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39. Combination Sum

中文文档

Description

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.

The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

The test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

 

Example 1:

Input: candidates = [2,3,6,7], target = 7
Output: [[2,2,3],[7]]
Explanation:
2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times.
7 is a candidate, and 7 = 7.
These are the only two combinations.

Example 2:

Input: candidates = [2,3,5], target = 8
Output: [[2,2,2,2],[2,3,3],[3,5]]

Example 3:

Input: candidates = [2], target = 1
Output: []

 

Constraints:

  • 1 <= candidates.length <= 30
  • 2 <= candidates[i] <= 40
  • All elements of candidates are distinct.
  • 1 <= target <= 40

Solutions

DFS.

Python3

class Solution:
    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
        def dfs(i: int, s: int):
            if s == 0:
                ans.append(t[:])
                return
            if s < candidates[i]:
                return
            for j in range(i, len(candidates)):
                t.append(candidates[j])
                dfs(j, s - candidates[j])
                t.pop()

        candidates.sort()
        t = []
        ans = []
        dfs(0, target)
        return ans
class Solution:
    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
        def dfs(i: int, s: int):
            if s == 0:
                ans.append(t[:])
                return
            if i >= len(candidates) or s < candidates[i]:
                return
            dfs(i + 1, s)
            t.append(candidates[i])
            dfs(i, s - candidates[i])
            t.pop()

        candidates.sort()
        t = []
        ans = []
        dfs(0, target)
        return ans

Java

class Solution {
    private List<List<Integer>> ans = new ArrayList<>();
    private List<Integer> t = new ArrayList<>();
    private int[] candidates;

    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        Arrays.sort(candidates);
        this.candidates = candidates;
        dfs(0, target);
        return ans;
    }

    private void dfs(int i, int s) {
        if (s == 0) {
            ans.add(new ArrayList(t));
            return;
        }
        if (s < candidates[i]) {
            return;
        }
        for (int j = i; j < candidates.length; ++j) {
            t.add(candidates[j]);
            dfs(j, s - candidates[j]);
            t.remove(t.size() - 1);
        }
    }
}
class Solution {
    private List<List<Integer>> ans = new ArrayList<>();
    private List<Integer> t = new ArrayList<>();
    private int[] candidates;

    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        Arrays.sort(candidates);
        this.candidates = candidates;
        dfs(0, target);
        return ans;
    }

    private void dfs(int i, int s) {
        if (s == 0) {
            ans.add(new ArrayList(t));
            return;
        }
        if (i >= candidates.length || s < candidates[i]) {
            return;
        }
        dfs(i + 1, s);
        t.add(candidates[i]);
        dfs(i, s - candidates[i]);
        t.remove(t.size() - 1);
    }
}

C++

class Solution {
public:
    vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
        sort(candidates.begin(), candidates.end());
        vector<vector<int>> ans;
        vector<int> t;
        function<void(int, int)> dfs = [&](int i, int s) {
            if (s == 0) {
                ans.emplace_back(t);
                return;
            }
            if (s < candidates[i]) {
                return;
            }
            for (int j = i; j < candidates.size(); ++j) {
                t.push_back(candidates[j]);
                dfs(j, s - candidates[j]);
                t.pop_back();
            }
        };
        dfs(0, target);
        return ans;
    }
};
class Solution {
public:
    vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
        sort(candidates.begin(), candidates.end());
        vector<vector<int>> ans;
        vector<int> t;
        function<void(int, int)> dfs = [&](int i, int s) {
            if (s == 0) {
                ans.emplace_back(t);
                return;
            }
            if (i >= candidates.size() || s < candidates[i]) {
                return;
            }
            dfs(i + 1, s);
            t.push_back(candidates[i]);
            dfs(i, s - candidates[i]);
            t.pop_back();
        };
        dfs(0, target);
        return ans;
    }
};

Go

func combinationSum(candidates []int, target int) (ans [][]int) {
	sort.Ints(candidates)
	t := []int{}
	var dfs func(i, s int)
	dfs = func(i, s int) {
		if s == 0 {
			cp := make([]int, len(t))
			copy(cp, t)
			ans = append(ans, cp)
			return
		}
		if s < candidates[i] {
			return
		}
		for j := i; j < len(candidates); j++ {
			t = append(t, candidates[j])
			dfs(j, s-candidates[j])
			t = t[:len(t)-1]
		}
	}
	dfs(0, target)
	return
}
func combinationSum(candidates []int, target int) (ans [][]int) {
	sort.Ints(candidates)
	t := []int{}
	var dfs func(i, s int)
	dfs = func(i, s int) {
		if s == 0 {
			cp := make([]int, len(t))
			copy(cp, t)
			ans = append(ans, cp)
			return
		}
		if i >= len(candidates) || s < candidates[i] {
			return
		}
		dfs(i+1, s)
		t = append(t, candidates[i])
		dfs(i, s-candidates[i])
		t = t[:len(t)-1]
	}
	dfs(0, target)
	return
}

