Finding the number of factors, choosing x to be the max power of 2

z-problems/codeforces/1981A.py

@@ -0,0 +1,190 @@
+"""
+செயல் பேசும் ஆழம் இங்கே சொற்கள் பேசுமா?
+
+Focus, Determination and Sheer-Will
+
+The woods are lovely, dark and deep,
+But I have promises to keep,
+And miles to go before I sleep,
+And miles to go before I sleep.
+"""
+
+# region imports
+
+import os, sys, math, cmath, time, collections
+from math import ceil, floor, log, log2, sqrt, gcd, factorial, pow, pi, log10
+from collections import deque, Counter, OrderedDict, defaultdict
+from bisect import bisect, bisect_left, bisect_right, insort, insort_left, insort_right
+from heapq import nsmallest, nlargest, heapify, heappop, heappush, heapreplace
+from itertools import accumulate, permutations, combinations, combinations_with_replacement
+from io import BytesIO, IOBase
+from functools import reduce
+
+
+# endregion
+
+# region solution
+
+
+def solve() -> None:
+    l, r = input_as_array()
+    x = 1
+    while x <= r:
+        x <<= 1
+    x >>= 1
+    print(int(log2(x)))
+
+# endregion
+
+# region testcase
+def main() -> None:
+    if os.path.exists("data.in"):
+        sys.stdin = open("data.in", "r")
+        sys.stdout = open("data.out", "w")
+
+    start_time = time.time()
+    testcases = int(input())
+
+    for i in range(testcases):
+        solve()
+        debug('-')
+
+    if os.path.exists("data.in"):
+        print(f"Time Elapsed: {time.time() - start_time} seconds")
+        sys.stdout.close()
+
+
+# endregion
+
+# region debug
+
+def input_as_array() -> list[int]:
+    return list(map(int, input().split()))
+
+
+def debug(char) -> None:
+    if os.path.exists("data.in"):
+        print(char * 25)
+
+
+def debug2(value) -> None:
+    if os.path.exists("data.in"):
+        print(value)
+
+
+# endregion
+
+# region math
+
+MOD = 1000000007
+# MOD=998244353
+alpha = "abcdefghijklmnopqrstuvwxyz"
+alpha = [chr(c) for c in range(ord("A"), ord("Z") + 1)]
+alpha_map = {}
+cnt = 1
+for c in alpha:
+    alpha_map[c] = cnt
+    cnt += 1
+
+def copy2d(lst):
+    return [x[:] for x in lst]  # Copy 2D list... Avoid Using Deepcopy
+
+
+def no_of_digits(num):
+    return 0 if num <= 0 else int(math.log10(num)) + 1
+
+
+def powm(num, power, mod=MOD):
+    return pow(num, power, mod)
+
+
+def isPowerOfTwo(x):
+    return x and (not (x & (x - 1)))
+
+
+def LSB(num):
+    """Returns Least Significant Bit of a number (Rightmost bit) in O(1)"""
+    return num & -num
+
+
+def MSB(num):
+    """Returns Most Significant Bit of a number (Leftmost bit) in O(logN)"""
+    if num <= 0:
+        return 0
+    ans = 1
+    num >>= 1
+    while num:
+        num >>= 1
+        ans <<= 1
+    return ans
+
+
+def gcd(x, y):
+    while y:
+        x, y = y, x % y
+    return x
+
+
+def lcm(x, y):
+    return (x * y) // gcd(x, y)
+
+
+# endregion
+
+# region fastio
+
+BUFSIZE = 8192
+
+
+class FastIO(IOBase):
+    newlines = 0
+
+    def __init__(self, file):
+        self._file = file
+        self._fd = file.fileno()
+        self.buffer = BytesIO()
+        self.writable = "x" in file.mode or "r" not in file.mode
+        self.write = self.buffer.write if self.writable else None
+
+    def read(self):
+        while True:
+            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
+            if not b:
+                break
+            ptr = self.buffer.tell()
+            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
+        self.newlines = 0
+        return self.buffer.read()
+
+    def readline(self):
+        while self.newlines == 0:
+            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
+            self.newlines = b.count(b"\n") + (not b)
+            ptr = self.buffer.tell()
+            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
+        self.newlines -= 1
+        return self.buffer.readline()
+
+    def flush(self):
+        if self.writable:
+            os.write(self._fd, self.buffer.getvalue())
+            self.buffer.truncate(0), self.buffer.seek(0)
+
+
+class IOWrapper(IOBase):
+    def __init__(self, file):
+        self.buffer = FastIO(file)
+        self.flush = self.buffer.flush
+        self.writable = self.buffer.writable
+        self.write = lambda s: self.buffer.write(s.encode("ascii"))
+        self.read = lambda: self.buffer.read().decode("ascii")
+        self.readline = lambda: self.buffer.readline().decode("ascii")
+
+
+sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
+input = lambda: sys.stdin.readline().rstrip("\r\n")
+
+# endregion
+
+if __name__ == "__main__":
+    main()