[Swift]LeetCode935. 骑士拨号器 | Knight Dialer
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➤微信公众号：山青咏芝（shanqingyongzhi）
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A chess knight can move as indicated in the chess diagram below:
. 
This time, we place our chess knight on any numbered key of a phone pad (indicated above), and the knight makes N-1 hops. Each hop must be from one key to another numbered key.
Each time it lands on a key (including the initial placement of the knight), it presses the number of that key, pressing N digits total.
How many distinct numbers can you dial in this manner?
Since the answer may be large, output the answer modulo 10^9 + 7.
Example 1:
Input: 1
Output: 10
Example 2:
Input: 2
Output: 20
Example 3:
Input: 3
Output: 46
Note:
1 <= N <= 5000
国际象棋中的骑士可以按下图所示进行移动：
. 
这一次，我们将 “骑士” 放在电话拨号盘的任意数字键（如上图所示）上，接下来，骑士将会跳 N-1 步。每一步必须是从一个数字键跳到另一个数字键。
每当它落在一个键上（包括骑士的初始位置），都会拨出键所对应的数字，总共按下 N 位数字。
你能用这种方式拨出多少个不同的号码？
因为答案可能很大，所以输出答案模 10^9 + 7。
示例 1：
输入：1 输出：10
示例 2：
输入：2 输出：20
示例 3：
输入：3 输出：46
提示：
1 <= N <= 5000
284ms
1 class Solution { 2 func knightDialer(_ N: Int) -> Int { 3 var N = N 4 var mod:Int64 = 1000000007 5 N -= 1 6 var dp:[Int64] = [Int64](repeating: 1,count: 10) 7 for i in 0..<N 8 { 9 var ndp:[Int64] = [Int64](repeating: 0,count: 10) 10 ndp[0] = dp[4] + dp[6] 11 ndp[1] = dp[6] + dp[8] 12 ndp[2] = dp[7] + dp[9] 13 ndp[3] = dp[4] + dp[8] 14 ndp[4] = dp[3] + dp[9] + dp[0] 15 ndp[6] = dp[1] + dp[7] + dp[0] 16 ndp[8] = dp[1] + dp[3] 17 ndp[7] = dp[2] + dp[6] 18 ndp[9] = dp[2] + dp[4] 19 for j in 0..<10 20 { 21 ndp[j] %= mod 22 } 23 dp = ndp 24 } 25 var ret:Int64 = 0 26 for i in 0..<10 27 { 28 ret += dp[i] 29 } 30 return Int(ret % mod) 31 } 32 }
1296ms
1 class Solution { 2 func knightDialer(_ N: Int) -> Int { 3 let navigationMap: [Int: [Int]] = [0: [4, 6], 4 1: [6,8], 5 2: [7,9], 6 3: [4,8], 7 4: [3,9,0], 8 5: [], 9 6: [1,7,0], 10 7: [2,6], 11 8: [1,3], 12 9: [2,4]] 13 14 var currentPathsStats = [1,1,1,1,1,1,1,1,1,1] 15 for i in 1..<N { 16 var newStats = [Int](repeating: 0, count: 10) 17 for currentDigit in 0...9 { 18 let numberOfPathsToCurrentDigit = currentPathsStats[currentDigit] 19 for nextDigit in navigationMap[currentDigit]! { 20 newStats[nextDigit] = newStats[nextDigit] + numberOfPathsToCurrentDigit 21 if newStats[nextDigit] >= 1000000007 { 22 23 newStats[nextDigit] = newStats[nextDigit] - 1000000007 24 } 25 } 26 } 27 currentPathsStats = newStats 28 } 29 30 var result = 0 31 for i in 0...9 { 32 result = result + currentPathsStats[i] 33 if result >= 1000000007 { 34 35 result = result - 1000000007 36 } 37 } 38 39 // if N == 1 { 40 // result = result + 1 41 // } 42 43 return result 44 } 45 }
1532ms
1 class Solution { 2 func knightDialer(_ N: Int) -> Int { 3 var d = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]] 4 let mod = 1000000007 5 var dp = [[Int]](repeating: [Int](repeating: 0, count: 10), count: N) 6 dp[0] = [Int](repeating: 1, count: 10) 7 guard N > 1 else { 8 return dp[0].reduce(0, +) 9 } 10 11 for i in 1 ..< N { 12 for j in 0 ... 9 { 13 let prev = d[j] 14 for k in prev { 15 dp[i][j] = (dp[i][j] + dp[i-1][k]) % mod 16 } 17 } 18 } 19 var sum = 0 20 for i in 0 ... 9 { 21 sum = (sum + dp[N-1][i]) % mod 22 } 23 return sum 24 } 25 }
