有重复字符串的排列组合。编写一种方法，计算某字符串的所有排列组合。
示例1:
输入：S = "qqe"
@@ -24,6 +25,19 @@
+**方法一：排序 + 回溯**
+
+我们可以先对字符串按照字符进行排序，这样就可以将重复的字符放在一起，方便我们进行去重。
+
+然后，我们设计一个函数 $dfs(i)$，表示当前需要填写第 $i$ 个位置的字符。函数的具体实现如下：
+
+- 如果 $i = n$，说明我们已经填写完毕，将当前排列加入答案数组中，然后返回。
+- 否则，我们枚举第 $i$ 个位置的字符 $s[j]$，其中 $j$ 的范围是 $[0, n - 1]$。我们需要保证 $s[j]$ 没有被使用过，并且与前面枚举的字符不同，这样才能保证当前排列不重复。如果满足条件，我们就可以填写 $s[j]$，并继续递归地填写下一个位置，即调用 $dfs(i + 1)$。在递归调用结束后，我们需要将 $s[j]$ 标记为未使用，以便于进行后面的枚举。
+
+在主函数中，我们首先对字符串进行排序，然后调用 $dfs(0)$，即从第 $0$ 个位置开始填写，最终返回答案数组即可。
+
+时间复杂度 $O(n \times n!)$，空间复杂度 $O(n)$。其中 $n$ 是字符串 $s$ 的长度。需要进行 $n!$ 次枚举，每次枚举需要 $O(n)$ 的时间来判断是否重复。另外，我们需要一个标记数组来标记每个位置是否被使用过，因此空间复杂度为 $O(n)$。
+
### **Python3**
@@ -31,7 +45,27 @@
```python
-
+class Solution:
+ def permutation(self, S: str) -> List[str]:
+ def dfs(i: int):
+ if i == n:
+ ans.append("".join(t))
+ return
+ for j in range(n):
+ if vis[j] or (j and cs[j] == cs[j - 1] and not vis[j - 1]):
+ continue
+ t[i] = cs[j]
+ vis[j] = True
+ dfs(i + 1)
+ vis[j] = False
+
+ cs = sorted(S)
+ n = len(cs)
+ ans = []
+ t = [None] * n
+ vis = [False] * n
+ dfs(0)
+ return ans
```
### **Java**
@@ -39,7 +73,134 @@
```java
+class Solution {
+ private int n;
+ private char[] cs;
+ private List ans = new ArrayList<>();
+ private boolean[] vis;
+ private StringBuilder t = new StringBuilder();
+
+ public String[] permutation(String S) {
+ cs = S.toCharArray();
+ n = cs.length;
+ Arrays.sort(cs);
+ vis = new boolean[n];
+ dfs(0);
+ return ans.toArray(new String[0]);
+ }
+
+ private void dfs(int i) {
+ if (i == n) {
+ ans.add(t.toString());
+ return;
+ }
+ for (int j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] == cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.append(cs[j]);
+ dfs(i + 1);
+ t.deleteCharAt(t.length() - 1);
+ vis[j] = false;
+ }
+ }
+}
+```
+### **C++**
+
+```cpp
+class Solution {
+public:
+ vector permutation(string S) {
+ vector cs(S.begin(), S.end());
+ sort(cs.begin(), cs.end());
+ int n = cs.size();
+ vector ans;
+ vector vis(n);
+ string t;
+ function dfs = [&](int i) {
+ if (i == n) {
+ ans.push_back(t);
+ return;
+ }
+ for (int j = 0; j < n; ++j) {
+ if (vis[j] || (j && !vis[j - 1] && cs[j] == cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push_back(cs[j]);
+ dfs(i + 1);
+ t.pop_back();
+ vis[j] = false;
+ }
+ };
+ dfs(0);
+ return ans;
+ }
+};
+```
+
+### **Go**
+
+```go
+func permutation(S string) (ans []string) {
+ cs := []byte(S)
+ sort.Slice(cs, func(i, j int) bool { return cs[i] < cs[j] })
+ t := []byte{}
+ n := len(cs)
+ vis := make([]bool, n)
+ var dfs func(int)
+ dfs = func(i int) {
+ if i == n {
+ ans = append(ans, string(t))
+ return
+ }
+ for j := 0; j < n; j++ {
+ if vis[j] || (j > 0 && !vis[j-1] && cs[j] == cs[j-1]) {
+ continue
+ }
+ vis[j] = true
+ t = append(t, cs[j])
+ dfs(i + 1)
+ t = t[:len(t)-1]
+ vis[j] = false
+ }
+ }
+ dfs(0)
+ return
+}
+```
+
+### **TypeScript**
+
+```ts
+function permutation(S: string): string[] {
+ const cs: string[] = S.split('').sort();
+ const ans: string[] = [];
+ const n = cs.length;
+ const vis: boolean[] = Array(n).fill(false);
+ const t: string[] = [];
+ const dfs = (i: number) => {
+ if (i === n) {
+ ans.push(t.join(''));
+ return;
+ }
+ for (let j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] === cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push(cs[j]);
+ dfs(i + 1);
+ t.pop();
+ vis[j] = false;
+ }
+ };
+ dfs(0);
+ return ans;
+}
```
