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Merged
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Mar 22, 2025
+74 −62
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Improved task 3283 #1946

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136 changes: 74 additions & 62 deletions src/main/java/g3201_3300/s3283_maximum_number_of_moves_to_kill_all_pawns/Solution.java
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Original file line number Diff line number Diff line change
@@ -1,86 +1,98 @@
package g3201_3300.s3283_maximum_number_of_moves_to_kill_all_pawns;

// #Hard #Array #Math #Breadth_First_Search #Bit_Manipulation #Bitmask #Game_Theory
// #2024_09_09_Time_250_ms_(98.43%)_Space_50.1_MB_(66.27%)
// #2025_03_22_Time_126_ms_(100.00%)_Space_48.23_MB_(72.09%)

import java.util.LinkedList;
import java.util.ArrayDeque;
import java.util.Queue;

public class Solution {
private static final int[][] KNIGHT_MOVES = {
{-2, -1}, {-2, 1}, {-1, -2}, {-1, 2},
{1, -2}, {1, 2}, {2, -1}, {2, 1}
private static final int[][] DIRECTIONS = {
{2, 1}, {1, 2}, {-1, 2}, {-2, 1}, {-2, -1}, {-1, -2}, {1, -2}, {2, -1}
};
private int[][] distances;
private Integer[][] memo;

public int maxMoves(int kx, int ky, int[][] positions) {
private void initializePositions(int[][] positions, int[][] pos, int kx, int ky) {
int n = positions.length;
distances = new int[n + 1][n + 1];
memo = new Integer[n + 1][1 << n];
// Calculate distances between all pairs of positions (including knight's initial position)
for (int i = 0; i < n; i++) {
distances[n][i] = calculateMoves(kx, ky, positions[i][0], positions[i][1]);
for (int j = i + 1; j < n; j++) {
int dist =
calculateMoves(
positions[i][0], positions[i][1], positions[j][0], positions[j][1]);
distances[i][j] = distances[j][i] = dist;
}
int x = positions[i][0];
int y = positions[i][1];
pos[x][y] = i;
}
return minimax(n, (1 << n) - 1, true);
pos[kx][ky] = n;
}

private int minimax(int lastPos, int remainingPawns, boolean isAlice) {
if (remainingPawns == 0) {
return 0;
}
if (memo[lastPos][remainingPawns] != null) {
return memo[lastPos][remainingPawns];
}
int result = isAlice ? 0 : Integer.MAX_VALUE;
for (int i = 0; i < distances.length - 1; i++) {
if ((remainingPawns & (1 << i)) != 0) {
int newRemainingPawns = remainingPawns & ~(1 << i);
int moveValue = distances[lastPos][i] + minimax(i, newRemainingPawns, !isAlice);

if (isAlice) {
result = Math.max(result, moveValue);
} else {
result = Math.min(result, moveValue);
private void calculateDistances(int[][] positions, int[][] pos, int[][] distances) {
int n = positions.length;
for (int i = 0; i < n; i++) {
int count = n - i;
boolean[][] visited = new boolean[50][50];
visited[positions[i][0]][positions[i][1]] = true;
Queue<int[]> que = new ArrayDeque<>();
que.offer(new int[] {positions[i][0], positions[i][1]});
int steps = 1;
while (!que.isEmpty() && count > 0) {
int size = que.size();
while (size-- > 0) {
int[] cur = que.poll();
int x = cur[0];
int y = cur[1];
for (int[] d : DIRECTIONS) {
int nx = x + d[0];
int ny = y + d[1];
if (0 <= nx && nx < 50 && 0 <= ny && ny < 50 && !visited[nx][ny]) {
que.offer(new int[] {nx, ny});
visited[nx][ny] = true;
int j = pos[nx][ny];
if (j > i) {
distances[i][j] = distances[j][i] = steps;
if (--count == 0) {
break;
}
}
}
}
if (count == 0) {
break;
}
}
steps++;
}
}
memo[lastPos][remainingPawns] = result;
return result;
}

private int calculateMoves(int x1, int y1, int x2, int y2) {
if (x1 == x2 && y1 == y2) {
return 0;
}
boolean[][] visited = new boolean[50][50];
Queue<int[]> queue = new LinkedList<>();
queue.offer(new int[] {x1, y1, 0});
visited[x1][y1] = true;
while (!queue.isEmpty()) {
int[] current = queue.poll();
int x = current[0];
int y = current[1];
int moves = current[2];
for (int[] move : KNIGHT_MOVES) {
int nx = x + move[0];
int ny = y + move[1];
if (nx == x2 && ny == y2) {
return moves + 1;
}
if (nx >= 0 && nx < 50 && ny >= 0 && ny < 50 && !visited[nx][ny]) {
queue.offer(new int[] {nx, ny, moves + 1});
visited[nx][ny] = true;
private int calculateDP(int n, int[][] distances) {
int m = (1 << n) - 1;
int[][] dp = new int[1 << n][n + 1];
for (int mask = 1; mask < (1 << n); mask++) {
boolean isEven = (Integer.bitCount(m ^ mask)) % 2 == 0;
for (int i = 0; i <= n; i++) {
int result = 0;
if (isEven) {
for (int j = 0; j < n; j++) {
if ((mask & (1 << j)) > 0) {
result = Math.max(result, dp[mask ^ (1 << j)][j] + distances[i][j]);
}
}
} else {
result = Integer.MAX_VALUE;
for (int j = 0; j < n; j++) {
if ((mask & (1 << j)) > 0) {
result = Math.min(result, dp[mask ^ (1 << j)][j] + distances[i][j]);
}
}
}
dp[mask][i] = result;
}
}
// Should never reach here if input is valid
return -1;
return dp[m][n];
}

public int maxMoves(int kx, int ky, int[][] positions) {
int n = positions.length;
int[][] pos = new int[50][50];
initializePositions(positions, pos, kx, ky);
int[][] distances = new int[n + 1][n + 1];
calculateDistances(positions, pos, distances);
return calculateDP(n, distances);
}
}
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