LeetCode-in-Java
3257. Maximum Value Sum by Placing Three Rooks II
Hard
You are given a m x n 2D array board representing a chessboard, where board[i][j] represents the value of the cell (i, j).
Rooks in the same row or column attack each other. You need to place three rooks on the chessboard such that the rooks do not attack each other.
Return the maximum sum of the cell values on which the rooks are placed.
Example 1:
Input: board = [[-3,1,1,1],[-3,1,-3,1],[-3,2,1,1]]
Output: 4
Explanation:
We can place the rooks in the cells (0, 2), (1, 3), and (2, 1) for a sum of 1 + 1 + 2 = 4.
Example 2:
Input: board = [[1,2,3],[4,5,6],[7,8,9]]
Output: 15
Explanation:
We can place the rooks in the cells (0, 0), (1, 1), and (2, 2) for a sum of 1 + 5 + 9 = 15.
Example 3:
Input: board = [[1,1,1],[1,1,1],[1,1,1]]
Output: 3
Explanation:
We can place the rooks in the cells (0, 2), (1, 1), and (2, 0) for a sum of 1 + 1 + 1 = 3.
Constraints:
3 <= m == board.length <= 5003 <= n == board[i].length <= 500-109 <= board[i][j] <= 109
Solution
import java.util.Arrays;
public class Solution {
public long maximumValueSum(int[][] board) {
int n = board.length;
int m = board[0].length;
int[][] tb = new int[n][m];
tb[0] = Arrays.copyOf(board[0], m);
for (int i = 1; i < n; i++) {
for (int j = 0; j < m; j++) {
tb[i][j] = Math.max(tb[i - 1][j], board[i][j]);
}
}
int[][] bt = new int[n][m];
bt[n - 1] = Arrays.copyOf(board[n - 1], m);
for (int i = n - 2; i >= 0; i--) {
for (int j = 0; j < m; j++) {
bt[i][j] = Math.max(bt[i + 1][j], board[i][j]);
}
}
long ans = Long.MIN_VALUE;
for (int i = 1; i < n - 1; i++) {
int[][] max3Top = getMax3(tb[i - 1]);
int[][] max3Cur = getMax3(board[i]);
int[][] max3Bottom = getMax3(bt[i + 1]);
for (int[] topCand : max3Top) {
for (int[] curCand : max3Cur) {
for (int[] bottomCand : max3Bottom) {
if (topCand[1] != curCand[1]
&& topCand[1] != bottomCand[1]
&& curCand[1] != bottomCand[1]) {
long cand = (long) topCand[0] + curCand[0] + bottomCand[0];
ans = Math.max(ans, cand);
}
}
}
}
}
return ans;
}
private int[][] getMax3(int[] row) {
int m = row.length;
int[][] ans = new int[3][2];
Arrays.fill(ans, new int[] {Integer.MIN_VALUE, -1});
for (int j = 0; j < m; j++) {
if (row[j] >= ans[0][0]) {
ans[2] = ans[1];
ans[1] = ans[0];
ans[0] = new int[] {row[j], j};
} else if (row[j] >= ans[1][0]) {
ans[2] = ans[1];
ans[1] = new int[] {row[j], j};
} else if (row[j] > ans[2][0]) {
ans[2] = new int[] {row[j], j};
}
}
return ans;
}
}