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feat: add solutions to lc problem: No.1155
No.1155.Number of Dice Rolls With Target Sum
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‎solution/1100-1199/1155.Number of Dice Rolls With Target Sum/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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我们定义 $f[i][j]$ 表示使用 $i$ 个骰子，和为 $j$ 的方案数。那么我们可以得到状态转移方程：
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$$
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f[i][j] = \sum_{h=1}^{\min(j, k)} f[i-1][j-h]
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$$
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其中 $h$ 表示第 $i$ 个骰子的点数。
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最终的答案即为 $f[n][target]$。
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时间复杂度 $O(n \times k \times target)$，空间复杂度 $O(n \times target)$。
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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 numRollsToTarget(self, n: int, k: int, target: int) -> int:
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f = [[0] * (target + 1) for _ in range(n + 1)]
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f[0][0] = 1
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mod = 10**9 + 7
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for i in range(1, n + 1):
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for j in range(1, min(i * k, target) + 1):
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for h in range(1, min(j, k) + 1):
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod
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return f[n][target]
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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 static final int MOD = (int) 1e9 + 7;
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public int numRollsToTarget(int n, int k, int target) {
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int[][] f = new int[n + 1][target + 1];
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f[0][0] = 1;
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for (int i = 1; i <= n; ++i) {
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for (int j = 1; j <= Math.min(target, i * k); ++j) {
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for (int h = 1; h <= Math.min(j, k); ++h) {
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % MOD;
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}
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}
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}
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return f[n][target];
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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 numRollsToTarget(int n, int k, int target) {
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const int mod = 1e9 + 7;
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int f[n + 1][target + 1];
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memset(f, 0, sizeof f);
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f[0][0] = 1;
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for (int i = 1; i <= n; ++i) {
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for (int j = 1; j <= min(target, i * k); ++j) {
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for (int h = 1; h <= min(j, k); ++h) {
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod;
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}
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}
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}
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return f[n][target];
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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 numRollsToTarget(n int, k int, target int) int {
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const mod int = 1e9 + 7
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f := make([][]int, n+1)
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for i := range f {
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f[i] = make([]int, target+1)
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}
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f[0][0] = 1
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for i := 1; i <= n; i++ {
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for j := 1; j <= min(target, i*k); j++ {
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for h := 1; h <= min(j, k); h++ {
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f[i][j] = (f[i][j] + f[i-1][j-h]) % mod
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}
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}
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}
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return f[n][target]
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **...**

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

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@@ -50,13 +50,87 @@ There are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
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### **Python3**
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```python
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class Solution:
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def numRollsToTarget(self, n: int, k: int, target: int) -> int:
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f = [[0] * (target + 1) for _ in range(n + 1)]
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f[0][0] = 1
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mod = 10**9 + 7
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for i in range(1, n + 1):
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for j in range(1, min(i * k, target) + 1):
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for h in range(1, min(j, k) + 1):
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod
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return f[n][target]
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```
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### **Java**
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```java
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class Solution {
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private static final int MOD = (int) 1e9 + 7;
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public int numRollsToTarget(int n, int k, int target) {
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int[][] f = new int[n + 1][target + 1];
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f[0][0] = 1;
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for (int i = 1; i <= n; ++i) {
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for (int j = 1; j <= Math.min(target, i * k); ++j) {
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for (int h = 1; h <= Math.min(j, k); ++h) {
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % MOD;
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}
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}
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}
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return f[n][target];
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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 numRollsToTarget(int n, int k, int target) {
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const int mod = 1e9 + 7;
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int f[n + 1][target + 1];
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memset(f, 0, sizeof f);
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f[0][0] = 1;
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for (int i = 1; i <= n; ++i) {
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for (int j = 1; j <= min(target, i * k); ++j) {
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for (int h = 1; h <= min(j, k); ++h) {
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod;
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}
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}
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}
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return f[n][target];
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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 numRollsToTarget(n int, k int, target int) int {
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const mod int = 1e9 + 7
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f := make([][]int, n+1)
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for i := range f {
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f[i] = make([]int, target+1)
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}
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f[0][0] = 1
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for i := 1; i <= n; i++ {
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for j := 1; j <= min(target, i*k); j++ {
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for h := 1; h <= min(j, k); h++ {
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f[i][j] = (f[i][j] + f[i-1][j-h]) % mod
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}
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}
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}
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return f[n][target]
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/1100-1199/1155.Number of Dice Rolls With Target Sum/Solution.cpp

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class Solution {
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public:
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int numRollsToTarget(int n, int k, int target) {
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const int mod = 1e9 + 7;
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int f[n + 1][target + 1];
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memset(f, 0, sizeof f);
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f[0][0] = 1;
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for (int i = 1; i <= n; ++i) {
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for (int j = 1; j <= min(target, i * k); ++j) {
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for (int h = 1; h <= min(j, k); ++h) {
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod;
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}
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}
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}
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return f[n][target];
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}
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};

‎solution/1100-1199/1155.Number of Dice Rolls With Target Sum/Solution.go

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func numRollsToTarget(n int, k int, target int) int {
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const mod int = 1e9 + 7
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f := make([][]int, n+1)
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for i := range f {
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f[i] = make([]int, target+1)
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}
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f[0][0] = 1
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for i := 1; i <= n; i++ {
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for j := 1; j <= min(target, i*k); j++ {
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for h := 1; h <= min(j, k); h++ {
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f[i][j] = (f[i][j] + f[i-1][j-h]) % mod
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}
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}
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}
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return f[n][target]
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}

‎solution/1100-1199/1155.Number of Dice Rolls With Target Sum/Solution.java

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class Solution {
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public int numRollsToTarget(int d, int f, int target) {
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int[][] dp = new int[d + 1][target + 1];
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dp[0][0] = 1;
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for (int i = 1; i <= d; ++i) {
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for (int j = 1; j <= target; ++j) {
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// j 大于当前所有骰子的最大和，不可能满足条件
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if (j > i * f) {
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break;
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}
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for (int k = 1; k <= f && k <= j; ++k) {
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dp[i][j] = (dp[i][j] + dp[i - 1][j - k]) % 1000000007;
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private static final int MOD = (int) 1e9 + 7;
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public int numRollsToTarget(int n, int k, int target) {
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int[][] f = new int[n + 1][target + 1];
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f[0][0] = 1;
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for (int i = 1; i <= n; ++i) {
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for (int j = 1; j <= Math.min(target, i * k); ++j) {
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for (int h = 1; h <= Math.min(j, k); ++h) {
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % MOD;
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}
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}
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}
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return dp[d][target];
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return f[n][target];
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}
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}
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}

‎solution/1100-1199/1155.Number of Dice Rolls With Target Sum/Solution.py

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class Solution:
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def numRollsToTarget(self, n: int, k: int, target: int) -> int:
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f = [[0] * (target + 1) for _ in range(n + 1)]
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f[0][0] = 1
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mod = 10**9 + 7
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for i in range(1, n + 1):
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for j in range(1, min(i * k, target) + 1):
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for h in range(1, min(j, k) + 1):
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f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod
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return f[n][target]

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