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20 def maximum3(a, b, c): 21 """Computes maximum of given three numbers. 22 23 >>> maximum3(2, 3, 5) 24 5 25 >>> maximum3(12, 3, 5) 26 12 27 >>> maximum3(2, 13, 5) 28 13 29 """

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1 def number_of_elements_equal_to_the_maximum(): 2 inputs = [] 3 number = None 4 while number is None or number != 0: 5 number = int(input()) 6 inputs.append(number) 7 sorted_inputs = sorted(inputs, reverse=True) 8 max_value = sorted_inputs[0] 9 count = 0 10 for element in sorted_inputs: 11 if element == max_value: 12 count += 1 13 else: 14 break 15 print(count)

1 def find_integer(f): 2 """Finds a (hopefully large) integer n such that f(n) is True and f(n + 1) 3 is False. Runs in O(log(n)). 4 5 f(0) is assumed to be True and will not be checked. May not terminate unless 6 f(n) is False for all sufficiently large n. 7 """ 8 # We first do a linear scan over the small numbers and only start to do 9 # anything intelligent if f(4) is true. This is because it's very hard to 10 # win big when the result is small. If the result is 0 and we try 2 first 11 # then we've done twice as much work as we needed to! 12 for i in range(1, 5): 13 if not f(i): 14 return i - 1 15 16 # We now know that f(4) is true. We want to find some number for which 17 # f(n) is *not* true. 18 # lo is the largest number for which we know that f(lo) is true. 19 lo = 4 20 21 # Exponential probe upwards until we find some value hi such that f(hi) 22 # is not true. Subsequently we maintain the invariant that hi is the 23 # smallest number for which we know that f(hi) is not true. 24 hi = 5 25 while f(hi): 26 lo = hi 27 hi *= 2 28 29 # Now binary search until lo + 1 = hi. At that point we have f(lo) and not 30 # f(lo + 1), as desired.. 31 while lo + 1 < hi: 32 mid = (lo + hi) // 2 33 if f(mid): 34 lo = mid 35 else: 36 hi = mid 37 return lo

4 def find_max_subarray(numbers): 5 max_till_here = [0]*len(numbers) 6 max_value = 0 7 for i in range(len(numbers)): 8 max_till_here[i] = max(numbers[i], max_till_here[i-1] + numbers[i]) 9 max_value = max(max_value, max_till_here[i]) 10 return max_value