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feat: add solutions to lc problem: No.0052
No.0052.N-Queens II
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‎solution/0000-0099/0052.N-Queens II/README.md

Lines changed: 124 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -43,22 +43,145 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：回溯**
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我们设计一个函数 $dfs(i)$，表示从第 $i$ 行开始搜索，搜索到的结果累加到答案中。
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在第 $i$ 行，我们枚举第 $i$ 行的每一列，如果当前列不与前面已经放置的皇后发生冲突，那么我们就可以放置一个皇后，然后继续搜索下一行，即调用 $dfs(i + 1)$。
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如果发生冲突，那么我们就跳过当前列，继续枚举下一列。
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判断是否发生冲突，我们需要用三个数组分别记录每一列、每一条正对角线、每一条反对角线是否已经放置了皇后。
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具体地，我们用 $cols$ 数组记录每一列是否已经放置了皇后，用 $dg$ 数组记录每一条正对角线是否已经放置了皇后，用 $udg$ 数组记录每一条反对角线是否已经放置了皇后。
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时间复杂度 $O(n!)$，空间复杂度 $O(n)$。其中 $n$ 是皇后的数量。
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
53-
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class Solution:
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def totalNQueens(self, n: int) -> int:
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def dfs(i):
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if i == n:
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nonlocal ans
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ans += 1
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return
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for j in range(n):
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a, b = i + j, i - j + n
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if cols[j] or dg[a] or udg[b]:
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continue
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cols[j] = dg[a] = udg[b] = True
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dfs(i + 1)
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cols[j] = dg[a] = udg[b] = False
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cols = [False] * 10
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dg = [False] * 20
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udg = [False] * 20
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ans = 0
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dfs(0)
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return ans
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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private int n;
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private int ans;
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private boolean[] cols = new boolean[10];
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private boolean[] dg = new boolean[20];
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private boolean[] udg = new boolean[20];
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public int totalNQueens(int n) {
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this.n = n;
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dfs(0);
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return ans;
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}
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private void dfs(int i) {
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if (i == n) {
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++ans;
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return;
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}
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for (int j = 0; j < n; ++j) {
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int a = i + j, b = i - j + n;
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if (cols[j] || dg[a] || udg[b]) {
116+
continue;
117+
}
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cols[j] = true;
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dg[a] = true;
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udg[b] = true;
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dfs(i + 1);
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cols[j] = false;
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dg[a] = false;
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udg[b] = false;
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}
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int totalNQueens(int n) {
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bitset<10> cols;
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bitset<20> dg;
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bitset<20> udg;
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int ans = 0;
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function<void(int)> dfs = [&](int i) {
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if (i == n) {
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++ans;
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return;
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}
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for (int j = 0; j < n; ++j) {
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int a = i + j, b = i - j + n;
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if (cols[j] || dg[a] || udg[b]) continue;
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cols[j] = dg[a] = udg[b] = 1;
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dfs(i + 1);
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cols[j] = dg[a] = udg[b] = 0;
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}
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};
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dfs(0);
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return ans;
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}
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};
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```
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### **Go**
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```go
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func totalNQueens(n int) (ans int) {
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cols := [10]bool{}
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dg := [20]bool{}
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udg := [20]bool{}
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var dfs func(int)
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dfs = func(i int) {
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if i == n {
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ans++
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return
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}
172+
for j := 0; j < n; j++ {
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a, b := i+j, i-j+n
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if cols[j] || dg[a] || udg[b] {
175+
continue
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}
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cols[j], dg[a], udg[b] = true, true, true
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dfs(i + 1)
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cols[j], dg[a], udg[b] = false, false, false
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}
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}
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dfs(0)
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return
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}
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```
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### **...**

‎solution/0000-0099/0052.N-Queens II/README_EN.md

Lines changed: 110 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -38,13 +38,122 @@
3838
### **Python3**
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```python
41-
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class Solution:
42+
def totalNQueens(self, n: int) -> int:
43+
def dfs(i):
44+
if i == n:
45+
nonlocal ans
46+
ans += 1
47+
return
48+
for j in range(n):
49+
a, b = i + j, i - j + n
50+
if cols[j] or dg[a] or udg[b]:
51+
continue
52+
cols[j] = dg[a] = udg[b] = True
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dfs(i + 1)
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cols[j] = dg[a] = udg[b] = False
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cols = [False] * 10
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dg = [False] * 20
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udg = [False] * 20
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ans = 0
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dfs(0)
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return ans
4262
```
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### **Java**
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```java
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class Solution {
68+
private int n;
69+
private int ans;
70+
private boolean[] cols = new boolean[10];
71+
private boolean[] dg = new boolean[20];
72+
private boolean[] udg = new boolean[20];
73+
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public int totalNQueens(int n) {
75+
this.n = n;
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dfs(0);
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return ans;
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}
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private void dfs(int i) {
81+
if (i == n) {
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++ans;
83+
return;
84+
}
85+
for (int j = 0; j < n; ++j) {
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int a = i + j, b = i - j + n;
87+
if (cols[j] || dg[a] || udg[b]) {
88+
continue;
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}
90+
cols[j] = true;
91+
dg[a] = true;
92+
udg[b] = true;
93+
dfs(i + 1);
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cols[j] = false;
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dg[a] = false;
96+
udg[b] = false;
97+
}
98+
}
99+
}
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```
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### **C++**
103+
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```cpp
105+
class Solution {
106+
public:
107+
int totalNQueens(int n) {
108+
bitset<10> cols;
109+
bitset<20> dg;
110+
bitset<20> udg;
111+
int ans = 0;
112+
function<void(int)> dfs = [&](int i) {
113+
if (i == n) {
114+
++ans;
115+
return;
116+
}
117+
for (int j = 0; j < n; ++j) {
118+
int a = i + j, b = i - j + n;
119+
if (cols[j] || dg[a] || udg[b]) continue;
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cols[j] = dg[a] = udg[b] = 1;
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dfs(i + 1);
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cols[j] = dg[a] = udg[b] = 0;
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}
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};
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dfs(0);
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return ans;
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}
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};
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```
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### **Go**
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```go
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func totalNQueens(n int) (ans int) {
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cols := [10]bool{}
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dg := [20]bool{}
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udg := [20]bool{}
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var dfs func(int)
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dfs = func(i int) {
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if i == n {
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ans++
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return
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}
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for j := 0; j < n; j++ {
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a, b := i+j, i-j+n
146+
if cols[j] || dg[a] || udg[b] {
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continue
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}
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cols[j], dg[a], udg[b] = true, true, true
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dfs(i + 1)
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cols[j], dg[a], udg[b] = false, false, false
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}
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}
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dfs(0)
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return
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}
48157
```
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### **...**