### **JavaScript**
@@ -50,35 +211,30 @@
* @return {string[]}
*/
var permutation = function (S) {
- let res = [];
- let arr = [...S];
- arr.sort();
- let prev = [];
- let record = new Array(S.length).fill(false);
- dfs(arr, 0, prev, record, res);
- return res;
-};
-function dfs(arr, depth, prev, record, res) {
- if (depth == arr.length) {
- res.push(prev.join(''));
- return;
- }
- for (let i = 0; i < arr.length; i++) {
- if (record[i]) {
- continue;
+ const cs = S.split('').sort();
+ const ans = [];
+ const n = cs.length;
+ const vis = Array(n).fill(false);
+ const t = [];
+ const dfs = i => {
+ if (i === n) {
+ ans.push(t.join(''));
+ return;
}
- // 剪枝
- if (i > 0 && arr[i] == arr[i - 1] && record[i - 1]) {
- continue;
+ for (let j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] === cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push(cs[j]);
+ dfs(i + 1);
+ t.pop();
+ vis[j] = false;
}
- prev.push(arr[i]);
- record[i] = true;
- dfs(arr, depth + 1, prev, record, res);
- // 回溯
- prev.pop();
- record[i] = false;
- }
-}
+ };
+ dfs(0);
+ return ans;
+};
```
### **...**
diff --git a/lcci/08.08.Permutation II/README_EN.md b/lcci/08.08.Permutation II/README_EN.md
index 479e46d2943c0..b1bdcae45f228 100644
--- a/lcci/08.08.Permutation II/README_EN.md
+++ b/lcci/08.08.Permutation II/README_EN.md
@@ -34,13 +34,160 @@
### **Python3**
```python
-
+class Solution:
+ def permutation(self, S: str) -> List[str]:
+ def dfs(i: int):
+ if i == n:
+ ans.append("".join(t))
+ return
+ for j in range(n):
+ if vis[j] or (j and cs[j] == cs[j - 1] and not vis[j - 1]):
+ continue
+ t[i] = cs[j]
+ vis[j] = True
+ dfs(i + 1)
+ vis[j] = False
+
+ cs = sorted(S)
+ n = len(cs)
+ ans = []
+ t = [None] * n
+ vis = [False] * n
+ dfs(0)
+ return ans
```
### **Java**
```java
+class Solution {
+ private int n;
+ private char[] cs;
+ private List ans = new ArrayList<>();
+ private boolean[] vis;
+ private StringBuilder t = new StringBuilder();
+
+ public String[] permutation(String S) {
+ cs = S.toCharArray();
+ n = cs.length;
+ Arrays.sort(cs);
+ vis = new boolean[n];
+ dfs(0);
+ return ans.toArray(new String[0]);
+ }
+
+ private void dfs(int i) {
+ if (i == n) {
+ ans.add(t.toString());
+ return;
+ }
+ for (int j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] == cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.append(cs[j]);
+ dfs(i + 1);
+ t.deleteCharAt(t.length() - 1);
+ vis[j] = false;
+ }
+ }
+}
+```
+### **C++**
+
+```cpp
+class Solution {
+public:
+ vector permutation(string S) {
+ vector cs(S.begin(), S.end());
+ sort(cs.begin(), cs.end());
+ int n = cs.size();
+ vector ans;
+ vector vis(n);
+ string t;
+ function dfs = [&](int i) {
+ if (i == n) {
+ ans.push_back(t);
+ return;
+ }
+ for (int j = 0; j < n; ++j) {
+ if (vis[j] || (j && !vis[j - 1] && cs[j] == cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push_back(cs[j]);
+ dfs(i + 1);
+ t.pop_back();
+ vis[j] = false;
+ }
+ };
+ dfs(0);
+ return ans;
+ }
+};
+```
+
+### **Go**
+
+```go
+func permutation(S string) (ans []string) {
+ cs := []byte(S)
+ sort.Slice(cs, func(i, j int) bool { return cs[i] < cs[j] })
+ t := []byte{}
+ n := len(cs)
+ vis := make([]bool, n)
+ var dfs func(int)
+ dfs = func(i int) {
+ if i == n {
+ ans = append(ans, string(t))
+ return
+ }
+ for j := 0; j < n; j++ {
+ if vis[j] || (j > 0 && !vis[j-1] && cs[j] == cs[j-1]) {
+ continue
+ }
+ vis[j] = true