2196ms
1 class Solution { 2 let modulo:Int = 1000000007 3 let availableNumbers: [Int:Set<Int>] = [ 4 0 : [4, 6], 5 1 : [6, 8], 6 2 : [7, 9], 7 3 : [4, 8], 8 4 : [0, 3, 9], 9 5 : [], 10 6 : [0, 1, 7], 11 7 : [2, 6], 12 8 : [1, 3], 13 9 : [2, 4] 14 ] 15 16 var moves:[Int:[Int:Int]] = [ 17 0:[0:1, 1:1, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1, 9:1], 18 1:[0:2, 1:2, 2:2, 3:2, 4:3, 5:0, 6:3, 7:2, 8:2, 9:2], 19 2:[0:6, 1:5, 2:4, 3:5, 4:6, 5:0, 6:6, 7:5, 8:4, 9:5] 20 ] 21 func knightDialer(_ N: Int) -> Int { 22 let dict = subDictFor(N-1) 23 var result = 0 24 for (_, value) in dict { 25 result += value 26 result %= modulo 27 } 28 return result 29 } 30 31 func subDictFor(_ movesCount: Int) -> [Int: Int] { 32 if let result = moves[movesCount] { 33 return result 34 } 35 36 let prevMoves = subDictFor(movesCount - 1) 37 var curMoves:[Int:Int] = [:] 38 for i in 0...9 { 39 var sum = 0 40 let nextSteps = availableNumbers[i]! 41 for nextStep in nextSteps { 42 sum += prevMoves[nextStep]! 43 } 44 sum %= modulo 45 curMoves[i] = sum 46 } 47 moves[movesCount] = curMoves 48 return curMoves 49 } 50 }
2476ms
1 class Solution { 2 func knightDialer(_ N: Int) -> Int { 3 var map: [Int64: Int64] = [0:1,1:1,2:1,3:1,4:1,6:1,7:1,8:1,9:1] 4 var sum: Int = 10 5 for n in (1..<N) { 6 let t = countLayer(map) 7 sum = t.0 8 map = t.1 9 //print(t) 10 } 11 12 return sum 13 } 14 15 func countLayer(_ map: [Int64: Int64]) -> (Int, [Int64: Int64]) { 16 var sum: Int64 = 0 17 var nextMap: [Int64: Int64] = [:] 18 for (key, value) in map { 19 var value = value % 1000000007 20 switch key { 21 case 0: sum += (Int64)(2 * value); 22 nextMap[6] = (nextMap[6] ?? 0) + value; 23 nextMap[4] = (nextMap[4] ?? 0) + value; 24 break; 25 case 1: sum += (Int64)(2 * value); 26 nextMap[6] = (nextMap[6] ?? 0) + value 27 nextMap[8] = (nextMap[8] ?? 0) + value; break; 28 case 2: sum += (Int64)(2 * value); 29 nextMap[7] = (nextMap[7] ?? 0) + value; 30 nextMap[9] = (nextMap[9] ?? 0) + value; break; 31 case 3: sum += (Int64)(2 * value); 32 nextMap[4] = (nextMap[4] ?? 0) + value; 33 nextMap[8] = (nextMap[8] ?? 0) + value; break; 34 case 4: sum += (Int64)(3 * value); 35 nextMap[0] = (nextMap[0] ?? 0) + value; 36 nextMap[3] = (nextMap[3] ?? 0) + value; 37 nextMap[9] = (nextMap[9] ?? 0) + value; break; 38 case 6: sum += (Int64)(3 * value); 39 nextMap[1] = (nextMap[1] ?? 0) + value; 40 nextMap[7] = (nextMap[7] ?? 0) + value; 41 nextMap[0] = (nextMap[0] ?? 0) + value; break; 42 case 7: sum += (Int64)(2 * value); 43 nextMap[2] = (nextMap[2] ?? 0) + value; 44 nextMap[6] = (nextMap[6] ?? 0) + value; break; 45 case 8: sum += (Int64)(2 * value); 46 nextMap[1] = (nextMap[1] ?? 0) + value; 47 nextMap[3] = (nextMap[3] ?? 0) + value; break; 48 case 9: sum += (Int64)(2 * value); 49 nextMap[4] = (nextMap[4] ?? 0) + value; 50 nextMap[2] = (nextMap[2] ?? 0) + value; break; 51 default: break 52 } 53 sum = sum % 1000000007 54 } 55 return (Int(sum % 1000000007), nextMap) 56 } 57 }