‎solution/0000-0099/0052.N-Queens II/Solution.cpp

Lines changed: 24 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,24 @@
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class Solution {
2+
public:
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int totalNQueens(int n) {
4+
bitset<10> cols;
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bitset<20> dg;
6+
bitset<20> udg;
7+
int ans = 0;
8+
function<void(int)> dfs = [&](int i) {
9+
if (i == n) {
10+
++ans;
11+
return;
12+
}
13+
for (int j = 0; j < n; ++j) {
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int a = i + j, b = i - j + n;
15+
if (cols[j] || dg[a] || udg[b]) continue;
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cols[j] = dg[a] = udg[b] = 1;
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dfs(i + 1);
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cols[j] = dg[a] = udg[b] = 0;
19+
}
20+
};
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dfs(0);
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return ans;
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}
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};

‎solution/0000-0099/0052.N-Queens II/Solution.go

Lines changed: 23 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,23 @@
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func totalNQueens(n int) (ans int) {
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cols := [10]bool{}
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dg := [20]bool{}
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udg := [20]bool{}
5+
var dfs func(int)
6+
dfs = func(i int) {
7+
if i == n {
8+
ans++
9+
return
10+
}
11+
for j := 0; j < n; j++ {
12+
a, b := i+j, i-j+n
13+
if cols[j] || dg[a] || udg[b] {
14+
continue
15+
}
16+
cols[j], dg[a], udg[b] = true, true, true
17+
dfs(i + 1)
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cols[j], dg[a], udg[b] = false, false, false
19+
}
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}
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dfs(0)
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return
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}

‎solution/0000-0099/0052.N-Queens II/Solution.java

Lines changed: 22 additions & 19 deletions
Original file line numberDiff line numberDiff line change
@@ -1,30 +1,33 @@
11
class Solution {
2-
3-
int count = 0;
2+
private int n;
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private int ans;
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private boolean[] cols = new boolean[10];
5+
private boolean[] dg = new boolean[20];
6+
private boolean[] udg = new boolean[20];
47

58
public int totalNQueens(int n) {
6-
int[] c = new int[n];
7-
search(0, n, c);
8-
return count;
9+
this.n = n;
10+
dfs(0);
11+
return ans;
912
}
1013

11-
public void search(int cur, int n, int[] c) {
12-
if (cur == n) {
13-
count++;
14+
private void dfs(int i) {
15+
if (i == n) {
16+
++ans;
1417
return;
1518
}
16-
17-
for (int i = 0; i < n; i++) {
18-
boolean flag = true;
19-
c[cur] = i;
20-
for (int j = 0; j < cur; j++) {
21-
if ((c[cur] == c[j]) || ((c[cur] - cur) == (c[j] - j))
22-
|| ((c[cur] + cur) == (c[j] + j))) {
23-
flag = false;
24-
break;
25-
}
19+
for (int j = 0; j < n; ++j) {
20+
int a = i + j, b = i - j + n;
21+
if (cols[j] || dg[a] || udg[b]) {
22+
continue;
2623
}
27-
if (flag) search(cur + 1, n, c);
24+
cols[j] = true;
25+
dg[a] = true;
26+
udg[b] = true;
27+
dfs(i + 1);
28+
cols[j] = false;
29+
dg[a] = false;
30+
udg[b] = false;
2831
}
2932
}
3033
}

‎solution/0000-0099/0052.N-Queens II/Solution.py

Lines changed: 21 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,21 @@
1+
class Solution:
2+
def totalNQueens(self, n: int) -> int:
3+
def dfs(i):
4+
if i == n:
5+
nonlocal ans
6+
ans += 1
7+
return
8+
for j in range(n):
9+
a, b = i + j, i - j + n
10+
if cols[j] or dg[a] or udg[b]:
11+
continue
12+
cols[j] = dg[a] = udg[b] = True
13+
dfs(i + 1)
14+
cols[j] = dg[a] = udg[b] = False
15+
16+
cols = [False] * 10
17+
dg = [False] * 20
18+
udg = [False] * 20
19+
ans = 0
20+
dfs(0)
21+
return ans

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