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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;
}
}

• // 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;
}
};

• 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

############

class Solution(object):
def numsSameConsecDiff(self, N, K):
"""
:type N: int
:type K: int
:rtype: List[int]
"""
if N == 1:
return [0, 1,2,3,4,5,6,7,8,9]
res = []
for i in range(1, 10):
self.dfs(res, i, N - 1, K)
return list(set(res))

def dfs(self, res, curint, N, K):
if N == 0:
res.append(curint)
return
last = curint % 10
if last + K <= 9:
self.dfs(res, curint * 10 + last + K, N - 1, K)
if last - K >= 0:
self.dfs(res, curint * 10 + last - K, N - 1, K)