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feat: update solutions to lc problem: No.0967 (#3397)
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No.0967.Numbers With Same Consecutive Differences
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@yanglbme
yanglbme authored Aug 10, 2024
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2 changes: 1 addition & 1 deletion solution/0700-0799/0737.Sentence Similarity II/README.md
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Expand Up @@ -30,7 +30,7 @@ tags:
<p>两个句子是相似的，如果:</p>

<ul>
<li>它们具有 <strong>相同的长度</strong> (即相同的字数)</li>
<li>它们具有 <strong>相同的长度</strong> (即相同的词数)</li>
<li><code>sentence1[i]</code>&nbsp;和&nbsp;<code>sentence2[i]</code>&nbsp;是相似的</li>
</ul>

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175 changes: 92 additions & 83 deletions solution/0900-0999/0967.Numbers With Same Consecutive Differences/README.md
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Expand Up @@ -68,7 +68,13 @@ tags:

<!-- solution:start -->

### 方法一
### 方法一：DFS

我们可以枚举所有长度为 $n$ 的数字的第一个数字，然后使用深度优先搜索的方法，递归地构造所有符合条件的数字。

具体地，我们首先定义一个边界值 $\textit{boundary} = 10^{n-1}$，表示我们需要构造的数字的最小值。然后，我们从 $1$ 到 $9$ 枚举第一个数字，对于每一个数字 $i$，我们递归地构造以 $i$ 为第一个数字的长度为 $n$ 的数字。

时间复杂度 $(n \times 2^n \times |\Sigma|)$，其中 $|\Sigma|$ 表示数字集合，本题中 $|\Sigma| = 9$。空间复杂度 $O(2^n)$。

<!-- tabs:start -->

Expand All @@ -77,50 +83,51 @@ tags:
```python
class Solution:
def numsSameConsecDiff(self, n: int, k: int) -> List[int]:
ans = []

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

ans = []
boundary = 10 ** (n - 1)
for i in range(1, 10):
dfs(n - 1, k, i)
dfs(i)
return ans
```

#### Java

```java
class Solution {
private List<Integer> ans = new ArrayList<>();
private int boundary;
private int k;

public int[] numsSameConsecDiff(int n, int k) {
List<Integer> res = new ArrayList<>();
this.k = k;
boundary = (int) Math.pow(10, n - 1);
for (int i = 1; i < 10; ++i) {
dfs(n - 1, k, i, res);
dfs(i);
}
int[] ans = new int[res.size()];
for (int i = 0; i < res.size(); ++i) {
ans[i] = res.get(i);
}
return ans;
return ans.stream().mapToInt(i -> i).toArray();
}

private void dfs(int n, int k, int t, List<Integer> res) {
if (n == 0) {
res.add(t);
private void dfs(int x) {
if (x >= boundary) {
ans.add(x);
return;
}
int last = t % 10;
if (last + k <= 9) {
dfs(n - 1, k, t * 10 + last + k, res);
int last = x % 10;
if (last + k < 10) {
dfs(x * 10 + last + k);
}
if (last - k >= 0 && k != 0) {
dfs(n - 1, k, t * 10 + last - k, res);
if (k != 0 && last - k >= 0) {
dfs(x * 10 + last - k);
}
}
}
Expand All @@ -131,109 +138,111 @@ class Solution {
```cpp
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;
vector<int> ans;
int boundary = pow(10, n - 1);
auto dfs = [&](auto&& dfs, int x) {
if (x >= boundary) {
ans.push_back(x);
return;
}
int last = x % 10;
if (last + k < 10) {
dfs(dfs, x * 10 + last + k);
}
if (k != 0 && last - k >= 0) {
dfs(dfs, x * 10 + last - k);
}
};
for (int i = 1; i < 10; ++i) {
dfs(dfs, i);
}
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);
return ans;
}
};
```
#### Go
```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)
func numsSameConsecDiff(n int, k int) (ans []int) {
bounary := int(math.Pow10(n - 1))
var dfs func(int)
dfs = func(x int) {
if x >= bounary {
ans = append(ans, x)
return
}
last := t % 10
if last+k <= 9 {
dfs(n-1, k, t*10+last+k)
last := x % 10
if last+k < 10 {
dfs(x*10 + last + k)
}
if last-k >= 0 && k != 0 {
dfs(n-1, k, t*10+last-k)
if k > 0 && last-k >= 0 {
dfs(x*10 + last - k)
}
}
for i := 1; i < 10; i++ {
dfs(n-1, k, i)
dfs(i)
}
return ans
return
}
```

#### TypeScript

```ts
function numsSameConsecDiff(n: number, k: number): number[] {
const ans = new Set<number>();
const ans: number[] = [];
const boundary = 10 ** (n - 1);

const dfs = (nums: number) => {
if (nums >= boundary) {
ans.add(nums);
const dfs = (x: number) => {
if (x >= boundary) {
ans.push(x);
return;
}

const num = nums % 10;
for (const x of [num + k, num - k]) {
if (0 <= x && x < 10) {
dfs(nums * 10 + x);
}
const last = x % 10;
if (last + k < 10) {
dfs(x * 10 + last + k);
}
if (k > 0 && last - k >= 0) {
dfs(x * 10 + last - k);
}
};

for (let i = 1; i < 10; i++) {
dfs(i);
}

return [...ans];
return ans;
}
```

#### JavaScript

```js
function numsSameConsecDiff(n, k) {
const ans = new Set();
/**
* @param {number} n
* @param {number} k
* @return {number[]}
*/
var numsSameConsecDiff = function (n, k) {
const ans = [];
const boundary = 10 ** (n - 1);

const dfs = nums => {
if (nums >= boundary) {
ans.add(nums);
const dfs = x => {
if (x >= boundary) {
ans.push(x);
return;
}

const num = nums % 10;
for (const x of [num + k, num - k]) {
if (0 <= x && x < 10) {
dfs(nums * 10 + x);
}
const last = x % 10;
if (last + k < 10) {
dfs(x * 10 + last + k);
}
if (k > 0 && last - k >= 0) {
dfs(x * 10 + last - k);
}
};

for (let i = 1; i < 10; i++) {
dfs(i);
}

return [...ans];
}
return ans;
};
```

<!-- tabs:end -->
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