Medium
A 0-indexed array derived
with length n
is derived by computing the bitwise XOR (⊕) of adjacent values in a binary array original
of length n
.
Specifically, for each index i
in the range [0, n - 1]
:
i = n - 1
, then derived[i] = original[i] ⊕ original[0]
.derived[i] = original[i] ⊕ original[i + 1]
.Given an array derived
, your task is to determine whether there exists a valid binary array original
that could have formed derived
.
Return true if such an array exists or false otherwise.
Example 1:
Input: derived = [1,1,0]
Output: true
Explanation: A valid original array that gives derived is [0,1,0].
derived[0] = original[0] ⊕ original[1] = 0 ⊕ 1 = 1
derived[1] = original[1] ⊕ original[2] = 1 ⊕ 0 = 1
derived[2] = original[2] ⊕ original[0] = 0 ⊕ 0 = 0
Example 2:
Input: derived = [1,1]
Output: true
Explanation: A valid original array that gives derived is [0,1].
derived[0] = original[0] ⊕ original[1] = 1
derived[1] = original[1] ⊕ original[0] = 1
Example 3:
Input: derived = [1,0]
Output: false
Explanation: There is no valid original array that gives derived.
Constraints:
n == derived.length
1 <= n <= 105
derived
are either 0’s or 1’sclass Solution {
fun doesValidArrayExist(derived: IntArray): Boolean {
var xor = 0
for (j in derived) {
xor = xor xor j
}
return xor == 0
}
}