1.1 KiB
Description Given an array X of positive integers, its elements are to be transformed by running the following operation on them as many times as required:
if X[i] > X[j] then X[i] = X[i] - X[j]
When no more transformations are possible, return its sum ("smallest possible sum").
For instance, the successive transformation of the elements of input X = [6, 9, 21] is detailed below:
X_1 = [6, 9, 12] # -> X_1[2] = X[2] - X[1] = 21 - 9 X_2 = [6, 9, 6] # -> X_2[2] = X_1[2] - X_1[0] = 12 - 6 X_3 = [6, 3, 6] # -> X_3[1] = X_2[1] - X_2[0] = 9 - 6 X_4 = [6, 3, 3] # -> X_4[2] = X_3[2] - X_3[1] = 6 - 3 X_5 = [3, 3, 3] # -> X_5[1] = X_4[0] - X_4[1] = 6 - 3 The returning output is the sum of the final transformation (here 9).
Example solution([6, 9, 21]) #-> 9 Solution steps: [6, 9, 12] #-> X[2] = 21 - 9 [6, 9, 6] #-> X[2] = 12 - 6 [6, 3, 6] #-> X[1] = 9 - 6 [6, 3, 3] #-> X[2] = 6 - 3 [3, 3, 3] #-> X[1] = 6 - 3 Additional notes: There are performance tests consisted of very big numbers and arrays of size at least 30000. Please write an efficient algorithm to prevent timeout.