Formatted question description: https://leetcode.ca/all/967.html

967. Numbers With Same Consecutive Differences (Medium)

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 except for the number 0 itself. For example, 01 has one leading zero and is invalid, but 0 is valid.

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]

 

Note:

1. 1 <= N <= 9
2. 0 <= K <= 9

Related Topics:
Dynamic Programming

Solution 1.

// OJ: https://leetcode.com/problems/numbers-with-same-consecutive-differences/

// Time: O(N)
// Space: O(N)
class Solution {
    vector<int> ans;
    void dfs(int num, int i, int N, int K) {
        if (i == N) {
            ans.push_back(num);
            return;
        }
        if (num % 10 + K <= 9) dfs(num * 10 + (num % 10 + K), i + 1, N, K);
        if (K != 0 && num % 10 - K >= 0) dfs(num * 10 + (num % 10 - K), i + 1, N, K);
    }
public:
    vector<int> numsSameConsecDiff(int N, int K) {
        for (int i = N == 1 ? 0 : 1; i <= 9; ++i) dfs(i, 1, N, K);
        return ans;
    }
};

Java

class Solution {
    public int[] numsSameConsecDiff(int N, int K) {
        if (N == 1) {
            int[] nums = new int[10];
            for (int i = 0; i < 10; i++)
                nums[i] = i;
            return nums;
        }
        Queue<Integer> queue = new LinkedList<Integer>();
        for (int i = 1; i <= 9; i++) {
            int nextDigit1 = i - K, nextDigit2 = i + K;
            if (nextDigit1 >= 0)
                queue.offer(i * 10 + nextDigit1);
            if (K != 0 && nextDigit2 < 10)
                queue.offer(i * 10 + nextDigit2);
        }
        for (int digits = 3; digits <= N; digits++) {
            int size = queue.size();
            for (int i = 0; i < size; i++) {
                int num = queue.poll();
                int lastDigit = num % 10;
                int nextDigit1 = lastDigit - K, nextDigit2 = lastDigit + K;
                if (nextDigit1 >= 0)
                    queue.offer(num * 10 + nextDigit1);
                if (K != 0 && nextDigit2 < 10)
                    queue.offer(num * 10 + nextDigit2);
            }
        }
        int length = queue.size();
        int[] nums = new int[length];
        for (int i = 0; i < length; i++)
            nums[i] = queue.poll();
        return nums;
    }
}

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