## 1155. Number of Dice Rolls With Target Sum

You have `d` dice, and each die has `f` faces numbered `1, 2, ..., f`.

Return the number of possible ways (out of `fd` total ways) modulo `10^9 + 7` to roll the dice so the sum of the face up numbers equals `target`.

Example 1:

```Input: d = 1, f = 6, target = 3
Output: 1
Explanation:
You throw one die with 6 faces.  There is only one way to get a sum of 3.
```

Example 2:

```Input: d = 2, f = 6, target = 7
Output: 6
Explanation:
You throw two dice, each with 6 faces.  There are 6 ways to get a sum of 7:
1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
```

Example 3:

```Input: d = 2, f = 5, target = 10
Output: 1
Explanation:
You throw two dice, each with 5 faces.  There is only one way to get a sum of 10: 5+5.
```

Example 4:

```Input: d = 1, f = 2, target = 3
Output: 0
Explanation:
You throw one die with 2 faces.  There is no way to get a sum of 3.
```

Example 5:

```Input: d = 30, f = 30, target = 500
Output: 222616187
Explanation:
The answer must be returned modulo 10^9 + 7.
```

Constraints:

• `1 <= d, f <= 30`
• `1 <= target <= 1000`

## Rust Solution

``````struct Solution;

use std::collections::HashMap;

impl Solution {
fn num_rolls_to_target(d: i32, f: i32, target: i32) -> i32 {
let mut memo: HashMap<(i32, i32), i32> = HashMap::new();
Self::dp(d, f, target, &mut memo)
}

fn dp(d: i32, f: i32, target: i32, memo: &mut HashMap<(i32, i32), i32>) -> i32 {
if let Some(&val) = memo.get(&(d, target)) {
return val;
}
let res = if d == 0 {
if target == 0 {
1
} else {
0
}
} else {
let mut sum = 0;
for i in 1..=f {
sum += Self::dp(d - 1, f, target - i, memo);
sum %= 1_000_000_007;
}
sum
};
memo.insert((d, target), res);
res
}
}

#[test]
fn test() {
let d = 1;
let f = 6;
let target = 3;
let res = 1;
assert_eq!(Solution::num_rolls_to_target(d, f, target), res);
let d = 2;
let f = 6;
let target = 7;
let res = 6;
assert_eq!(Solution::num_rolls_to_target(d, f, target), res);
let d = 2;
let f = 5;
let target = 10;
let res = 1;
assert_eq!(Solution::num_rolls_to_target(d, f, target), res);
let d = 1;
let f = 2;
let target = 3;
let res = 0;
assert_eq!(Solution::num_rolls_to_target(d, f, target), res);
let d = 30;
let f = 30;
let target = 500;
let res = 222_616_187;
assert_eq!(Solution::num_rolls_to_target(d, f, target), res);
}
``````

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