{"id":34300,"date":"2024-11-01T09:26:33","date_gmt":"2024-11-01T09:26:33","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=34300"},"modified":"2024-11-01T10:57:48","modified_gmt":"2024-11-01T10:57:48","slug":"c-coding-test-course-understanding-combinations-2","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/34300\/","title":{"rendered":"C++ Coding Test Course, Understanding Combinations"},"content":{"rendered":"

<\/p>\n

Hello, everyone! In this session, we will talk about preparing for coding tests using C++. Specifically, we will solve a problem to deepen our understanding of the Combination algorithm. Combinations are a very useful algorithm for finding ways to select items that meet specific conditions.<\/p>\n

Definition of Combination<\/h2>\n

Combination refers to the way of selecting a specific number of elements from a given set. For example, when selecting 2 elements from the set {A, B, C}, the possible selections are {A, B}, {A, C}, and {B, C}. The important point here is that the order of the selected elements does not matter. This is a significant distinction from permutations.<\/p>\n

Problem Description<\/h2>\n

Problem: Sum of Combinations<\/h3>\n

Given an integer array nums<\/code> and an integer target<\/code>, find and output all combinations that can sum up to target<\/code>. Each number in the combination can be used multiple times, and combinations with the same numbers should not be included multiple times.<\/p>\n

Input Example<\/h3>\n
nums = [2, 3, 6, 7]\ntarget = 7<\/code><\/pre>\n
Output Example<\/h3>\n
[[2, 2, 3], [7]]<\/code><\/pre>\n
Problem Solving Process<\/h2>\n
1. Understanding the Problem<\/h3>\n
To solve the problem, we will use the Backtracking algorithm. Backtracking explores possible choices during the problem-solving process and, if a choice is invalid or does not lead to an optimal solution, goes back to a previous step to try another choice.<\/p>\n
2. Algorithm Design<\/h3>\n
The algorithm for this problem consists of the following steps.<\/p>\n
    \n
  1. Add the current combination to the array.<\/li>\n
  2. If the sum of the combination equals target<\/code>, add that combination to the result array.<\/li>\n
  3. If the current combination exceeds target<\/code>, terminate the recursive call.<\/li>\n
  4. Add possible numbers to the combination and make a recursive call to include the same number.<\/li>\n
  5. Finally, remove the last selected number to return to the previous state.<\/li>\n<\/ol>\n
    3. Implementing the Code<\/h3>\n
    Now, let’s look at the code implemented in C++.<\/p>\n
    #include <iostream>\n#include <vector>\nusing namespace std;\n\nvoid backtrack(vector<int> &combination, vector<vector<int>> &result, vector<int> &nums, int target, int start) {\n    if (target == 0) {\n        result.push_back(combination);\n        return;\n    }\n    \n    for (int i = start; i < nums.size(); i++) {\n        if (nums[i] > target) continue; \/\/ Skip if the current number exceeds target\n        combination.push_back(nums[i]); \/\/ Add number to the combination\n        backtrack(combination, result, nums, target - nums[i], i); \/\/ Recursive call\n        combination.pop_back(); \/\/ Remove the last number to backtrack\n    }\n}\n\nvector<vector<int>> combinationSum(vector<int> &nums, int target) {\n    vector<vector<int>> result;\n    vector<int> combination;\n    backtrack(combination, result, nums, target, 0);\n    return result;\n}\n\nint main() {\n    vector<int> nums = {2, 3, 6, 7};\n    int target = 7;\n    vector<vector<int>> result = combinationSum(nums, target);\n    \n    for (const auto &comb : result) {\n        cout << \"[ \";\n        for (int num : comb) {\n            cout << num << \" \";\n        }\n        cout << \"]\" << endl;\n    }\n    \n    return 0;\n}<\/code><\/pre>\n
    4. Explanation of the Code<\/h2>\n
    The above code is a function called combinationSum<\/code> that takes a given array of numbers and a target value, returning an array of all possible combinations. Inside the function, a recursive function called backtrack<\/code> is called to generate combinations.<\/p>\n