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Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
from math import ceil class Solution: def minSetSize(self, arr: List[int]) -> int: arr.sort() brr = [] count = 1 cur = arr[0] for i in range(1,len(arr)): if cur == arr[i]: count += 1 else: brr.append([cur,count]) cur = arr[i] count = 1 brr.append([cur,count]) brr.sort(key = lambda x:x[1],reverse = True) temp = 0 temp1 = 0 for i in brr: if temp >=ceil(len(arr)/2): return temp1 temp1 += 1 temp += i[1] return 1
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: numsdict = {} for i in arr: numsdict[i] = numsdict.get(i,0) + 1 sortarr = sorted(numsdict.items(), key = lambda x: -x[1]) count = 0 i = 0 while 2*count < len(arr): count += sortarr[i][1] i += 1 return i
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: d = collections.defaultdict(int) for i in arr: d[i] += 1 s = sorted([(d[i],i) for i in d],reverse=True) res = 0 ans = 0 for i,v in s: res += i ans += 1 if res >= (len(arr) + 1) // 2: return ans return len(d)
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: c = Counter(arr) l = len(arr) tup = c.most_common(len(c)) i = 0 while l > len(arr)/2: l -= tup[i][1] i += 1 return i
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
import numpy as np class Solution: def minSetSize(self, arr: List[int]) -> int: n = len(arr) dict_model = {} for it in arr: if it in dict_model.keys(): dict_model[it] += 1 else: dict_model[it] = 1 min_deactivate = np.ceil(n/2) generators = list(dict_model.values()) generators.sort() turn_off = 0 i = 1 while turn_off < min_deactivate: turn_off += generators[-i] i += 1 return i-1
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: if not arr: return 0 int_freq = collections.Counter(arr) size = len(arr) cur_size = size count = 0 for num, freq in int_freq.most_common(): cur_size -= freq count += 1 if cur_size <= size // 2: return count
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: # L, C = len(arr), collections.Counter(arr) # S = sorted(C.values(), reverse = True) # T = itertools.accumulate(S) # for i,v in enumerate(T): # if v >= len(arr)//2: return i + 1 h = [(val*(-1),key) for key,val in list(Counter(arr).items())] heapify(h) #print(h) num_int = 0 count = 0 while 2*count*(-1) < len(arr): c,i = heappop(h) count += c num_int +=1 #print(seen) return num_int
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: l=len(arr) s=0 cnt= Counter(arr) cnt= [j for i,j in cnt.items()] cnt.sort(reverse=True) for ind,i in enumerate(cnt): s+=i if s>=l//2: break return ind+1
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: # L, C = len(arr), collections.Counter(arr) # S = sorted(C.values(), reverse = True) # T = itertools.accumulate(S) # for i,v in enumerate(T): # if v >= len(arr)//2: return i + 1 dic = Counter(arr) h = [(val*(-1),key) for key,val in list(dic.items())] heapify(h) #print(h) num_int = 0 count = 0 while 2*count*(-1) < len(arr): c,i = heappop(h) count += c num_int +=1 #print(seen) return num_int
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: d = {} n,half = len(arr), len(arr) // 2 seen = set() for i in arr: d[i] = d.get(i,0) + 1 d = sorted(d.items(), key=lambda x: -x[1]) for k,v in d: if n - v > half: n -= v seen.add(k) else: seen.add(k) return len(seen)
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: h = {} for el in arr: if el not in h: h[el] = 0 h[el] += 1 tmp = [] for key in list(h.keys()): tmp.append(h[key]) tmp.sort() count = 0 size = 0 for i in range(len(tmp) - 1, -1, -1): size += tmp[i] count += 1 if size >= math.ceil(len(arr) / 2): break return count
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: dic = Counter(arr) h = [(val*(-1),key) for key,val in list(dic.items())] heapify(h) #print(h) seen = set() count = 0 while 2*count*(-1) < len(arr): c,i = heappop(h) count += c seen.add(i) #print(seen) return len(seen)
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
from collections import defaultdict class Solution: def minSetSize(self, arr: List[int]) -> int: # we will store the frequency of all the elements in a dictionary and from the dictionary we will pick the ones with the maximum value and remove them till we do not get half size # we keep two dictionaries ones from number to their frequency and another from frequency to number for better manipulation num_fre = defaultdict(int) fre_num = defaultdict(set) for i in range(len(arr)): num_fre[arr[i]] += 1 fre_num[num_fre[arr[i]]].add(arr[i]) if fre_num[num_fre[arr[i]] - 1] != set(): fre_num[num_fre[arr[i]] - 1].remove(arr[i]) del num_fre answer = set() removed_elements = 0 for fre in sorted(fre_num.keys(),reverse = True): for element in fre_num[fre]: if removed_elements < len(arr) // 2: removed_elements += fre answer.add(element) else: break return len(answer)
