g0201_0300.s0216_combination_sum_iii.Solution Maven / Gradle / Ivy

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Java-based LeetCode algorithm problem solutions, regularly updated

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package g0201_0300.s0216_combination_sum_iii;

// #Medium #Array #Backtracking #Udemy_Backtracking/Recursion
// #2022_07_02_Time_1_ms_(81.35%)_Space_41.8_MB_(46.36%)

import java.util.ArrayList;
import java.util.List;

/**
 * 216 - Combination Sum III\.
 *
 * Medium
 *
 * Find all valid combinations of `k` numbers that sum up to `n` such that the following conditions are true:
 *
 * *   Only numbers `1` through `9` are used.
 * *   Each number is used **at most once**.
 *
 * Return _a list of all possible valid combinations_. The list must not contain the same combination twice, and the combinations may be returned in any order.
 *
 * **Example 1:**
 *
 * **Input:** k = 3, n = 7
 *
 * **Output:** [[1,2,4]]
 *
 * **Explanation:**
 *
 *     1 + 2 + 4 = 7
 *     There are no other valid combinations.
 *
 * **Example 2:**
 *
 * **Input:** k = 3, n = 9
 *
 * **Output:** [[1,2,6],[1,3,5],[2,3,4]]
 *
 * **Explanation:**
 *
 *     1 + 2 + 6 = 9
 *     1 + 3 + 5 = 9
 *     2 + 3 + 4 = 9
 *     There are no other valid combinations. 
 *
 * **Example 3:**
 *
 * **Input:** k = 4, n = 1
 *
 * **Output:** []
 *
 * **Explanation:**
 *
 *     There are no valid combinations.
 *     Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 > 1, there are no valid combination. 
 *
 * **Example 4:**
 *
 * **Input:** k = 3, n = 2
 *
 * **Output:** []
 *
 * **Explanation:** There are no valid combinations. 
 *
 * **Example 5:**
 *
 * **Input:** k = 9, n = 45
 *
 * **Output:** [[1,2,3,4,5,6,7,8,9]]
 *
 * **Explanation:**
 *
 *     1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
 *     There are no other valid combinations. 
 *
 * **Constraints:**
 *
 * *   `2 <= k <= 9`
 * *   `1 <= n <= 60`
**/
@SuppressWarnings("java:S5413")
public class Solution {
    public List> combinationSum3(int k, int n) {
        List> res = new ArrayList<>();
        solve(k, n, new ArrayList<>(), res, 0, 1);
        return res;
    }

    private void solve(
            int k, int target, List temp, List> res, int sum, int start) {
        if (sum == target && temp.size() == k) {
            res.add(new ArrayList<>(temp));
            return;
        }
        if (temp.size() >= k) {
            return;
        }
        if (sum > target) {
            return;
        }
        for (int i = start; i <= 9; i++) {
            temp.add(i);
            solve(k, target, temp, res, sum + i, i + 1);
            temp.remove(temp.size() - 1);
        }
    }
}