|
| 1 | +[](https://github.com/javadev/LeetCode-in-Kotlin) |
| 2 | +[](https://github.com/javadev/LeetCode-in-Kotlin/fork) |
| 3 | + |
| 4 | +## 3283\. Maximum Number of Moves to Kill All Pawns |
| 5 | + |
| 6 | +Hard |
| 7 | + |
| 8 | +There is a `50 x 50` chessboard with **one** knight and some pawns on it. You are given two integers `kx` and `ky` where `(kx, ky)` denotes the position of the knight, and a 2D array `positions` where <code>positions[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> denotes the position of the pawns on the chessboard. |
| 9 | + |
| 10 | +Alice and Bob play a _turn-based_ game, where Alice goes first. In each player's turn: |
| 11 | + |
| 12 | +* The player _selects_ a pawn that still exists on the board and captures it with the knight in the **fewest** possible **moves**. **Note** that the player can select **any** pawn, it **might not** be one that can be captured in the **least** number of moves. |
| 13 | +* In the process of capturing the _selected_ pawn, the knight **may** pass other pawns **without** capturing them. **Only** the _selected_ pawn can be captured in _this_ turn. |
| 14 | + |
| 15 | +Alice is trying to **maximize** the **sum** of the number of moves made by _both_ players until there are no more pawns on the board, whereas Bob tries to **minimize** them. |
| 16 | + |
| 17 | +Return the **maximum** _total_ number of moves made during the game that Alice can achieve, assuming both players play **optimally**. |
| 18 | + |
| 19 | +Note that in one **move,** a chess knight has eight possible positions it can move to, as illustrated below. Each move is two cells in a cardinal direction, then one cell in an orthogonal direction. |
| 20 | + |
| 21 | + |
| 22 | + |
| 23 | +**Example 1:** |
| 24 | + |
| 25 | +**Input:** kx = 1, ky = 1, positions = \[\[0,0]] |
| 26 | + |
| 27 | +**Output:** 4 |
| 28 | + |
| 29 | +**Explanation:** |
| 30 | + |
| 31 | + |
| 32 | + |
| 33 | +The knight takes 4 moves to reach the pawn at `(0, 0)`. |
| 34 | + |
| 35 | +**Example 2:** |
| 36 | + |
| 37 | +**Input:** kx = 0, ky = 2, positions = \[\[1,1],[2,2],[3,3]] |
| 38 | + |
| 39 | +**Output:** 8 |
| 40 | + |
| 41 | +**Explanation:** |
| 42 | + |
| 43 | +**** |
| 44 | + |
| 45 | +* Alice picks the pawn at `(2, 2)` and captures it in two moves: `(0, 2) -> (1, 4) -> (2, 2)`. |
| 46 | +* Bob picks the pawn at `(3, 3)` and captures it in two moves: `(2, 2) -> (4, 1) -> (3, 3)`. |
| 47 | +* Alice picks the pawn at `(1, 1)` and captures it in four moves: `(3, 3) -> (4, 1) -> (2, 2) -> (0, 3) -> (1, 1)`. |
| 48 | + |
| 49 | +**Example 3:** |
| 50 | + |
| 51 | +**Input:** kx = 0, ky = 0, positions = \[\[1,2],[2,4]] |
| 52 | + |
| 53 | +**Output:** 3 |
| 54 | + |
| 55 | +**Explanation:** |
| 56 | + |
| 57 | +* Alice picks the pawn at `(2, 4)` and captures it in two moves: `(0, 0) -> (1, 2) -> (2, 4)`. Note that the pawn at `(1, 2)` is not captured. |
| 58 | +* Bob picks the pawn at `(1, 2)` and captures it in one move: `(2, 4) -> (1, 2)`. |
| 59 | + |
| 60 | +**Constraints:** |
| 61 | + |
| 62 | +* `0 <= kx, ky <= 49` |
| 63 | +* `1 <= positions.length <= 15` |
| 64 | +* `positions[i].length == 2` |
| 65 | +* `0 <= positions[i][0], positions[i][1] <= 49` |
| 66 | +* All `positions[i]` are unique. |
| 67 | +* The input is generated such that `positions[i] != [kx, ky]` for all `0 <= i < positions.length`. |
| 68 | + |
| 69 | +## Solution |
| 70 | + |
| 71 | +```kotlin |