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
from collections import Counter class Solution: def minSetSize(self, arr: List[int]) -> int: tot = n = len(arr) count = Counter(arr) res = 0 for k, v in sorted(count.items(), key=lambda x: -x[1]): # print(k,v) tot -= v res += 1 if tot <= n // 2: return res return n
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
from collections import defaultdict class Solution: def minSetSize(self, arr: List[int]) -> int: # we will store the frequency of all the elements in a dictionary and from the dictionary we will pick the ones with the maximum value and remove them till we do not get half size # we keep two dictionaries ones from number to their frequency and another from frequency to number for better manipulation num_fre = defaultdict(int) fre_num = defaultdict(set) for i in range(len(arr)): num_fre[arr[i]] += 1 fre_num[num_fre[arr[i]]].add(arr[i]) if fre_num[num_fre[arr[i]] - 1] != set(): fre_num[num_fre[arr[i]] - 1].remove(arr[i]) answer = set() removed_elements = 0 for fre in sorted(fre_num.keys(),reverse = True): for element in fre_num[fre]: if removed_elements < len(arr) // 2: removed_elements += fre answer.add(element) else: break return len(answer)
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: # count = Counter(arr) # count = sorted(count.items(), key=lambda item: item[1], reverse=1) # total = len(arr) # i = 0 # res = set() # while total > len(arr) // 2: # total -= count[i][1] # res.add(count[i][0]) # i += 1 # return res count = sorted(Counter(arr).values(), reverse=1) target = (len(arr)) // 2 res = curr = 0 for val in count: curr += val res += 1 if curr >= target: break return res
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: N = len(arr) count = collections.Counter() for n in arr: count[n] += 1 sorted_count = sorted(list(count.keys()), key=lambda c: count[c], reverse=True) removed_count = 0 res = 0 for c in sorted_count: removed_count += count[c] res += 1 if removed_count >= (N + 1) // 2: break return res
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: d = {} h = [] for num in arr: if num not in d: d[num] = 1 else: d[num] += 1 for k, v in list(d.items()): h.append((-v, k)) heapq.heapify(h) ans = 0 count = 0 while count < len(arr)//2: v, k = heapq.heappop(h) count -= v ans += 1 return ans
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: freqs = Counter(arr) sorted_freqs = sorted(list(freqs.items()), key = lambda x : x[1], reverse=True) print(sorted_freqs) half_len = len(arr) / 2 current_len = 0 res = 0 for (i, j) in sorted_freqs: res += 1 current_len += j if current_len >= half_len: return res
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, a: List[int]) -> int: d={} n=len(a)//2 for i in a: if (i not in d): d[i]=1 else: d[i]+=1 d=sorted(d.items(),key=lambda x:x[1], reverse=True) print(d) sum=0 count=0 for i in d: x=i[1] sum+=x count+=1 if(sum>=n): break return count
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: hashMap = dict() for item in arr: if item not in hashMap: hashMap[item] = 0 hashMap[item] += 1 length = len(arr) itemToBeRemoved = 0 halfOflength = len(arr) // 2 for value in sorted(list(hashMap.values()), reverse = True): length -= value itemToBeRemoved += 1 if length <= halfOflength: return itemToBeRemoved
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: counter = {} for num in arr: if num in counter: counter[num] += 1 else: counter[num] = 1 heap = [] for num in list(counter.keys()): heapq.heappush(heap, (-counter[num], num)) n = len(arr) i = 0 cumSum = 0 while i < n and cumSum < n//2: freq, num = heapq.heappop(heap) cumSum += abs(freq) i+=1 return i
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: checked, answer = [],0 count_d,total = [],0 if len(arr) == len(set(arr)): return int(len(arr)/2) for num in arr: if num not in checked: count_d.append(arr.count(num)) checked.append(num) #count_d = sorted(count_d.items(), key=operator.itemgetter(1)) count_d.sort() for d in range(1, len(count_d)+1): total += count_d[-d] answer += 1 if total >= len(arr)/2: return answer
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: d = {} for el in arr: if d.get(el): d[el] += 1 else: d[el] = 1 s = sorted(d.values()) l = len(arr) / 2 c = 0 for i in reversed(range(len(s))): l -= s[i] c += 1 if l <= 0: break return c
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: numsdict = {} for i in arr: numsdict[i] = numsdict.get(i,0) + 1 sortarr = sorted(numsdict.values(), reverse = True) count = 0 i = 0 while 2*count < len(arr): count += sortarr[i] i += 1 return i
