Given two integers L and R which denotes a range, the task is to find the largest co-prime set of integers in range L to R.
Examples:
Input: L = 10, R = 25
Output: 10 11 13 17 19 21 23Input: L = 45, R = 57
Output: 45 46 47 49 53
Approach: The idea is to iterate from L to R and try to place the integer in a set such that the Greatest common divisor of the set remains 1. This can be done by storing the LCM of the set and each time before adding the element into the set check that the GCD of the number with LCM of the set remains 1. Finally, find the largest such set of the integers.
For Example:
Let L = 10, R = 14
Element 10:
// Co-prime Sets
S = {{10}},
LCM of Co-prime sets
A = {10}
Element 11:
// Element 11 can be added to
// the first set
S = {{10, 11}}
A = {110}
Element 12:
S = {{10, 11}, {12}}
A = {110, 12}
Element 13:
S = {{10, 11, 13}, {12}}
A = {1430, 12}
Element 14:
S = {{10, 11, 13}, {12}, {14}}
A = {1430, 12, 14}
Python
# Python implementation to find # the largest co-prime set in a # given range import math # Function to find the largest # co-prime set of the integers def findCoPrime(n, m): # Initialize sets # with starting integers a =[n] b =[[n]] # Iterate over all the possible # values of the integers for i in range(n + 1, m + 1): # lcm of each list in array # 'b' stored in list 'a' # so go through list 'a' for j in range(len(a)): # if there gcd is 1 then # element add in that # list corresponding to b if math.gcd(i, a[j])== 1: # update the new lcm value q =(i * a[j])//math.gcd(i, a[j]) r = b[j] r.append(i) b[j]= r a[j]= q else: a.append(i) b.append([i]) maxi = [] for i in b: if len(i) > len(maxi): maxi = i print(*maxi) # Driver Code if __name__ == "__main__": n = 10 m = 14 findCoPrime(n, m) |
10 11 13
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