README_EN.md

967. Numbers With Same Consecutive Differences

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Description

Return all non-negative integers of length n such that the absolute difference between every two consecutive digits is k.

Note that every number in the answer must not have leading zeros. For example, 01 has one leading zero and is invalid.

You may return the answer in any order.

 

Example 1:

Input: n = 3, k = 7
Output: [181,292,707,818,929]
Explanation: Note that 070 is not a valid number, because it has leading zeroes.

Example 2:

Input: n = 2, k = 1
Output: [10,12,21,23,32,34,43,45,54,56,65,67,76,78,87,89,98]

Example 3:

Input: n = 2, k = 0
Output: [11,22,33,44,55,66,77,88,99]

Example 4:

Input: n = 2, k = 2
Output: [13,20,24,31,35,42,46,53,57,64,68,75,79,86,97]

 

Constraints:

• 2 <= n <= 9
• 0 <= k <= 9

Solutions

DFS.

Python3

class Solution:
    def numsSameConsecDiff(self, n: int, k: int) -> List[int]:
        ans = []

        def dfs(n, k, t):
            if n == 0:
                ans.append(t)
                return
            last = t % 10
            if last + k <= 9:
                dfs(n - 1, k, t * 10 + last + k)
            if last - k >= 0 and k != 0:
                dfs(n - 1, k, t * 10 + last - k)

        for i in range(1, 10):
            dfs(n - 1, k, i)
        return ans

Java

class Solution {
    public int[] numsSameConsecDiff(int n, int k) {
        List<Integer> res = new ArrayList<>();
        for (int i = 1; i < 10; ++i) {
            dfs(n - 1, k, i, res);
        }
        int[] ans = new int[res.size()];
        for (int i = 0; i < res.size(); ++i) {
            ans[i] = res.get(i);
        }
        return ans;
    }

    private void dfs(int n, int k, int t, List<Integer> res) {
        if (n == 0) {
            res.add(t);
            return;
        }
        int last = t % 10;
        if (last + k <= 9) {
            dfs(n - 1, k, t * 10 + last + k, res);
        }
        if (last - k >= 0 && k != 0) {
            dfs(n - 1, k, t * 10 + last - k, res);
        }
    }
}

C++

class Solution {
public:
    vector<int> ans;

    vector<int> numsSameConsecDiff(int n, int k) {
        for (int i = 1; i < 10; ++i)
            dfs(n - 1, k, i);
        return ans;
    }

    void dfs(int n, int k, int t) {
        if (n == 0)
        {
            ans.push_back(t);
            return;
        }
        int last = t % 10;
        if (last + k <= 9) dfs(n - 1, k, t * 10 + last + k);
        if (last - k >= 0 && k != 0) dfs(n - 1, k, t * 10 + last - k);
    }
};

Go

func numsSameConsecDiff(n int, k int) []int {
	var ans []int
	var dfs func(n, k, t int)
	dfs = func(n, k, t int) {
		if n == 0 {
			ans = append(ans, t)
			return
		}
		last := t % 10
		if last+k <= 9 {
			dfs(n-1, k, t*10+last+k)
		}
		if last-k >= 0 && k != 0 {
			dfs(n-1, k, t*10+last-k)
		}
	}

	for i := 1; i < 10; i++ {
		dfs(n-1, k, i)
	}
	return ans
}

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