Given an array arr.  You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.   Example 1: Input: arr = [3,3,3,3,5,5,5,2,2,7] Output: 2 Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array). Possible sets of size 2 are {3,5},{3,2},{5,2}. Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has size greater than half of the size of the old array. Example 2: Input: arr = [7,7,7,7,7,7] Output: 1 Explanation: The only possible set you can choose is {7}. This will make the new array empty. Example 3: Input: arr = [1,9] Output: 1 Example 4: Input: arr = [1000,1000,3,7] Output: 1 Example 5: Input: arr = [1,2,3,4,5,6,7,8,9,10] Output: 5   Constraints: 1 <= arr.length <= 10^5 arr.length is even. 1 <= arr[i] <= 10^5
class Solution: def minSetSize(self, arr: List[int]) -> int: d = {} for i in arr: if i in d: d[i]+=1 else: d[i] = 1 d = sorted(d.items(), key = lambda x:x[1], reverse=True) print(d) total, count = 0, 0 for i in d: total += i[1] count+=1 if total >= len(arr)//2: return count
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ target,rem=divmod(sum(nums),k) if rem or max(nums)>target: return False n=len(nums) seen=[0]*n nums.sort(reverse=True) def dfs(k,index,current_sum): if k==1: return True if current_sum==target: return dfs(k-1,0,0) for i in range(index,n): if not seen[i] and current_sum+nums[i]<=target: seen[i]=1 if dfs(k,i+1,current_sum+nums[i]): return True seen[i]=0 return False return dfs(k,0,0)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): quotient = sum(nums)/k if quotient % 1 != 0: return False for num in nums: if num > quotient: return False if num == quotient: nums.remove(quotient) k -= 1 nums.sort(reverse=True) self.nums = nums self.quotient = quotient print(self.nums) answer = self.dfs([0]*len(nums), 0, k) return answer # print(answer) def dfs(self, visit, accu, k): if k == 1: # print(visit) return True for i in range(len(self.nums)): if not visit[i]: #print(visit) if self.nums[i] + accu < self.quotient: visit[i] = 1 if self.dfs(visit, self.nums[i] + accu, k): return True visit[i] = 0 if self.nums[i] + accu == self.quotient: visit[i] = 1 accu = self.nums[i] + accu return self.dfs(visit, 0, k-1) return False
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def partition(self, nums, target, current, pos, fill): if fill == 0: return True for i in range(pos, len(nums)): next = nums[:i] + nums[i+1:] if current + nums[i] == target: if self.partition(next, target, 0, 0, fill - 1): return True elif current + nums[i] < target: if self.partition(next, target, current + nums[i], i, fill): return True elif current == 0: return False return False def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ s = sum(nums) if s % k > 0: return False target = s // k return self.partition(nums, target, 0, 0, k)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): if sum(nums) % k or len(nums) < k: return False if k == 1: return True target, used = sum(nums) / k, [False for i in range(len(nums))] def dfs(start, sum_, k): if k == 1: return True if sum_ == target: return dfs(0, 0, k - 1) for i in range(start, len(nums)): if not used[i] and sum_ < target: used[i] = True if dfs(i + 1, sum_ + nums[i], k): return True used[i] = False return False return dfs(0, 0, k)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): if sum(nums) % k or len(nums) < k: return False if k == 1: return True target, used = sum(nums) / k, [False for i in range(len(nums))] def dfs(start, sum_, k): if k == 1: return True if sum_ == target: return dfs(0, 0, k - 1) for i in range(start, len(nums)): if not used[i] and sum_ < target: used[i] = True if dfs(i + 1, sum_ + nums[i], k): return True used[i] = False return False return dfs(0, 0, k)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ target, rem = divmod(sum(nums), k) if rem: return False def dfs(groups): if not nums: return True v = nums.pop() for i, group in enumerate(groups): if group + v <= target: groups[i] += v if dfs(groups): return True groups[i] -= v if not group: break nums.append(v) return False nums.sort() if nums[-1] > target: return False while nums and nums[-1] == target: k -= 1 nums.pop() return dfs([0] * k)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ total = sum(nums) if total%k != 0: return False target = total//k nums.sort() if nums[-1] > target: return False while nums and nums[-1] == target: nums.pop() k -= 1 return self.helper(nums, target, [0]*k) def helper(self, nums, target, dp): if not nums: return True num = nums.pop() for i in range(len(dp)): if dp[i] + num <= target: dp[i] += num if self.helper(nums, target, dp): return True dp[i] -= num if dp[i] == 0: break nums.append(num) return False
