feat: finish no.967

BaffinLee · BaffinLee · commit 48819af99fc0 · 2023-04-16T19:46:48.000+08:00
diff --git a/901-1000/967. Numbers With Same Consecutive Differences.md b/901-1000/967. Numbers With Same Consecutive Differences.md
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+# 967. Numbers With Same Consecutive Differences
+
+- Difficulty: Medium.
+- Related Topics: Backtracking, Breadth-First Search.
+- Similar Questions: .
+
+## Problem
+
+Given two integers n and k, return an array of all the integers of length ```n``` where the difference between every two consecutive digits is ```k```. You may return the answer in **any order**.
+
+Note that the integers should not have leading zeros. Integers as ```02``` and ```043``` are not allowed.
+
+ 
+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]
+```
+
+ 
+**Constraints:**
+
+
+	
+- ```2 <= n <= 9```
+	
+- ```0 <= k <= 9```
+
+
+
+## Solution
+
+```javascript
+/**
+ * @param {number} n
+ * @param {number} k
+ * @return {number[]}
+ */
+var numsSameConsecDiff = function(n, k) {
+    var res = [];
+    for (var i = 1; i < 10; i++) {
+        helper([i], n - 1, k, res);
+    }
+    return res;
+};
+
+var helper = function(arr, n, k, res) {
+    if (n === 0) {
+        res.push(+arr.join(''));
+        return;
+    }
+    if (n < 0 || n > 9) {
+        return;
+    }
+    var last = arr[arr.length - 1];
+    if (last - k >= 0) {
+        arr.push(last - k);
+        helper(arr, n - 1, k, res);
+        arr.pop();
+    }
+    if (k !== 0 && last + k < 10) {
+        arr.push(last + k);
+        helper(arr, n - 1, k, res);
+        arr.pop();
+    }
+};
+```
+
+**Explain:**
+
+Start with 1 ~ 9, dfs (top down) to get all answers.
+
+**Complexity:**
+
+* Time complexity : O(n).
+* Space complexity : O(n).