+ t = append(t, cs[j])
+ dfs(i + 1)
+ t = t[:len(t)-1]
+ vis[j] = false
+ }
+ }
+ dfs(0)
+ return
+}
+```
+
+### **TypeScript**
+
+```ts
+function permutation(S: string): string[] {
+ const cs: string[] = S.split('').sort();
+ const ans: string[] = [];
+ const n = cs.length;
+ const vis: boolean[] = Array(n).fill(false);
+ const t: string[] = [];
+ const dfs = (i: number) => {
+ if (i === n) {
+ ans.push(t.join(''));
+ return;
+ }
+ for (let j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] === cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push(cs[j]);
+ dfs(i + 1);
+ t.pop();
+ vis[j] = false;
+ }
+ };
+ dfs(0);
+ return ans;
+}
```
### **JavaScript**
@@ -51,35 +198,30 @@
* @return {string[]}
*/
var permutation = function (S) {
- let res = [];
- let arr = [...S];
- arr.sort();
- let prev = [];
- let record = new Array(S.length).fill(false);
- dfs(arr, 0, prev, record, res);
- return res;
-};
-function dfs(arr, depth, prev, record, res) {
- if (depth == arr.length) {
- res.push(prev.join(''));
- return;
- }
- for (let i = 0; i < arr.length; i++) {
- if (record[i]) {
- continue;
+ const cs = S.split('').sort();
+ const ans = [];
+ const n = cs.length;
+ const vis = Array(n).fill(false);
+ const t = [];
+ const dfs = i => {
+ if (i === n) {
+ ans.push(t.join(''));
+ return;
}
- // 剪枝
- if (i > 0 && arr[i] == arr[i - 1] && record[i - 1]) {
- continue;
+ for (let j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] === cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push(cs[j]);
+ dfs(i + 1);
+ t.pop();
+ vis[j] = false;
}
- prev.push(arr[i]);
- record[i] = true;
- dfs(arr, depth + 1, prev, record, res);
- // 回溯
- prev.pop();
- record[i] = false;
- }
-}
+ };
+ dfs(0);
+ return ans;
+};
```
### **...**
diff --git a/lcci/08.08.Permutation II/Solution.cpp b/lcci/08.08.Permutation II/Solution.cpp
new file mode 100644
index 0000000000000..89418c7dd37e3
--- /dev/null
+++ b/lcci/08.08.Permutation II/Solution.cpp
@@ -0,0 +1,29 @@
+class Solution {
+public:
+ vector permutation(string S) {
+ vector cs(S.begin(), S.end());
+ sort(cs.begin(), cs.end());
+ int n = cs.size();
+ vector ans;
+ vector vis(n);
+ string t;
+ function dfs = [&](int i) {
+ if (i == n) {
+ ans.push_back(t);
+ return;
+ }
+ for (int j = 0; j < n; ++j) {
+ if (vis[j] || (j && !vis[j - 1] && cs[j] == cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push_back(cs[j]);
+ dfs(i + 1);
+ t.pop_back();
+ vis[j] = false;
+ }
+ };
+ dfs(0);
+ return ans;
+ }
+};
\ No newline at end of file
diff --git a/lcci/08.08.Permutation II/Solution.go b/lcci/08.08.Permutation II/Solution.go
new file mode 100644
index 0000000000000..e53c94550e2fb
--- /dev/null
+++ b/lcci/08.08.Permutation II/Solution.go
@@ -0,0 +1,26 @@
+func permutation(S string) (ans []string) {
+ cs := []byte(S)
+ sort.Slice(cs, func(i, j int) bool { return cs[i] < cs[j] })
+ t := []byte{}
+ n := len(cs)
+ vis := make([]bool, n)
+ var dfs func(int)
+ dfs = func(i int) {
+ if i == n {
+ ans = append(ans, string(t))
+ return
+ }
+ for j := 0; j < n; j++ {
+ if vis[j] || (j > 0 && !vis[j-1] && cs[j] == cs[j-1]) {
+ continue
+ }
+ vis[j] = true
+ t = append(t, cs[j])
+ dfs(i + 1)
+ t = t[:len(t)-1]
+ vis[j] = false
+ }
+ }
+ dfs(0)
+ return
+}
\ No newline at end of file
diff --git a/lcci/08.08.Permutation II/Solution.java b/lcci/08.08.Permutation II/Solution.java
new file mode 100644
index 0000000000000..ca44d0d3d3023
