Given two positive integers a and b, the task is to write a program in python to find all pairs of consecutive odd numbers which are smaller than the first number a and their sum should be greater than the second number b.
Examples:
Input: a = 60 b = 100 Output: Pairs of consecutive number are: 51 , 53 53 , 55 55 , 57 57 , 59 Input: a = 20 b = 200 Output: None
Approach:
Two numbers are given and then check if they are a positive integer and checked for the first number to be greater than the half of the second number. Then we will check for odd positive integer and assigned in a variable a. In the while statement, pairs of the odd consecutive integers are found and printed.
Example 1:
Python3
# input first and second numbera = 60b = 100print('a =', a)print('b =', b)# check the first number should be greater# than the half of second number and both number# should be positive integerif(a > 0 and b > 0 and a > b/2): # to ensure value in firstNum variable # must be odd positive integer if(a % 2 == 0): a -= 1 else: a -= 2 b //= 2 print("Pairs of consecutive number are:") # find the pairs of odd # consecutive positive integer while(b <= a): if(b % 2 != 0): x = b if(x + 2 <= a): print(x, ',', x+2) b += 1else: print("None") |
Output:
a = 60 b = 100 Pairs of consecutive number are: 51 , 53 53 , 55 55 , 57 57 , 59
Time complexity: O(n)
Auxiliary space: O(1)
Example 2:
Python3
# input first and second numbera = 20b = 200print('a =', a)print('b =', b)# check the first number should be greater# than the half of second number and both number# should be positive integerif(a > 0 and b > 0 and a > b/2): # to ensure value in firstNum variable # must be odd positive integer if(a % 2 == 0): a -= 1 else: a -= 2 b //= 2 print("Pairs of consecutive number are:") # find the pairs of odd # consecutive positive integer while(b <= a): if(b % 2 != 0): x = b if(x + 2 <= a): print(x, ',', x+2) b += 1else: print("None") |
Output:
a = 20 b = 200 None
Complexity analysis for all examples :
Time complexity: O(n) where n is the length of the string.
Auxiliary Space: O(1)
Iterative Search for Consecutive Odd Integer Pairs
Steps:
- Iterate through all odd integers from 1 to a-1.
- For each odd integer i, check if the next odd integer i+2 is also less than a.
- If i and i+2 are both less than a, check if their sum is greater than b.
- If the sum of i and i+2 is greater than b, add the pair (i, i+2) to a list of pairs.
- Return the list of pairs.
Python3
def find_pairs(a, b): pairs = [] for i in range(1, a-1, 2): if i+2 < a: if i + i+2 > b: pairs.append((i, i+2)) return pairsa = 60b = 100pairs = find_pairs(a, b)print("Pairs of consecutive number are:")for pair in pairs: print(pair[0], ",", pair[1]) |
Pairs of consecutive number are: 51 , 53 53 , 55 55 , 57 57 , 59
The time complexity of this approach is O(a).
The auxiliary space required is O(1)