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ if not nums: return True if sum(nums) % k != 0: return False target = sum(nums) / k nums.sort() if nums[-1] > target: return False while nums and nums[-1] == target: nums.pop() k -= 1 def partition(nums, subsets, target): if not nums: return True selected = nums.pop() for i in range(len(subsets)): if subsets[i] + selected <= target: subsets[i] += selected if partition(nums, subsets, target): return True subsets[i] -= selected if subsets[i] == 0: # this line is important, otherwise TLE. # if subsets[i] is 0 then later subsets are all zeros. No need to try them all. break nums.append(selected) return False return partition(nums, subsets=[0]*k, target=target)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ total = sum(nums) if total%k!=0: return False target = total/k used = [False]*len(nums) nums = sorted(nums) # print(nums) def check(nums, k, cur, pos): # print(used, k, cur, pos) if k==1: return True for i in range(pos, -1, -1): if not used[i]: if nums[i]+cur<target: used[i] = True if check(nums, k, cur+nums[i], i-1): return True used[i] = False elif nums[i]+cur==target: used[i] = True if check(nums, k-1, 0, len(nums)-1): return True used[i] = False return False return check(nums, k, 0, len(nums)-1)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ target, rem = divmod(sum(nums), k) if rem: return False def search(groups): if not nums: return True v = nums.pop() for i, group in enumerate(groups): if group + v <= target: groups[i] += v if search(groups): return True groups[i] -= v if not group: break nums.append(v) return False nums.sort() if nums[-1] > target: return False while nums and nums[-1] == target: nums.pop() k -= 1 return search([0] * k)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution(object): def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ he = sum(nums) if he % k != 0: return False target = he // k visit = [0 for _ in range(len(nums))] def dfs(k,ind,cur,cnt): if k == 0:return True if cur == target and cnt > 0: return dfs(k-1,0,0,0) for i in range(ind,len(nums)): if not visit[i] and cur+nums[i] <= target: visit[i] = 1 if dfs(k,i+1,cur+nums[i],cnt+1): return True visit[i] = 0 return False return dfs(k,0,0,0)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ total = sum(nums) if total % k != 0: return False subsetTotal = total // k visited = [0] * len(nums) return self.helper(k, 0, 0, visited, nums, k, subsetTotal) def helper(self, remainingSets, index, s, visited, nums, k, subsetTotal): if remainingSets == 1: return True if s == subsetTotal: return self.helper(remainingSets - 1, 0, 0, visited, nums, k, subsetTotal) for i in range(index, len(nums)): if visited[i] == 0 and s + nums[i] <= subsetTotal: visited[i] = 1 if self.helper(remainingSets, i + 1, s + nums[i], visited, nums, k, subsetTotal): return True visited[i] = 0 return False
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ tot = sum(nums) if k <= 0 or tot % k != 0: return False visited = [0] * len(nums) def canPart(nums, visited, idx, curSum, k, target): if k == 1: return True if curSum == target: return canPart(nums, visited, 0, 0, k - 1, target) if curSum > target: return False for i in range(idx, len(nums)): if not visited[i]: visited[i] = 1 if canPart(nums, visited, i + 1, curSum + nums[i], k, target): return True visited[i] = 0 return False return canPart(nums, visited, 0, 0, k, tot / k)
Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Example 1: Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums. Note: 1 . 0 < nums[i] < 10000.
class Solution: def canPartitionKSubsets(self, nums, k): """ :type nums: List[int] :type k: int :rtype: bool """ if k <= 0: return False nums_sum = sum(nums) if nums_sum % k != 0: return False visited = [False] * len(nums) nums.sort(reverse=True) return self.canPartition(nums, visited, k, 0, 0, nums_sum/k) def canPartition(self, nums, visited, k, currentIndex, currentSum, target): if k == 1: return True if currentSum == target: return self.canPartition(nums, visited, k-1, 0, 0, target) for i in range(currentIndex, len(nums)): if visited[i] is False and currentSum + nums[i] <= target: visited[i] = True if(self.canPartition(nums, visited, k, i+1, currentSum + nums[i], target)): return True visited[i] = False return False
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: counters = [0] * (1 << 16) counters[0] = len(A) for num in A: mask = (~num) & ((1 << 16) - 1) sm = mask while sm != 0: counters[sm] += 1 sm = (sm - 1) & mask return sum(counters[num1 & num2] for num1 in A for num2 in A)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: d = defaultdict(int) for a in A: for b in A: d[a & b] += 1 return sum(d[ab] for c in A for ab in d if not(ab & c))
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import Counter class Solution(object): def countTriplets(self, A): c = Counter(x & y for x in A for y in A) return sum(c[xy] for xy in c for z in A if xy & z == 0)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: and_values = {} for x in A: for y in A: c = x & y if c in and_values: and_values[c] += 1 else: and_values[c] = 1 triplet_count = 0 for a in and_values: for z in A: if a & z == 0: triplet_count += and_values[a] return triplet_count
