|
| 1 | +// Recursion + Memoization |
| 2 | +classSolution { |
| 3 | +funfindPaths(m:Int,n:Int,maxMove:Int,startRow:Int,startColumn:Int):Int { |
| 4 | +val mod=1_000_000_007 |
| 5 | +val dirs= intArrayOf(0,1,0,-1,0) |
| 6 | +val dp=Array (m) {Array (n) {LongArray (maxMove+1) {-1L } } } |
| 7 | + |
| 8 | +funoutOfBounds(i:Int,j:Int)= i<0|| i== m|| j<0|| j== n |
| 9 | + |
| 10 | +fundfs(i:Int,j:Int,k:Int):Long { |
| 11 | +if (outOfBounds(i, j))return1L |
| 12 | +if (k==0)return0L |
| 13 | +if (dp[i][j][k]!=-1L)return dp[i][j][k] |
| 14 | + |
| 15 | + dp[i][j][k]=0 |
| 16 | +for (nin0..3) |
| 17 | + dp[i][j][k]= (dp[i][j][k]+ dfs(i+ dirs[n], j+ dirs[n+1], k-1))% mod |
| 18 | + |
| 19 | +return dp[i][j][k] |
| 20 | + } |
| 21 | + |
| 22 | +return dfs(startRow, startColumn, maxMove).toInt() |
| 23 | + } |
| 24 | +} |
| 25 | + |
| 26 | +// Bottom-up DP |
| 27 | +classSolution { |
| 28 | +funfindPaths(m:Int,n:Int,maxMove:Int,startRow:Int,startColumn:Int):Int { |
| 29 | +val mod=1_000_000_007 |
| 30 | +val dirs= intArrayOf(0,1,0,-1,0) |
| 31 | +val dp=Array (m) {Array (n) {LongArray (maxMove+1) } } |
| 32 | + |
| 33 | +funoutOfBounds(i:Int,j:Int)= i<0|| i== m|| j<0|| j== n |
| 34 | + |
| 35 | +for (kin1..maxMove) { |
| 36 | +for (iin0 until m) { |
| 37 | +for (jin0 until n) { |
| 38 | +for (dirin0..3) { |
| 39 | +val i2= i+ dirs[dir] |
| 40 | +val j2= j+ dirs[dir+1] |
| 41 | +if (outOfBounds(i2, j2)) |
| 42 | + dp[i][j][k]++ |
| 43 | +else |
| 44 | + dp[i][j][k]= (dp[i][j][k]+ dp[i2][j2][k-1])% mod |
| 45 | + } |
| 46 | + } |
| 47 | + } |
| 48 | + } |
| 49 | + |
| 50 | +return dp[startRow][startColumn][maxMove].toInt() |
| 51 | + } |
| 52 | +} |
| 53 | + |
| 54 | +// Top-down DP |
| 55 | +classSolution { |
| 56 | +funfindPaths(m:Int,n:Int,maxMove:Int,startRow:Int,startColumn:Int):Int { |
| 57 | +val mod=1_000_000_007 |
| 58 | +val dirs= intArrayOf(0,1,0,-1,0) |
| 59 | +val dp=Array(m) {Array(n) {LongArray(maxMove+1) } } |
| 60 | + |
| 61 | +funoutOfBounds(i:Int,j:Int)= i<0|| i== m|| j<0|| j== n |
| 62 | + |
| 63 | +for (kin1..maxMove) { |
| 64 | +for (iin m-1 downTo0) { |
| 65 | +for (jin n-1 downTo0) { |
| 66 | +for (dirin0..3) { |
| 67 | +val i2= i+ dirs[dir] |
| 68 | +val j2= j+ dirs[dir+1] |
| 69 | +if (outOfBounds(i2, j2)) |
| 70 | + dp[i][j][k]++ |
| 71 | +else |
| 72 | + dp[i][j][k]= (dp[i][j][k]+ dp[i2][j2][k-1])% mod |
| 73 | + } |
| 74 | + } |
| 75 | + } |
| 76 | + } |
| 77 | + |
| 78 | +return dp[startRow][startColumn][maxMove].toInt() |
| 79 | + } |
| 80 | +} |