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<?php | |
/** | |
* Counts squares in matrix by loop. | |
* | |
* @param int $n | |
* @param int $m | |
* @return int | |
*/ | |
function countSquares(int $m, int $n): int | |
{ | |
if ($n === 0 || $m === 0) { | |
return 0; | |
} | |
if ($n < $m) { | |
$side = $n; | |
$count = 0; | |
} else if ($n > $m) { | |
$side = $m; | |
$count = 0; | |
} else { | |
$side = $n - 1; | |
$count = 1; | |
} | |
while ($side > 0) { | |
for ($i = 0; $i <= $n - $side; $i++) { | |
for ($j = 0; $j <= $m - $side; $j++) { | |
if ($i + $side <= $n && $j + $side <= $m) { | |
$count++; | |
} | |
} | |
} | |
$side--; | |
} | |
return $count; | |
} | |
/** | |
* Counts squares in matrix by formula. | |
* @link https://www.geeksforgeeks.org/count-number-of-squares-in-a-rectangle/ | |
* | |
* @param int $n | |
* @param int $m | |
* @return int | |
*/ | |
function countSquaresFormula(int $m, int $n): int | |
{ | |
if ($n < $m) { | |
list($m, $n) = array($n, $m); | |
} | |
return $m * ($m + 1) * (2 * $m + 1) / 6 + ($n - $m) * $m * ($m + 1) / 2; | |
} | |
$i = 0; | |
do { | |
printf("%dx%d = %d - %d\n", $i, $i, countSquares($i, $i), countSquaresFormula($i, $i)); | |
printf("%dx%d = %d - %d\n", $i + 1, $i, countSquares($i + 1, $i), countSquaresFormula($i + 1, $i)); | |
printf("%dx%d = %d - %d\n", $i, $i + 1, countSquares($i, $i + 1), countSquaresFormula($i, $i + 1)); | |
} while ($i++ < 10); | |
// 0x0 = 0 - 0 | |
// 1x0 = 0 - 0 | |
// 0x1 = 0 - 0 | |
// 1x1 = 1 - 1 | |
// 2x1 = 2 - 2 | |
// 1x2 = 2 - 2 | |
// 2x2 = 5 - 5 | |
// 3x2 = 8 - 8 | |
// 2x3 = 8 - 8 | |
// 3x3 = 14 - 14 | |
// 4x3 = 20 - 20 | |
// 3x4 = 20 - 20 | |
// 4x4 = 30 - 30 | |
// 5x4 = 40 - 40 | |
// 4x5 = 40 - 40 | |
// 5x5 = 55 - 55 | |
// 6x5 = 70 - 70 | |
// 5x6 = 70 - 70 | |
// 6x6 = 91 - 91 | |
// 7x6 = 112 - 112 | |
// 6x7 = 112 - 112 | |
// 7x7 = 140 - 140 | |
// 8x7 = 168 - 168 | |
// 7x8 = 168 - 168 | |
// 8x8 = 204 - 204 | |
// 9x8 = 240 - 240 | |
// 8x9 = 240 - 240 | |
// 9x9 = 285 - 285 | |
// 10x9 = 330 - 330 | |
// 9x10 = 330 - 330 | |
// 10x10 = 385 - 385 | |
// 11x10 = 440 - 440 | |
// 10x11 = 440 - 440 |
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