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import Counter from functools import lru_cache from itertools import product class Solution: def countTriplets(self, A: List[int]) -> int: @lru_cache(None) def count_and_zero(x): return sum(1 for a in A if a & x == 0) pair_and_count = Counter( x & y for x, y in product(A, A) ) return sum( count_and_zero(x) * cnt for x, cnt in list(pair_and_count.items()) )
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: memo = {} for i in A: for j in A: memo[i&j] = memo.get(i&j, 0)+1 res = 0 for num in A: for k in memo: if num&k==0: res += memo[k] return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: t=0 d={} for i in A: for j in A: a=i&j if a in d: d[a]+=1 else: d[a]=1 for k in d: for i in A: if k&i==0: t+=d[k] return t
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: count =collections.defaultdict(int) ret = 0 for i in A: for j in A: count[i & j] += 1 for i in A: for j in count: if i & j == 0: ret += count[j] return ret
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n=len(A) count=0 dic=collections.defaultdict(int) for i in range(n): for j in range(n): dic[(A[i]&A[j])]+=1 ans=0 # print(dic) for ele in A: for res in dic: if res&ele==0: ans+=dic[res] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: c = Counter(x&y for x in A for y in A) return sum([c[xy] for xy in c for z in A if xy&z == 0])
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: d = defaultdict(int) mask = (1<<16) - 1 for i in A: high = mask ^ i j = high while j: d[j] += 1 j = (j-1) & high d[0] += 1 res = 0 for i in A: for j in A: res += d[i&j] return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
# # @lc app=leetcode id=982 lang=python3 # # [982] Triples with Bitwise AND Equal To Zero # # https://leetcode.com/problems/triples-with-bitwise-and-equal-to-zero/description/ # # algorithms # Hard (54.38%) # Likes: 67 # Dislikes: 91 # Total Accepted: 5.5K # Total Submissions: 10.2K # Testcase Example: '[2,1,3]' # # Given an array of integers A, find the number of triples of indices (i, j, k) # such that: # # # 0 <= i < A.length # 0 <= j < A.length # 0 <= k < A.length # A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator. # # # # # Example 1: # # # Input: [2,1,3] # Output: 12 # Explanation: We could choose the following i, j, k triples: # (i=0, j=0, k=1) : 2 & 2 & 1 # (i=0, j=1, k=0) : 2 & 1 & 2 # (i=0, j=1, k=1) : 2 & 1 & 1 # (i=0, j=1, k=2) : 2 & 1 & 3 # (i=0, j=2, k=1) : 2 & 3 & 1 # (i=1, j=0, k=0) : 1 & 2 & 2 # (i=1, j=0, k=1) : 1 & 2 & 1 # (i=1, j=0, k=2) : 1 & 2 & 3 # (i=1, j=1, k=0) : 1 & 1 & 2 # (i=1, j=2, k=0) : 1 & 3 & 2 # (i=2, j=0, k=1) : 3 & 2 & 1 # (i=2, j=1, k=0) : 3 & 1 & 2 # # # # # Note: # # # 1 <= A.length <= 1000 # 0 <= A[i] < 2^16 # # # from collections import Counter class Solution: def countTriplets(self, A: List[int]) -> int: c = Counter(x & y for x in A for y in A) return sum(c[xy] for xy in c for z in A if xy & z == 0)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: l = len(A) Memo = {} for i in range(l): for j in range(i+1): t = A[i]&A[j] if t not in Memo: Memo[t] = 0 if i == j: Memo[t] += 1 else: Memo[t] += 2 r = 0 for a in A: for key in Memo: if key&a == 0: r += Memo[key] return r
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: d={} for i in A: for j in A: if(i&j in d): d[i&j]+=1 else: d[i&j]=1 c=0 for i in A: for j in d: if(i&j==0): c+=d[j] return c
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: tmp = {} for a in A: for b in A: if a&b in tmp: tmp[a&b]+=1 else: tmp[a&b]=1 ans = 0 for k, t in tmp.items(): for c in A: if c&k==0: ans +=t return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: mp = {} for i in A: for j in A: k = i & j mp[k] = mp.get(k, 0) + 1 result = 0 for i in A: for j in mp: if i & j == 0: result += mp[j] return result
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: counter = Counter() for a in A: for b in A: counter[a&b] += 1 res = 0 for a in A: for b in counter: if a&b==0: res += counter[b] return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: dic = defaultdict(int) res = 0 for i in A: for j in A: tmp = i&j dic[tmp] += 1 for i in A: for j in dic: if i&j == 0: res += dic[j] return res ''' class Solution: def countTriplets(self, A: List[int]) -> int: dic = defaultdict(int) res = 0 for i in range(len(A)): for j in range(len(A)): num = A[i] & A[j] dic[num] += 1 for i in range(len(A)): for j in dic: if A[i] & j == 0: res += dic[j] return res '''
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: cnt = collections.defaultdict(int) for i in A: for j in A: cnt[i&j]+=1 res = 0 for i in A: for j in cnt: if i & j == 0: res += cnt[j] return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: counts = defaultdict(int) for x in A: for y in A: counts[x & y] += 1 def dfs(z, xy, k): if k == -1: return counts[xy] answer = dfs(z, xy << 1, k - 1) if (z >> k & 1) == 0: answer += dfs(z, (xy << 1 | 1), k - 1) return answer answer = 0 for z in A: answer += dfs(z, 0, 16) return answer
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: counts = defaultdict(int) for x in A: for y in A: counts[x & y] += 1 def dfs(xy, z, k): if k == -1: return counts[xy] answer = dfs(xy << 1, z, k - 1) if (z >> k & 1) == 0: answer += dfs(xy << 1 | 1, z, k - 1) return answer answer = 0 for z in A: answer += dfs(0, z, 16) return answer
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: B = [bin(a)[2:] for a in A] M, N = len(B), max(list(map(len, B))) B = [b.zfill(N) for b in B] dic = collections.defaultdict(set) for i in range(M): for j in range(N): if B[i][j] == '1': dic[j].add(i) Venn = collections.defaultdict(list) cnt = 0 for j in range(N): if len(dic[j]): cnt += (len(dic[j])) ** 3 for i in range(j, 0, -1): for prv in Venn[i]: intersec = prv & dic[j] if len(intersec): cnt += ((-1) ** i) * (len(intersec)) ** 3 Venn[i + 1].append(intersec) Venn[1].append(dic[j]) return M ** 3 - cnt # # ans = 0 # n = len(A) # @lru_cache(None) # def dfs(i, pre): # if i == 4 and not pre: # return 1 # ans = 0 # for a in A: # if (i > 1 and not pre & a) or (i == 1 and not a): # ans += n ** (3 - i) # elif i < 3: # ans += dfs(i + 1, pre & a if i > 1 else a) # return ans # return dfs(1, None)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, nums): count_map = collections.Counter(i & j for i in nums for j in nums) return sum(count_map[key] for num in nums for key in count_map if num & key == 0)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: # O(2**16*n), since a&b<= a,b<= 2**16 dp = collections.defaultdict(int) for n1 in A: for n2 in A: dp[n1&n2]+=1 res = 0 for n in A: for k,v in dp.items(): if not k&n: res+=v return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: pairs = defaultdict(int) for a in A: for b in A: pairs[a & b] += 1 res = 0 for a in A: for p, cnt in pairs.items(): if not a & p: res += cnt return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: # O(N^2) two_and_count = collections.Counter() res = 0 for idx, x in enumerate(A): if x == 0: # x & x & x res += 1 # y & x & x -> 3 new_two_and = collections.Counter([x]) for idy in range(idx): if x & A[idy] == 0: res += 3 new_two_and[A[idy] & x] += 2 for v, c in two_and_count.items(): if x & v == 0: res += 3 * c two_and_count += new_two_and return res def countTriplets_II(self, A: List[int]) -> int: M = 3 N = 1 << 16 dp = [[0] * (N) for _ in range(M + 1)] dp[0][N - 1] = 1 for m in range(1, M + 1): for v in range(N): for a in A: dp[m][v & a] += dp[m - 1][v] return dp[M][0]
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: counter = collections.Counter() for i in A: for j in A: counter[i&j] += 1 result = 0 for k in A: for v in counter: if k & v == 0: result += counter[v] return result
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
import numpy as np class Solution: def countTriplets(self, A: List[int]) -> int: memo=dict() for i in range(len(A)): for j in range(i,len(A)): r=A[i]&A[j] memo[r]=memo.get(r,0)+(1 if i==j else 2) ret=0 for i in range(len(A)): for k in memo: if A[i]&k==0: ret+=memo[k] return ret
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: d={} res=0 for a in A: for b in A: t=a&b if t in d: d[t]+=1 else: d[t]=1 for a in A: for k,v in list(d.items()): if a&k==0: res+=v return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) cnt = collections.Counter() A = list(collections.Counter(A).items()) result = 0 for i, k1 in A: for j, k2 in A: cnt[i & j] += k1 * k2 cnt = list(cnt.items()) for i, k1 in A: if i == 0: result += k1 * n * n continue for j, k2 in cnt: if i & j == 0: result += k1 * k2 return result
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: # N = 1 << 16 # M = 3 # dp = [[0]*N for _ in range(M+1)] # dp[0][N - 1] = 1 # for i in range(M): # for k in range(N): # for a in A: # dp[i+1][k&a] += dp[i][k] # return dp[M][0] N = len(A) ans = 0 count = collections.Counter() for i in range(N): for j in range(N): count[A[i]&A[j]] += 1 for k in range(N): for v in count: if A[k] & v == 0: ans += count[v] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: umap = collections.Counter(A) n = len(A) mask = (1 << 16) - 1 for i in range(n): for j in range(i+1, n): key = A[i] & A[j] if key not in umap: umap[key] = 0 umap[key] += 2 result = 0 for a in A: d = (~a) & mask key = d result += umap.get(d, 0) while d > 0: d = (d-1)&key result += umap.get(d, 0) return result
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: N = len(A) ans = 0 count = collections.Counter() for i in range(N): for j in range(N): count[A[i] & A[j]] += 1 for k in range(N): for v in count: if A[k] & v == 0: ans += count[v] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) cnt = collections.Counter() result = 0 for i in A: for j in A: cnt[i & j] += 1 for i in A: for j, k in cnt.items(): if i & j == 0: result += k return result
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: cnt=0 d={} for i in range(len(A)): for j in range(len(A)): if A[i]&A[j] not in d: d[A[i]&A[j]]=1 else: d[A[i]&A[j]]+=1 for i in range(len(A)): for j in d: if A[i]&j==0: cnt+=d[j] return cnt
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
# class Solution: # def countTriplets(self, A: List[int]) -> int: # N, M = 1<<16, 3 # dp = [[0]*N for _ in range(M+1)] # dp[0][-1] = 1 # for m in range(M): # for n in range(N): # for a in A: # dp[m+1][a&n] += dp[m][n] # return dp[-1][0] class Solution: def countTriplets(self, A: 'List[int]') -> 'int': N = len(A) ans = 0 count = collections.Counter() for i in range(N): for j in range(N): count[A[i]&A[j]] += 1 for k in range(N): for v in count: if A[k] & v == 0: ans += count[v] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict from collections import Counter class Solution: def countTriplets(self, A: List[int]) -> int: combo = collections.Counter(x&y for x in A for y in A) res = 0 for a in A: for k,v in list(combo.items()): if a&k==0: res+=v return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: combo = collections.Counter(x&y for x in A for y in A) return sum(combo[k] for z in A for k in combo if z&k == 0)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) ans = 0 A_counts = defaultdict(lambda: 0) for num in A: A_counts[num] += 1 counts = defaultdict(lambda: 0) for n1, count1 in list(A_counts.items()): for n2, count2 in list(A_counts.items()): counts[n1&n2] += count1*count2 for n1, count1 in list(A_counts.items()): for n2, count2 in list(counts.items()): if n1 & n2 == 0: ans += count1*count2 return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import Counter class Solution: def countTriplets(self, A: List[int]) -> int: ## https://leetcode.com/problems/triples-with-bitwise-and-equal-to-zero/discuss/227309/C%2B%2B-naive-O(n-*-n) cnt = Counter() for a in A: for b in A: cnt[a&b] += 1 res = 0 for a in A: for k, v in cnt.items(): if a&k==0: res += v return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) ans = 0 A_counts = defaultdict(lambda: 0) for num in A: A_counts[num] += 1 counts = defaultdict(lambda: 0) for n1, count1 in list(A_counts.items()): for n2, count2 in list(A_counts.items()): counts[n1&n2] += count1*count2 for n in A: for num, count in list(counts.items()): if num & n == 0: ans += count return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: count=0 dic=dict() for i in range(len(A)): for j in range(i,len(A)): r=A[i]&A[j] dic[r]=dic.get(r,0)+(1 if i==j else 2) result=0 for i in range(len(A)): for k in dic: if A[i]&k==0: result+=dic[k] return result
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: counters = defaultdict(int) counters[0] = len(A) for num in A: mask = (~num) & ((1 << 16) - 1) sm = mask while sm != 0: counters[sm] += 1 sm = (sm - 1) & mask return sum(counters[num1 & num2] for num1 in A for num2 in A)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: N = len(A) ans = 0 count = dict() for i in range(N): for j in range(N): tmp = A[i]&A[j] if tmp not in count: count[tmp] = 1 else: count[tmp] += 1 for k in range(N): for v in count: if A[k] & v == 0: ans += count[v] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: d={} ans=0 for i in range(len(A)): for j in range(len(A)): a=A[i]&A[j] d[a]=d.get(a,0)+1 for i in range(len(A)): for j in list(d.keys()): if A[i]&j==0: ans+=d[j] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
import collections class Solution: def countTriplets(self, A: List[int]) -> int: N = len(A) ans = 0 count = collections.Counter() for i in range(N): for j in range(N): count[A[i]&A[j]] += 1 for k in range(N): for v in count: if A[k] & v == 0: ans += count[v] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) C = defaultdict(int) for i in range(n): C[A[i]] += 1 for j in range(i + 1, n): C[A[i] & A[j]] += 2 return sum(c * sum((x & y) == 0 for y in A) for x, c in C.items())
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) C = defaultdict(int) for i, x in enumerate(A): C[x] += 1 for j in range(i + 1, n): C[x & A[j]] += 2 return sum(c * sum((x & y) == 0 for y in A) for x, c in C.items())
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) C = defaultdict(int) for i in range(n): C[A[i]] += 1 for j in range(i + 1, n): C[A[i] & A[j]] += 2 res = 0 for x, c in C.items(): res += c * sum((x & y) == 0 for y in A) return res
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: memo = dict() for i in range(len(A)): for j in range(i,len(A)): r=A[i]&A[j] memo[r]=memo.get(r,0)+(1 if i==j else 2) ret=0 for i in range(len(A)): for k in memo: if A[i]&k==0: ret+=memo[k] return ret
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) n2 = n*n dp = {} ways = 0 for i in range(n): for j in range(n): res = A[i] & A[j] dp[res] = dp.get(res, 0) + 1 for i in range(n): for tgt, ct in dp.items(): if A[i] & tgt == 0: ways += ct #print(A[i], tgt, ct) return ways
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: n = len(A) ans = 0 counts = defaultdict(lambda: 0) for i in range(n): for j in range(n): counts[A[i]&A[j]] += 1 for k in range(n): for num, count in list(counts.items()): if num & A[k] == 0: ans += count return ans # (a & b) & c== 0 # # 0010 # # 0001 # # 1101 # # 0011 # # 1110
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import defaultdict class Solution: def countTriplets(self, A: List[int]) -> int: mp = defaultdict(int) # key: elem_value, value: number_of_complement_elements mask = (1 << 16) - 1 for x in A: y = mask ^ x s = y while s: mp[s] += 1 s = (s - 1) & y n = len(A) cnt = 0 for i in range(n): if A[i] == 0: cnt += n * n continue for j in range(n): if A[i] & A[j] == 0: cnt += n continue cnt += mp[A[i] & A[j]] return cnt
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: from collections import defaultdict dic=defaultdict(int) n=len(A) dp=defaultdict(int) for i in range(n): for j in range(n): dic[(i,j)] = A[i]&A[j] dp[A[i]&A[j]]+=1 ans=0 for i in range(n): for x in dp: if x&A[i]==0: ans+=dp[x] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: d = dict() for i in range(len(A)): for j in range(len(A)): product = A[i] & A[j] if product in d: d[product]+=1 else: d[product] = 1 ans = 0 for i in range(len(A)): for k,v in d.items(): if A[i]& k == 0: ans+=v return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: c = Counter(x & y for x in A for y in A) return sum(c[xy] for xy in c for z in A if xy & z == 0) # bitsOneDict = {\"@\": 20} # ans = 0 # ALen = len(A) # for j, num in enumerate(A): # i = 0 # pointer = bitsOneDict # while num > 0: # if num & 1: # if i not in pointer: # pointer[i] = {} # if \"@\" not in pointer: # pointer[\"@\"] = i # else: # pointer[\"@\"] = max(i, pointer[\"@\"]) # pointer = pointer[i] # num >>= 1 # i += 1 # if \"$\" in pointer: # pointer[\"$\"].add(j) # else: # pointer[\"$\"] = set([j]) # if \"@\" not in pointer: # pointer[\"@\"] = i+1 # else: # pointer[\"@\"] = max(i+1, pointer[\"@\"]) # for j1, num1 in enumerate(A): # for j2 in range(j1, ALen): # num2 = A[j2] # num12 = num1 & num2 # if num12 == 0: # if j1 == j2: # ans += ALen # else: # ans += ALen*2 # else: # pointers = [bitsOneDict] # i = 0 # subAns = set() # while i < 16: # if num12 & 1 == 0: # newPointers = [] # for k in range(len(pointers)-1, -1, -1): # pointer = pointers[k] # if i in pointer: # newPointers.append(pointer[i]) # else: # if i > pointer[\"@\"]: # if \"$\" in pointer: # subAns |= pointer[\"$\"] # pointers.pop(k) # pointers += newPointers # num12 >>= 1 # i += 1 # for pointer in pointers: # if \"$\" in pointer: # subAns |= pointer[\"$\"] # if j1 == j2: # ans += len(subAns) # else: # ans += len(subAns)*2 # return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: # ans = 0 n = len(A) @lru_cache(None) def dfs(i, pre): if i == 4 and not pre: return 1 ans = 0 for a in A: if (i > 1 and not pre & a) or (i == 1 and not a): ans += n ** (3 - i) elif i < 3: ans += dfs(i + 1, pre & a if i > 1 else a) return ans return dfs(1, None)
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: memo=dict() for i in range(len(A)): for j in range(i,len(A)): r=A[i]&A[j] memo[r]=memo.get(r,0)+(1 if i==j else 2) ret=0 for i in range(len(A)): for k in memo: if A[i]&k==0: ret+=memo[k] return ret
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
from collections import Counter class Solution: def countTriplets(self, A: List[int]) -> int: c = Counter() for val in A: val = (~val) & 0xffff mask = val c[val] += 1 while val > 0: val = (val-1) & mask c[val] += 1 ans = 0 for v1 in A: for v2 in A: val = v1 & v2 if val in c: ans += c[val] return ans
Given an array of integers A, find the number of triples of indices (i, j, k) such that: 0 <= i < A.length 0 <= j < A.length 0 <= k < A.length A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.   Example 1: Input: [2,1,3] Output: 12 Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2   Note: 1 <= A.length <= 1000 0 <= A[i] < 2^16
class Solution: def countTriplets(self, A: List[int]) -> int: tot = 1<<16 cnt = [0 for _ in range(tot)] for a in A: for b in A: cnt[a&b]+=1 ans = 0 for e in A: s = 0 while s<tot: if s&e==0: ans += cnt[s] s += 1 else: s += (e&s) return ans