68 lines
1.5 KiB
Java
68 lines
1.5 KiB
Java
class Solution {
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private static final int SQUARE_SIZE = 3;
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private int sum(int[][] grid, int y, int x, int dy, int dx) {
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int total = 0;
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for (int d = 0; d < SQUARE_SIZE; ++d) {
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total += grid[y + d * dy][x + d * dx];
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}
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return total;
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}
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private static final int ALL_DIGITS = (~(((~0) >> 9) << 9));
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private boolean isMagicSquare(int[][] grid, int y, int x) {
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// check the digits
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int seen = 0;
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for (int d = 0; d < SQUARE_SIZE * SQUARE_SIZE; ++d) {
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int dy = d / SQUARE_SIZE, dx = d % SQUARE_SIZE;
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int digit = grid[y + dy][x + dx];
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if (digit < 1 || digit > 9) {
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// out of range
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return false;
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}
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seen |= 1 << (digit - 1);
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}
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if (seen != ALL_DIGITS) {
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// repeated digits
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return false;
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}
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// check the sums
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int expectedSum = sum(grid, y, x, 1, 1);
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int diag2 = sum(grid, y, x + 2, 1, -1);
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if (diag2 != expectedSum) {
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// diagonals are broken
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return false;
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}
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for (int d = 0; d < SQUARE_SIZE; ++d) {
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if (sum(grid, y + d, x, 0, 1) != expectedSum) {
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return false;
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}
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if (sum(grid, y, x + d, 1, 0) != expectedSum) {
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return false;
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}
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}
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return true;
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}
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public int numMagicSquaresInside(int[][] grid) {
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int squares = 0;
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for (int y = 0; y + 2 < grid.length; ++y) {
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for (int x = 0; x + 2 < grid[y].length; ++x) {
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if (isMagicSquare(grid, y, x)) {
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++squares;
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}
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}
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}
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return squares;
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}
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}
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