**source:**https://leetcode.com/problems/combinations/**C/C++**

**Solution to LeetCode**problem

**77**.

**Combinations**.

## Problem

Given two integers `n`

and `k`

, return *all possible combinations of k numbers chosen from the range [1, n]*.

You may return the answer in **any order**.

## Examples

**Example 1:**

Input:n = 4, k = 2

Output:[[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]

Explanation:There are 4 choose 2 = 6 total combinations.

Note that combinations are unordered, i.e., [1,2] and [2,1] are considered to be the same combination.

**Example 2:**

Input:n = 1, k = 1

Output:[[1]]

Explanation:There is 1 choose 1 = 1 total combination.

## Constraints

`1 <= n <= 20`

`1 <= k <= n`

## Solution

This one is easily solved using **Backtracking**

- Becasue there should not be repeated combinations, for recursive call we set the initial index to be one more than the previous call.
- And we add
`1`

to the number when adding to the combination (because the range is from`1`

to`n`

).

For this solution I’m pushing/poping an element to generate the combination, and alternative (a couple of milliseconds faster) is to have a vector of fixed `k`

size and just handle the index of the current element to set.

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class Solution {
vector<vector<int>> result;
void generateCombinations(int n, int k, int ci, vector<int>& c) {
if (c.size() == k) {
result.push_back(c);
return;
}
for (int i=ci; i<n; i++) {
c.push_back(i+1);
generateCombinations(n, k, i+1, c);
c.pop_back();
}
}
public:
vector<vector<int>> combine(int n, int k) {
result.clear();
vector<int> sol;
generateCombinations(n, k, 0, sol);
return result;
}
};