216. Combination Sum III #

Problem #

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Note:

• All numbers will be positive integers.
• The solution set must not contain duplicate combinations.

Example 1:

Input: k = 3, n = 7
Output: [[1,2,4]]

Example 2:

Input: k = 3, n = 9
Output: [[1,2,6], [1,3,5], [2,3,4]]

Summary #

Find all combinations of k numbers that add up to n. Each combination may only contain positive integers from 1 - 9, and no combination contains duplicate numbers.

Note:

• All numbers are positive integers.
• The solution set must not contain duplicate combinations.

Solution Approach #

• This problem is even simpler than Problem 39; with a slight modification to the solution for Problem 39, this problem can be solved.
• In Problem 39, an array is given; in this problem, the array is fixed as [1,2,3,4,5,6,7,8,9], and numbers cannot be reused.

Code #

package leetcode

func combinationSum3(k int, n int) [][]int {
	if k == 0 {
		return [][]int{}
	}
	c, res := []int{}, [][]int{}
	findcombinationSum3(k, n, 1, c, &res)
	return res
}

func findcombinationSum3(k, target, index int, c []int, res *[][]int) {
	if target == 0 {
		if len(c) == k {
			b := make([]int, len(c))
			copy(b, c)
			*res = append(*res, b)
		}
		return
	}
	for i := index; i < 10; i++ {
		if target >= i {
			c = append(c, i)
			findcombinationSum3(k, target-i, i+1, c, res)
			c = c[:len(c)-1]
		}
	}
}