1442. Count Triplets That Can Form Two Arrays of Equal XOR #275
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Topics: Given an array of integers We want to select three indices Let's define
Note that ^ denotes the bitwise-xor operation. Return the number of triplets ( Example 1:
Example 2:
Constraints:
Hint:
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The problem asks us to count the number of triplets The XOR operation is a bitwise operation where each bit is evaluated independently, and the result is Key Points:
Approach:To solve this problem efficiently, we can utilize the concept of prefix XORs, which allows us to calculate the XOR of any subarray in constant time. The main idea is to compute the cumulative XOR for each element and use it to determine if the conditions of the triplets are met. Plan:
Let's implement this solution in PHP: 1442. Count Triplets That Can Form Two Arrays of Equal XOR <?php
/**
* @param Integer[] $arr
* @return Integer
*/
function countTriplets($arr) {
$ans = 0;
$xors = [0];
$prefix = 0;
foreach ($arr as $key => $a) {
$prefix ^= $a;
$xors[] = $prefix;
}
for ($j = 1; $j < count($arr); $j++) {
for ($i = 0; $i < $j; $i++) {
$xors_i = $xors[$j] ^ $xors[$i];
for ($k = $j; $k < count($arr); $k++) {
$xors_k = $xors[$k + 1] ^ $xors[$j];
if ($xors_i == $xors_k) {
$ans += 1;
}
}
}
}
return $ans;
}
// Example usage:
$arr1 = [2,3,1,6,7];
$arr2 = [1,1,1,1,1];
echo countTriplets($arr1) . "\n"; // Output: 4
echo countTriplets($arr2) . "\n"; // Output: 10
?> Explanation:
Example Walkthrough:Example 1:Input:
Now, we loop through possible values for
Thus, the output is Example 2:Input:
Now, loop through possible values for
Output: Time Complexity:
Output for Example:
This solution efficiently calculates the number of valid triplets using prefix XORs. While the time complexity can be improved further, the approach provides a straightforward way to solve the problem by utilizing properties of the XOR operation. |
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The problem asks us to count the number of triplets
(i, j, k)
where the XOR of elements betweeni
andj-1
(inclusive) equals the XOR of elements betweenj
andk
(inclusive) in the given arrayarr
.The XOR operation is a bitwise operation where each bit is evaluated independently, and the result is
1
if the corresponding bits in the operands are different, and0
if they are the same.Key Points:
arr
.(i, j, k)
such that the XOR of elements from indexi
toj-1
equals the XOR of elements from indexj
tok
.x ^ x = 0
andx ^ 0 = x
, which can help optimize the solution.Approach: