Menene gumakun sadarwar bit na gaida?

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**Sadarwar bit** yana aiki kai-kai akan wakilcin binary na lamba ta amfani da AND, OR, XOR, NOT da shifta. Yana ba da damar aiki da gaida, rashin shashi, da sauri sosai. ## Aibuka na cikakke ```python x & 1 # is x odd? (lowest bit) x << 1 # multiply by 2 x >> 1 # integer divide by 2 x & (1 << k) # is bit k set? x | (1 << k) # set bit k x & ~(1 << k) # clear bit k x ^ (1 << k) # toggle bit k ``` ## Gumakun da ke da amfani ```python x & (x - 1) # clears the lowest set bit x & (x - 1) == 0 # is x a power of two? (x>0) x & (-x) # isolates the lowest set bit bin(x).count('1') # popcount (number of set bits) ``` ## Misali: nemo lamba daya (gumakun XOR) ```python def single_number(nums): result = 0 for n in nums: result ^= n # pairs cancel: a ^ a == 0 return result # the lone unpaired value remains single_number([4, 1, 2, 1, 2]) # -> 4 ``` ## Hadowa Bit ops su ne O(1); XOR scan da baje'u ne **O(n) lokaci, O(1) sarari**. ## Lokacin amfani / rashin kyau Yi amfani da **bitmasks** (ƙidayewa subset, DP akan jiha), flags, ilimi mai sauri, da koda ƙananan-matakin/katabarau. Kula da bit sigina, jujjuyawar shawa da ta dace da harshe, da karanta — jaje gumakun da ba a faɗi ba. ## Me yasa hakan muhimmi Sadarwar bit yana ba da warware O(1)-sarari da ke da kyau (kamar gumakun XOR-gida) wanda ke firgije a zabe. Bitmask DP yana ba da damar abubuwan matsanancin sararin jiha mai nisbewa. Yana da mahimmanci a cikin tsarin, zane-zane, matsi, da koda da ke da nauyi na wuyar gida inda kowane halkoki ya be da mahimmanci.