| 72 | +import java.util.LinkedList |
| 73 | +import java.util.Queue |
| 74 | +import kotlin.math.max |
| 75 | +import kotlin.math.min |
| 76 | + |
| 77 | +class Solution { |
| 78 | + private lateinit var distances: Array<IntArray> |
| 79 | + private lateinit var memo: Array<Array<Int?>?> |
| 80 | + |
| 81 | + fun maxMoves(kx: Int, ky: Int, positions: Array<IntArray>): Int { |
| 82 | + val n = positions.size |
| 83 | + distances = Array<IntArray>(n + 1) { IntArray(n + 1) { 0 } } |
| 84 | + memo = Array<Array<Int?>?>(n + 1) { arrayOfNulls<Int>(1 shl n) } |
| 85 | + // Calculate distances between all pairs of positions (including knight's initial position) |
| 86 | + for (i in 0 until n) { |
| 87 | + distances[n][i] = calculateMoves(kx, ky, positions[i][0], positions[i][1]) |
| 88 | + for (j in i + 1 until n) { |
| 89 | + val dist = |
| 90 | + calculateMoves( |
| 91 | + positions[i][0], positions[i][1], positions[j][0], positions[j][1] |
| 92 | + ) |
| 93 | + distances[j][i] = dist |
| 94 | + distances[i][j] = distances[j][i] |
| 95 | + } |
| 96 | + } |
| 97 | + return minimax(n, (1 shl n) - 1, true) |
| 98 | + } |
| 99 | + |
| 100 | + private fun minimax(lastPos: Int, remainingPawns: Int, isAlice: Boolean): Int { |
| 101 | + if (remainingPawns == 0) { |
| 102 | + return 0 |
| 103 | + } |
| 104 | + if (memo[lastPos]!![remainingPawns] != null) { |
| 105 | + return memo[lastPos]!![remainingPawns]!! |
| 106 | + } |
| 107 | + var result = if (isAlice) 0 else Int.Companion.MAX_VALUE |
| 108 | + for (i in 0 until distances.size - 1) { |
| 109 | + if ((remainingPawns and (1 shl i)) != 0) { |
| 110 | + val newRemainingPawns = remainingPawns and (1 shl i).inv() |
| 111 | + val moveValue = distances[lastPos][i] + minimax(i, newRemainingPawns, !isAlice) |
| 112 | + result = if (isAlice) { |
| 113 | + max(result, moveValue) |
| 114 | + } else { |
| 115 | + min(result, moveValue) |
| 116 | + } |
| 117 | + } |
| 118 | + } |
| 119 | + memo[lastPos]!![remainingPawns] = result |
| 120 | + return result |
| 121 | + } |
| 122 | + |
| 123 | + private fun calculateMoves(x1: Int, y1: Int, x2: Int, y2: Int): Int { |
| 124 | + if (x1 == x2 && y1 == y2) { |
| 125 | + return 0 |
| 126 | + } |
| 127 | + val visited = Array<BooleanArray?>(50) { BooleanArray(50) } |
| 128 | + val queue: Queue<IntArray> = LinkedList<IntArray>() |
| 129 | + queue.offer(intArrayOf(x1, y1, 0)) |
| 130 | + visited[x1]!![y1] = true |
| 131 | + while (queue.isNotEmpty()) { |
| 132 | + val current = queue.poll() |
| 133 | + val x = current[0] |
| 134 | + val y = current[1] |
| 135 | + val moves = current[2] |
| 136 | + for (move in KNIGHT_MOVES) { |
| 137 | + val nx = x + move[0] |
| 138 | + val ny = y + move[1] |
| 139 | + if (nx == x2 && ny == y2) { |
| 140 | + return moves + 1 |
| 141 | + } |
| 142 | + if (nx >= 0 && nx < 50 && ny >= 0 && ny < 50 && !visited[nx]!![ny]) { |
| 143 | + queue.offer(intArrayOf(nx, ny, moves + 1)) |
| 144 | + visited[nx]!![ny] = true |
| 145 | + } |
| 146 | + } |
| 147 | + } |
| 148 | + // Should never reach here if input is valid |
| 149 | + return -1 |
| 150 | + } |
| 151 | + |
| 152 | + companion object { |
| 153 | + private val KNIGHT_MOVES = arrayOf<IntArray>( |
| 154 | + intArrayOf(-2, -1), intArrayOf(-2, 1), intArrayOf(-1, -2), intArrayOf(-1, 2), |
| 155 | + intArrayOf(1, -2), intArrayOf(1, 2), intArrayOf(2, -1), intArrayOf(2, 1) |
| 156 | + ) |
| 157 | + } |
| 158 | +} |
| 159 | +``` |
0 commit comments