#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/data-structures/fenwick-trees/bit-for-xor-queries

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████████████████████████████████████████

#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/data-structures/fenwick-trees/bit-for-xor-queries

Repovive

BIT for XOR Queries - Fenwick Trees | Data Structures | Repovive

Repovive.

Data Structures19 sections · 729 units49h total

Open in Course

BIT for XOR Queries

Another invertible operation

BIT works for any invertible operation. XOR is self-inverse: $a \oplus a = 0$ .

def queryXOR(i):
    result = 0
    while i > 0:
        result ^= tree[i]
        i -= i & (-i)
    return result

def updateXOR(i, val):
    while i <= n:
        tree[i] ^= val
        i += i & (-i)

Range XOR from $l$ to $r$ : $\text{prefix}(r) \oplus \text{prefix}(l-1)$ .

Use case: problems involving XOR of subarrays, toggling bits in ranges, or maintaining XOR over dynamic data.