
            numbers.push_back(i);
            findCombinations(numbers, n, k - 1);
            numbers.pop_back();
        }
    }
}

int main() {
    int n; // 元素数量
    int k; // 需要选择的元素数量
    cin >> n >> k;

    vector<int> numbers;
    findCombinations(numbers, n, k);

    return 0;
}

Program description:

• Enter the number of elements and the number of elements to be selected.
• Initialize an empty collection to store combinations.
• Call the recursive function findCombinations, which enumerates all possible combinations and outputs the results.

Execution example:

Input:

5 3

Output:

012
013
014
023
024
034
123
124
134
234

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