[Swift]LeetCode1223. 掷骰子模拟 | Dice Roll Simulation

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A die simulator generates a random number from 1 to 6 for each roll. You introduced a constraint to the generator such that it cannot roll the number i more than rollMax[i] (1-indexed) consecutive times. 

Given an array of integers rollMax and an integer n, return the number of distinct sequences that can be obtained with exact n rolls.

Two sequences are considered different if at least one element differs from each other. Since the answer may be too large, return it modulo 10^9 + 7.

Example 1:

Input: n = 2, rollMax = [1,1,2,2,2,3]
Output: 34
Explanation: There will be 2 rolls of die, if there are no constraints on the die, there are 6 * 6 = 36 possible combinations. In this case, looking at rollMax array, the numbers 1 and 2 appear at most once consecutively, therefore sequences (1,1) and (2,2) cannot occur, so the final answer is 36-2 = 34.
Example 2:

Input: n = 2, rollMax = [1,1,1,1,1,1]
Output: 30
Example 3:

Input: n = 3, rollMax = [1,1,1,2,2,3]
Output: 181

Constraints:

1 <= n <= 5000
rollMax.length == 6
1 <= rollMax[i] <= 15

---

有一个骰子模拟器会每次投掷的时候生成一个 1 到 6 的随机数。

不过我们在使用它时有个约束，就是使得投掷骰子时，连续 掷出数字 i 的次数不能超过 rollMax[i]（i 从 1 开始编号）。

现在，给你一个整数数组 rollMax 和一个整数 n，请你来计算掷 n 次骰子可得到的不同点数序列的数量。

假如两个序列中至少存在一个元素不同，就认为这两个序列是不同的。由于答案可能很大，所以请返回 模 10^9 + 7 之后的结果。 

示例 1：

输入：n = 2, rollMax = [1,1,2,2,2,3]
输出：34
解释：我们掷 2 次骰子，如果没有约束的话，共有 6 * 6 = 36 种可能的组合。但是根据 rollMax 数组，数字 1 和 2 最多连续出现一次，所以不会出现序列 (1,1) 和 (2,2)。因此，最终答案是 36-2 = 34。
示例 2：

输入：n = 2, rollMax = [1,1,1,1,1,1]
输出：30
示例 3：

输入：n = 3, rollMax = [1,1,1,2,2,3]
输出：181

提示：

1 <= n <= 5000
rollMax.length == 6
1 <= rollMax[i] <= 15

---

Runtime: 20 ms

Memory Usage: 21.6 MB

class Solution {
    func dieSimulator(_ n: Int, _ rollMax: [Int]) -> Int {
        let divisor:Int = 1000000007
        var dp:[[Int]] = [[Int]](repeating:[Int](repeating:0,count:7),count:n)
        for i in 0..<6
        {
            dp[0][i] = 1
        }
        dp[0][6] = 6
        for i in 1..<n
        {
            var sum:Int = 0
            for j in 0..<6
            {
                dp[i][j] = dp[i - 1][6]
                if i - rollMax[j] < 0
                {
                    sum = (sum + dp[i][j]) % divisor
                }
                else
                {
                    if i - rollMax[j] - 1 >= 0
                    {
                        dp[i][j] = (dp[i][j] - (dp[i - rollMax[j] - 1][6] - dp[i - rollMax[j] - 1][j])) % divisor + divisor
                    }
                    else
                    {
                        dp[i][j] = (dp[i][j] - 1) % divisor
                    }
                    sum = (sum + dp[i][j]) % divisor
                }
            }
            dp[i][6] = sum
        }
        return dp[n - 1][6]
    }
}

---

340ms

class Solution {
    func dieSimulator(_ n: Int, _ rollMax: [Int]) -> Int {
                
        let MOD = 1000_000_007
        let SIDES = 6
        let MAX_ROLLS = 15
        let STATES = SIDES * MAX_ROLLS

        var dp = [Int](repeating: 0, count: STATES)

        for side in 0..<6 {
            dp[side] = 1
        }

        for i in 0..<n-1 {
            var next_dp = [Int](repeating: 0, count: STATES)
            for state in 0..<STATES {
                let rolls = state / SIDES + 1
                let side = state % SIDES
                for die in 0..<6 {
                    let new_rolls = side == die ? rolls + 1 : 1
                    if new_rolls > rollMax[die] {
                        continue
                    }
                    next_dp[(new_rolls - 1) * SIDES + die] += dp[state]
                }
            }
            for s in 0..<STATES {
                next_dp[s] %= MOD
            }
            dp = next_dp
        }
        return dp.reduce(0, +)%MOD
    }
}

---

796ms

class Solution {
    func dieSimulator(_ n1: Int, _ rollMax: [Int]) -> Int {
        let MOD = 1000_000_007

        var memo = [[[Int]]](repeating: [[Int]](repeating: [Int](repeating: 0, count: 6), count: 16), count: 5001)

        func dfs(_ n: Int, _ k: Int, _ idx: Int) -> Int {
            if n == 0 {
                return 1
            }

            if memo[n][k][idx] != 0 {
                return memo[n][k][idx]
            }

            var v = 0
            for i in 0..<6 {
                if i != idx {
                    v += dfs(n-1, 1, i)%MOD
                } else {
                    if k < rollMax[i] {
                        v += dfs(n-1, k+1, i)%MOD
                    }
                }
            }
            memo[n][k][idx] = v%MOD
            return v
        }

        var ans = 0
        for i in 0..<6 {
            ans += dfs(n1-1, 1, i)%MOD
        }
        return ans%MOD
    }
}