DataStructure_Algorithm_HandBook_PreForLeetCode

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.

Constraints:

2 <= k <= 9
1 <= n <= 60

solution

这道题目是需要满足和为n，然后有 k 个值然后数组返回是 1 到 9 其实这里我们就可以直接利用 i 来当做数组，为了保证不重复，只要index 每次加一就可以；

var combinationSum3 = function(k, n) {
    let result = [];
    dfs(1,0,[],k,n,result);
    return result; 

};
function dfs(index,sum,path,k,n,result){
    if(sum > n) return;
    if(sum === n){
        if(path.length === k){
            result.push([...path]);
            return; 
        }
    }
    for(let i = index;i<=9; i++){
        path.push(i);
        dfs(i+1,sum+i,path,k,n,result);
        path.pop();
    }
}