g1801_1900.s1895_largest_magic_square.Solution Maven / Gradle / Ivy
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Java-based LeetCode algorithm problem solutions, regularly updated
package g1801_1900.s1895_largest_magic_square;
// #Medium #Array #Matrix #Prefix_Sum #2022_05_03_Time_7_ms_(80.72%)_Space_45.1_MB_(62.65%)
public class Solution {
public int largestMagicSquare(int[][] grid) {
int m = grid.length;
int n = grid[0].length;
int[][] rows = new int[m][n + 1];
int[][] cols = new int[m + 1][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
// cumulative sum for each row
rows[i][j + 1] = rows[i][j] + grid[i][j];
// cumulative sum for each column
cols[i + 1][j] = cols[i][j] + grid[i][j];
}
}
// start with the biggest side possible
for (int side = Math.min(m, n); side > 1; side--) {
// check every square
for (int i = 0; i <= m - side; i++) {
for (int j = 0; j <= n - side; j++) {
// checks if a square with top left [i, j] and side length is magic
if (magic(grid, rows, cols, i, j, side)) {
return side;
}
}
}
}
return 1;
}
private boolean magic(int[][] grid, int[][] rows, int[][] cols, int r, int c, int side) {
int sum = rows[r][c + side] - rows[r][c];
int d1 = 0;
int d2 = 0;
for (int k = 0; k < side; k++) {
d1 += grid[r + k][c + k];
d2 += grid[r + side - 1 - k][c + k];
// check each row and column
if (rows[r + k][c + side] - rows[r + k][c] != sum
|| cols[r + side][c + k] - cols[r][c + k] != sum) {
return false;
}
}
// checks both diagonals
return d1 == sum && d2 == sum;
}
}