[Swift]LeetCode1155. 掷骰子的N种方法 | Number of Dice Rolls With Target Sum

★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
➤微信公众号：山青咏芝（shanqingyongzhi）
➤博客园地址：山青咏芝（www.zengqiang.org）
➤GitHub地址：https://github.com/strengthen/LeetCode
➤原文地址：https://www.cnblogs.com/strengthen/p/11333871.html 
➤如果链接不是山青咏芝的博客园地址，则可能是爬取作者的文章。
➤原文已修改更新！强烈建议点击原文地址阅读！支持作者！支持原创！
★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★

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

Example 2:

Input: d = 2, f = 6, target = 7
Output: 6

Example 3:

Input: d = 2, f = 5, target = 10
Output: 1

Example 4:

Input: d = 1, f = 2, target = 3
Output: 0

Example 5:

Input: d = 30, f = 30, target = 500
Output: 222616187 

Constraints:

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

---

这里有 d 个一样的骰子，每个骰子上都有 f 个面，分别标号为 1, 2, ..., f。

我们约定：掷骰子的得到总点数为各骰子面朝上的数字的总和。

如果需要掷出的总点数为 target，请你计算出有多少种不同的组合情况（所有的组合情况总共有 f^d种），模 10^9 + 7 后返回。

示例 1：

输入：d = 1, f = 6, target = 3
输出：1

示例 2：

输入：d = 2, f = 6, target = 7
输出：6

示例 3：

输入：d = 2, f = 5, target = 10
输出：1

示例 4：

输入：d = 1, f = 2, target = 3
输出：0

示例 5：

输入：d = 30, f = 30, target = 500
输出：222616187 

提示：

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

---

108ms

class Solution {
    
    var dp = [[Int]]()
    
    func numRollsToTarget(_ d: Int, _ f: Int, _ target: Int) -> Int {
        // var result = 0
        // dp = Array(repeating: Array(repeating: -1, count: target + 1), count: d + 1)
        // return rollsHelper(d, f, target)
        
        var newDP = Array(repeating: 0, count: target + 1)
        newDP[0] = 1
        for i in 0..<d {
            var newDP1 = Array(repeating: 0, count: target + 1)
            for j in 1...f {
                if j > target {
                    continue
                }
                for k in j...target {
                    newDP1[k] = (newDP1[k] + newDP[k - j]) % 1000000007
                }
            }
            newDP = newDP1
        }
        //print(newDP)
        return newDP[target]
    }
    
    func rollsHelper(_ d: Int, _ f: Int, _ target: Int) -> Int {
        
        if (d == 0 || target <= 0) { 
            return d == target ? 1 : 0
        }
        
        if dp[d][target] != -1 {
            return (dp[d][target] - 1)
        }
        
        var result = 0
        for i in 1...f {
            result = result + rollsHelper(d - 1, f, target - i) % 1000000007
        }
        
        dp[d][target] = (result + 1) 
        return result % 1000000007
    }
}

---

120ms

class Solution {
    func numRollsToTarget(_ d: Int, _ f: Int, _ target: Int) -> Int {     
        var dp = [[Int]](repeating: [Int](repeating: 0, count: max(target+1, f+1)), count: d)
        for i in 0..<f { dp[0][i+1] = 1 }
        for i in 1..<d {
            for j in 1..<target {               
                for k in 0..<f{ 
                    if dp[i-1][j] > 0 {
                        let cur = j + k + 1
                        if cur <= target {
                            dp[i][cur] = (dp[i][cur] + dp[i-1][j])%(1000_000_007)
                        }
                    } else {
                        break
                    }
                }
            }
        }
        return dp[d-1][target]
    }
}

---

140ms

class Solution {
    func numRollsToTarget(_ d: Int, _ f: Int, _ target: Int) -> Int {     
        var len = max(target+1, f+1)
        var dp = [[Int]](repeating: [Int](repeating: 0, count: len), count: d)
        for i in 0..<f { dp[0][i+1] = 1 }
        for i in 1..<d {
            for j in 1..<target {               
                for k in 0..<f{ 
                    if dp[i-1][j] > 0 {
                        let cur = j + k + 1
                        if cur <= target {
                            dp[i][cur] = (dp[i][cur] + dp[i-1][j])%(1000_000_007)
                        }
                    } else {
                        break
                    }
                }
            }
        }
        return dp[d-1][target]
    }
}

---

Runtime: 144 ms

Memory Usage: 21.1 MB

class Solution {
    func numRollsToTarget(_ d: Int, _ f: Int, _ target: Int) -> Int {
        var dp:[Int] = [Int](repeating:0,count:target + 1)
        dp[0] = 1
        for c in 0..<d
        {
            for i in stride(from:target,through:0,by:-1)
            {
                dp[i] = 0
                var x:Int = 1
                while(x <= f && x <= i)
                {
                    dp[i] = (dp[i] + dp[i - x]) % 1000000007
                    x += 1
                }
            }
        }
        return dp[target]
    }
}

---

168ms

class Solution {
    
    var dp = [[Int]]()
    
    func numRollsToTarget(_ d: Int, _ f: Int, _ target: Int) -> Int {
        var result = 0
        dp = Array(repeating: Array(repeating: -1, count: target + 1), count: d + 1)
        return rollsHelper(d, f, target)
    }
    
    func rollsHelper(_ d: Int, _ f: Int, _ target: Int) -> Int {
        
        if (d == 0 || target <= 0) { 
            return d == target ? 1 : 0
        }
        
        if dp[d][target] != -1 {
            return (dp[d][target] - 1)
        }
        
        var result = 0
        for i in 1...f {
            result = result + rollsHelper(d - 1, f, target - i) % 1000000007
        }
        
        dp[d][target] = (result + 1) 
        return result % 1000000007
    }
}

---

176ms

class Solution {
    func numRollsToTarget(_ d: Int, _ f: Int, _ target: Int) -> Int {
        var dp = [Int](repeating: 0, count: target + 1)
        dp[0] = 1
        for i in 1...d {
            var dp1 = [Int](repeating: 0, count: target + 1)
            for j in 1...f {
                for k in stride(from: max(i, j), through: min(target, i * f), by: 1) {
                    dp1[k] = (dp1[k] + dp[k-j]) % 1_000_000_007
                }
            }
            dp = dp1
        }
        return dp[target]
    }
}