TypeScript

function combinationSum(candidates: number[], target: number): number[][] {
    candidates.sort((a, b) => a - b);
    const ans: number[][] = [];
    const t: number[] = [];
    const dfs = (i: number, s: number) => {
        if (s === 0) {
            ans.push(t.slice());
            return;
        }
        if (s < candidates[i]) {
            return;
        }
        for (let j = i; j < candidates.length; ++j) {
            t.push(candidates[j]);
            dfs(j, s - candidates[j]);
            t.pop();
        }
    };
    dfs(0, target);
    return ans;
}
function combinationSum(candidates: number[], target: number): number[][] {
    candidates.sort((a, b) => a - b);
    const ans: number[][] = [];
    const t: number[] = [];
    const dfs = (i: number, s: number) => {
        if (s === 0) {
            ans.push(t.slice());
            return;
        }
        if (i >= candidates.length || s < candidates[i]) {
            return;
        }
        dfs(i + 1, s);
        t.push(candidates[i]);
        dfs(i, s - candidates[i]);
        t.pop();
    };
    dfs(0, target);
    return ans;
}

Rust

impl Solution {
    fn dfs(i: usize, s: i32, candidates: &Vec<i32>, t: &mut Vec<i32>, ans: &mut Vec<Vec<i32>>) {
        if s == 0 {
            ans.push(t.clone());
            return;
        }
        if s < candidates[i] {
            return;
        }
        for j in i..candidates.len() {
            t.push(candidates[j]);
            Self::dfs(j, s - candidates[j], candidates, t, ans);
            t.pop();
        }
    }

    pub fn combination_sum(mut candidates: Vec<i32>, target: i32) -> Vec<Vec<i32>> {
        candidates.sort();
        let mut ans = Vec::new();
        Self::dfs(0, target, &candidates, &mut vec![], &mut ans);
        ans
    }
}
impl Solution {
    fn dfs(i: usize, s: i32, candidates: &Vec<i32>, t: &mut Vec<i32>, ans: &mut Vec<Vec<i32>>) {
        if s == 0 {
            ans.push(t.clone());
            return;
        }
        if i >= candidates.len() || s < candidates[i] {
            return;
        }
        Self::dfs(i + 1, s, candidates, t, ans);
        t.push(candidates[i]);
        Self::dfs(i, s - candidates[i], candidates, t, ans);
        t.pop();
    }

    pub fn combination_sum(mut candidates: Vec<i32>, target: i32) -> Vec<Vec<i32>> {
        candidates.sort();
        let mut ans = Vec::new();
        Self::dfs(0, target, &candidates, &mut vec![], &mut ans);
        ans
    }
}

C#

public class Solution {
    private List<IList<int>> ans = new List<IList<int>>();
    private List<int> t = new List<int>();
    private int[] candidates;

    public IList<IList<int>> CombinationSum(int[] candidates, int target) {
        Array.Sort(candidates);
        this.candidates = candidates;
        dfs(0, target);
        return ans;
    }

    private void dfs(int i, int s) {
        if (s == 0) {
            ans.Add(new List<int>(t));
            return;
        }
        if (s < candidates[i]) {
            return;
        }
        for (int j = i; j < candidates.Length; ++j) {
            t.Add(candidates[j]);
            dfs(j, s - candidates[j]);
            t.RemoveAt(t.Count - 1);
        }
    }
}
public class Solution {
    private List<IList<int>> ans = new List<IList<int>>();
    private List<int> t = new List<int>();
    private int[] candidates;

    public IList<IList<int>> CombinationSum(int[] candidates, int target) {
        Array.Sort(candidates);
        this.candidates = candidates;
        dfs(0, target);
        return ans;
    }

    private void dfs(int i, int s) {
        if (s == 0) {
            ans.Add(new List<int>(t));
            return;
        }
        if (i >= candidates.Length || s < candidates[i]) {
            return;
        }
        dfs(i + 1, s);
        t.Add(candidates[i]);
        dfs(i, s - candidates[i]);
        t.RemoveAt(t.Count - 1);
    }
}

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