## 967. Numbers With Same Consecutive Differences

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

## Rust Solution

struct Solution;

impl Solution {
fn nums_same_consec_diff(n: i32, k: i32) -> Vec<i32> {
let n = n as usize;
let mut cur: Vec<i32> = vec![];
let mut res = vec![];
for i in 0..10 {
if i == 0 && n != 1 {
continue;
}
cur.push(i);
Self::dfs(1, &mut cur, &mut res, k, n);
cur.pop();
}
res
}
fn dfs(start: usize, cur: &mut Vec<i32>, all: &mut Vec<i32>, k: i32, n: usize) {
if start == n {
let mut x = 0;
for i in 0..n {
x *= 10;
x += cur[i];
}
all.push(x);
} else {
for i in 0..10 {
if (cur[start - 1] - i).abs() != k {
continue;
}
cur.push(i);
Self::dfs(start + 1, cur, all, k, n);
cur.pop();
}
}
}
}

#[test]
fn test() {
let n = 3;
let k = 7;
let res = vec![181, 292, 707, 818, 929];
assert_eq!(Solution::nums_same_consec_diff(n, k), res);
let n = 2;
let k = 1;
let res = vec![
10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98,
];
assert_eq!(Solution::nums_same_consec_diff(n, k), res);
}

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