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feat: add solutions to lc problem: No.0790
No.0790.Domino and Tromino Tiling
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‎solution/0700-0799/0790.Domino and Tromino Tiling/README.md

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<!-- 这里可写通用的实现逻辑 -->
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**方法一：动态规划**
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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
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class Solution:
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def numTilings(self, n: int) -> int:
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@cache
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def dfs(i, j):
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if i > n or j > n:
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return 0
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if i == n and j == n:
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return 1
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ans = 0
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if i == j:
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ans = dfs(i + 2, j + 2) + dfs(i + 1, j + 1) + dfs(i + 2, j + 1) + dfs(i + 1, j + 2)
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elif i > j:
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ans = dfs(i, j + 2) + dfs(i + 1, j + 2)
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else:
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ans = dfs(i + 2, j) + dfs(i + 2, j + 1)
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return ans % mod
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mod = 10**9 + 7
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return dfs(0, 0)
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```
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```python
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class Solution:
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def numTilings(self, n: int) -> int:
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f = [1, 0, 0, 0]
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mod = 10**9 + 7
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for i in range(1, n + 1):
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g = [0] * 4
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod
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g[1] = (f[2] + f[3]) % mod
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g[2] = (f[1] + f[3]) % mod
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g[3] = f[0]
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f = g
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return f[0]
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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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public int numTilings(int n) {
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long[] f = {1, 0, 0, 0};
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int mod = (int) 1e9 + 7;
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for (int i = 1; i <= n; ++i) {
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long[] g = new long[4];
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod;
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g[1] = (f[2] + f[3]) % mod;
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g[2] = (f[1] + f[3]) % mod;
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g[3] = f[0];
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f = g;
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}
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return (int) f[0];
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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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const int mod = 1e9 + 7;
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int numTilings(int n) {
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long f[4] = {1, 0, 0, 0};
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for (int i = 1; i <= n; ++i) {
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long g[4] = {0, 0, 0, 0};
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod;
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g[1] = (f[2] + f[3]) % mod;
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g[2] = (f[1] + f[3]) % mod;
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g[3] = f[0];
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memcpy(f, g, sizeof(g));
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}
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return f[0];
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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 numTilings(n int) int {
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f := [4]int{}
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f[0] = 1
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const mod int = 1e9 + 7
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for i := 1; i <= n; i++ {
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g := [4]int{}
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod
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g[1] = (f[2] + f[3]) % mod
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g[2] = (f[1] + f[3]) % mod
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g[3] = f[0]
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f = g
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}
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return f[0]
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}
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```
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### **...**

‎solution/0700-0799/0790.Domino and Tromino Tiling/README_EN.md

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### **Python3**
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```python
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class Solution:
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def numTilings(self, n: int) -> int:
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@cache
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def dfs(i, j):
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if i > n or j > n:
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return 0
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if i == n and j == n:
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return 1
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ans = 0
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if i == j:
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ans = dfs(i + 2, j + 2) + dfs(i + 1, j + 1) + dfs(i + 2, j + 1) + dfs(i + 1, j + 2)
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elif i > j:
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ans = dfs(i, j + 2) + dfs(i + 1, j + 2)
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else:
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ans = dfs(i + 2, j) + dfs(i + 2, j + 1)
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return ans % mod
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mod = 10**9 + 7
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return dfs(0, 0)
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```
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```python
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class Solution:
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def numTilings(self, n: int) -> int:
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f = [1, 0, 0, 0]
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mod = 10**9 + 7
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for i in range(1, n + 1):
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g = [0] * 4
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod
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g[1] = (f[2] + f[3]) % mod
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g[2] = (f[1] + f[3]) % mod
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g[3] = f[0]
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f = g
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return f[0]
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```
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### **Java**
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```java
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class Solution {
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public int numTilings(int n) {
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long[] f = {1, 0, 0, 0};
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int mod = (int) 1e9 + 7;
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for (int i = 1; i <= n; ++i) {
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long[] g = new long[4];
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod;
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g[1] = (f[2] + f[3]) % mod;
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g[2] = (f[1] + f[3]) % mod;
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g[3] = f[0];
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f = g;
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}
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return (int) f[0];
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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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const int mod = 1e9 + 7;
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int numTilings(int n) {
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long f[4] = {1, 0, 0, 0};
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for (int i = 1; i <= n; ++i) {
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long g[4] = {0, 0, 0, 0};
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod;
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g[1] = (f[2] + f[3]) % mod;
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g[2] = (f[1] + f[3]) % mod;
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g[3] = f[0];
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memcpy(f, g, sizeof(g));
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}
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return f[0];
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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 numTilings(n int) int {
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f := [4]int{}
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f[0] = 1
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const mod int = 1e9 + 7
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for i := 1; i <= n; i++ {
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g := [4]int{}
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod
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g[1] = (f[2] + f[3]) % mod
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g[2] = (f[1] + f[3]) % mod
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g[3] = f[0]
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f = g
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}
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return f[0]
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}
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```
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### **...**

‎solution/0700-0799/0790.Domino and Tromino Tiling/Solution.cpp

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class Solution {
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public:
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const int mod = 1e9 + 7;
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int numTilings(int n) {
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long f[4] = {1, 0, 0, 0};
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for (int i = 1; i <= n; ++i) {
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long g[4] = {0, 0, 0, 0};
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod;
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g[1] = (f[2] + f[3]) % mod;
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g[2] = (f[1] + f[3]) % mod;
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g[3] = f[0];
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memcpy(f, g, sizeof(g));
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}
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return f[0];
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}
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};

‎solution/0700-0799/0790.Domino and Tromino Tiling/Solution.go

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func numTilings(n int) int {
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f := [4]int{}
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f[0] = 1
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const mod int = 1e9 + 7
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for i := 1; i <= n; i++ {
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g := [4]int{}
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod
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g[1] = (f[2] + f[3]) % mod
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g[2] = (f[1] + f[3]) % mod
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g[3] = f[0]
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f = g
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}
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return f[0]
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}

‎solution/0700-0799/0790.Domino and Tromino Tiling/Solution.java

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class Solution {
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public int numTilings(int n) {
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long[] f = {1, 0, 0, 0};
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int mod = (int) 1e9 + 7;
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for (int i = 1; i <= n; ++i) {
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long[] g = new long[4];
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g[0] = (f[0] + f[1] + f[2] + f[3]) % mod;
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g[1] = (f[2] + f[3]) % mod;
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g[2] = (f[1] + f[3]) % mod;
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g[3] = f[0];
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f = g;
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}
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return (int) f[0];
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}
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}

‎solution/0700-0799/0790.Domino and Tromino Tiling/Solution.py

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class Solution:
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def numTilings(self, n: int) -> int:
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@cache
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def dfs(i, j):
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if i > n or j > n:
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return 0
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if i == n and j == n:
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return 1
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ans = 0
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if i == j:
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ans = dfs(i + 2, j + 2) + dfs(i + 1, j + 1) + dfs(i + 2, j + 1) + dfs(i + 1, j + 2)
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elif i > j:
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ans = dfs(i, j + 2) + dfs(i + 1, j + 2)
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else:
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ans = dfs(i + 2, j) + dfs(i + 2, j + 1)
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return ans % mod
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mod = 10**9 + 7
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return dfs(0, 0)

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