--- /dev/null
+++ b/lcci/08.08.Permutation II/Solution.java
@@ -0,0 +1,33 @@
+class Solution {
+ private int n;
+ private char[] cs;
+ private List ans = new ArrayList<>();
+ private boolean[] vis;
+ private StringBuilder t = new StringBuilder();
+
+ public String[] permutation(String S) {
+ cs = S.toCharArray();
+ n = cs.length;
+ Arrays.sort(cs);
+ vis = new boolean[n];
+ dfs(0);
+ return ans.toArray(new String[0]);
+ }
+
+ private void dfs(int i) {
+ if (i == n) {
+ ans.add(t.toString());
+ return;
+ }
+ for (int j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] == cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.append(cs[j]);
+ dfs(i + 1);
+ t.deleteCharAt(t.length() - 1);
+ vis[j] = false;
+ }
+ }
+}
\ No newline at end of file
diff --git a/lcci/08.08.Permutation II/Solution.js b/lcci/08.08.Permutation II/Solution.js
index d4df4efb9e28d..44aed97be109c 100644
--- a/lcci/08.08.Permutation II/Solution.js
+++ b/lcci/08.08.Permutation II/Solution.js
@@ -3,33 +3,27 @@
* @return {string[]}
*/
var permutation = function (S) {
- let res = [];
- let arr = [...S];
- arr.sort();
- let prev = [];
- let record = new Array(S.length).fill(false);
- dfs(arr, 0, prev, record, res);
- return res;
-};
-
-function dfs(arr, depth, prev, record, res) {
- if (depth == arr.length) {
- res.push(prev.join(''));
- return;
- }
- for (let i = 0; i < arr.length; i++) {
- if (record[i]) {
- continue;
+ const cs = S.split('').sort();
+ const ans = [];
+ const n = cs.length;
+ const vis = Array(n).fill(false);
+ const t = [];
+ const dfs = i => {
+ if (i === n) {
+ ans.push(t.join(''));
+ return;
}
- // 剪枝
- if (i > 0 && arr[i] == arr[i - 1] && record[i - 1]) {
- continue;
+ for (let j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] === cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push(cs[j]);
+ dfs(i + 1);
+ t.pop();
+ vis[j] = false;
}
- prev.push(arr[i]);
- record[i] = true;
- dfs(arr, depth + 1, prev, record, res);
- // 回溯
- prev.pop();
- record[i] = false;
- }
-}
+ };
+ dfs(0);
+ return ans;
+};
diff --git a/lcci/08.08.Permutation II/Solution.py b/lcci/08.08.Permutation II/Solution.py
new file mode 100644
index 0000000000000..5731468cfdea6
--- /dev/null
+++ b/lcci/08.08.Permutation II/Solution.py
@@ -0,0 +1,21 @@
+class Solution:
+ def permutation(self, S: str) -> List[str]:
+ def dfs(i: int):
+ if i == n:
+ ans.append("".join(t))
+ return
+ for j in range(n):
+ if vis[j] or (j and cs[j] == cs[j - 1] and not vis[j - 1]):
+ continue
+ t[i] = cs[j]
+ vis[j] = True
+ dfs(i + 1)
+ vis[j] = False
+
+ cs = sorted(S)
+ n = len(cs)
+ ans = []
+ t = [None] * n
+ vis = [False] * n
+ dfs(0)
+ return ans
diff --git a/lcci/08.08.Permutation II/Solution.ts b/lcci/08.08.Permutation II/Solution.ts
new file mode 100644
index 0000000000000..44aed97be109c
--- /dev/null
+++ b/lcci/08.08.Permutation II/Solution.ts
@@ -0,0 +1,29 @@
+/**
+ * @param {string} S
+ * @return {string[]}
+ */
+var permutation = function (S) {
+ const cs = S.split('').sort();
+ const ans = [];
+ const n = cs.length;
+ const vis = Array(n).fill(false);
+ const t = [];
+ const dfs = i => {
+ if (i === n) {
+ ans.push(t.join(''));
+ return;
+ }
+ for (let j = 0; j < n; ++j) {
+ if (vis[j] || (j > 0 && !vis[j - 1] && cs[j] === cs[j - 1])) {
+ continue;
+ }
+ vis[j] = true;
+ t.push(cs[j]);
+ dfs(i + 1);
+ t.pop();
+ vis[j] = false;
+ }
+ };
+ dfs(0);
+ return ans;
+};