feat: add solutions to lc problem: No.1155

solution/1100-1199/1155.Number of Dice Rolls With Target Sum/README.md

@@ -62,10 +62,12 @@ $$
 
 其中 $h$ 表示第 $i$ 个骰子的点数。
 
-最终的答案即为 $f[n][target]$。
+初始时 $f[0][0] = 1$，最终的答案即为 $f[n][target]$。
 
 时间复杂度 $O(n \times k \times target)$，空间复杂度 $O(n \times target)$。
 
+我们注意到，状态 $f[i][j]$ 只和 $f[i-1][]$ 有关，因此我们可以使用滚动数组的方式，将空间复杂度优化到 $O(target)$。
+
 <!-- tabs:start -->
 
 ### **Python3**
@@ -85,6 +87,20 @@ class Solution:
         return f[n][target]
 ```
 
+```python
+class Solution:
+    def numRollsToTarget(self, n: int, k: int, target: int) -> int:
+        f = [1] + [0] * target
+        mod = 10**9 + 7
+        for i in range(1, n + 1):
+            g = [0] * (target + 1)
+            for j in range(1, min(i * k, target) + 1):
+                for h in range(1, min(j, k) + 1):
+                    g[j] = (g[j] + f[j - h]) % mod
+            f = g
+        return f[target]
+```
+
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
@@ -107,6 +123,26 @@ class Solution {
 }
 ```
 
+```java
+class Solution {
+    public int numRollsToTarget(int n, int k, int target) {
+        final int mod = (int) 1e9 + 7;
+        int[] f = new int[target + 1];
+        f[0] = 1;
+        for (int i = 1; i <= n; ++i) {
+            int[] g = new int[target + 1];
+            for (int j = 1; j <= Math.min(target, i * k); ++j) {
+                for (int h = 1; h <= Math.min(j, k); ++h) {
+                    g[j] = (g[j] + f[j - h]) % mod;
+                }
+            }
+            f = g;
+        }
+        return f[target];
+    }
+}
+```
+
 ### **C++**
 
 ```cpp
@@ -129,6 +165,27 @@ public:
 };
 ```
 
+```cpp
+class Solution {
+public:
+    int numRollsToTarget(int n, int k, int target) {
+        const int mod = 1e9 + 7;
+        vector<int> f(target + 1);
+        f[0] = 1;
+        for (int i = 1; i <= n; ++i) {
+            vector<int> g(target + 1);
+            for (int j = 1; j <= min(target, i * k); ++j) {
+                for (int h = 1; h <= min(j, k); ++h) {
+                    g[j] = (g[j] + f[j - h]) % mod;
+                }
+            }
+            f = move(g);
+        }
+        return f[target];
+    }
+};
+```
+
 ### **Go**
 
 ```go
@@ -157,13 +214,36 @@ func min(a, b int) int {
 }
 ```
 
+```go
+func numRollsToTarget(n int, k int, target int) int {
+	const mod int = 1e9 + 7
+	f := make([]int, target+1)
+	f[0] = 1
+	for i := 1; i <= n; i++ {
+		g := make([]int, target+1)
+		for j := 1; j <= min(target, i*k); j++ {
+			for h := 1; h <= min(j, k); h++ {
+				g[j] = (g[j] + f[j-h]) % mod
+			}
+		}
+		f = g
+	}
+	return f[target]
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+```
+
 ### **TypeScript**
 
 ```ts
 function numRollsToTarget(n: number, k: number, target: number): number {
-    const f = Array(n + 1)
-        .fill(0)
-        .map(() => Array(target + 1).fill(0));
+    const f = Array.from({ length: n + 1 }, () => Array(target + 1).fill(0));
     f[0][0] = 1;
     const mod = 1e9 + 7;
     for (let i = 1; i <= n; ++i) {
@@ -177,6 +257,74 @@ function numRollsToTarget(n: number, k: number, target: number): number {
 }
 ```
 
+```ts
+function numRollsToTarget(n: number, k: number, target: number): number {
+    const f = Array(target + 1).fill(0);
+    f[0] = 1;
+    const mod = 1e9 + 7;
+    for (let i = 1; i <= n; ++i) {
+        const g = Array(target + 1).fill(0);
+        for (let j = 1; j <= Math.min(i * k, target); ++j) {
+            for (let h = 1; h <= Math.min(j, k); ++h) {
+                g[j] = (g[j] + f[j - h]) % mod;
+            }
+        }
+        f.splice(0, target + 1, ...g);
+    }
+    return f[target];
+}
+```
+
+### **Rust**
+
+```rust
+impl Solution {
+    pub fn num_rolls_to_target(n: i32, k: i32, target: i32) -> i32 {
+        let _mod = 1_000_000_007;
+        let n = n as usize;
+        let k = k as usize;
+        let target = target as usize;
+        let mut f = vec![vec![0; target + 1]; n + 1];
+        f[0][0] = 1;
+
+        for i in 1..=n {
+            for j in 1..=target.min(i * k) {
+                for h in 1..=j.min(k) {
+                    f[i][j] = (f[i][j] + f[i - 1][j - h]) % _mod;
+                }
+            }
+        }
+
+        f[n][target]
+    }
+}
+```
+
+```rust
+impl Solution {
+    pub fn num_rolls_to_target(n: i32, k: i32, target: i32) -> i32 {
+        let _mod = 1_000_000_007;
+        let n = n as usize;
+        let k = k as usize;
+        let target = target as usize;
+        let mut f = vec![0; target + 1];
+        f[0] = 1;
+
+        for i in 1..=n {
+            let mut g = vec![0; target + 1];
+            for j in 1..=target {
+                for h in 1..=j.min(k) {
+                    g[j] = (g[j] + f[j - h]) % _mod;
+                }
+            }
+            f = g;
+        }
+
+        f[target]
+    }
+}
+```
+
 ### **...**
 
 ```