Hi everyone, in this article we’ll guide you through the Python program to print from 1 to N without loops [Problem Link]. Comprehensively with its examples, 2 approaches, their codes & explanation. So let’s begin.
Examples of Python Program to Print from 1 to N Without Loops:
Example 1:
Input: n = 10
Output: 1 2 3 4 5 6 7 8 9 10
Example 2:
Input: n = 5
Output: 1 2 3 4 5
Example 3:
Input: n = 1
Output: 1
Constraints: 1 <= n <= 1000
Also read about the Python Program to Print Divisors/Factors of an Integer.
1.Recursion Solution (Without Backtracking)
This solution utilizes recursion to print numbers from 1 to N without using loops. The function relies on the recursive nature of function calls to iterate over the range of numbers.
Instead of iterating explicitly with a loop, the recursion takes care of the repetition by calling the same function with updated parameters.
Key Steps in the Approach:
- Base Case:
- The recursion stops when the current value of “i“ exceeds “n“
- This ensures that the function terminates and avoids infinite recursion
- Recursive Call:
- In each call, the current value of “i“ is printed
- The function is then called recursively with i+1, effectively moving to the next number
- Wrapper Function:
- A wrapper function (printNos) initializes the recursion by calling the recursive function (func) with the starting value i=1
Code:
class Solution:
def func(self, i, n):
if i > n: # Base case: stop recursion when i exceeds n
return
print(i, end=" ") # Print the current number
self.func(i + 1, n) # Recursive call with the next number
def printNos(self, n):
self.func(1, n) # Start recursion from 1 to n
Code Explanation:
- Recursive Function (func):
- Parameters:
- i: The current number to be printed
- n: The maximum number to print
- Logic:
- If i>n, the function terminates (base case)
- Otherwise, it prints i and recursively calls itself with i+1
- Parameters:
- Wrapper Function (printNos):
- Initializes the recursive process by calling func(1, n)
- Starts printing from 1 up to n
Dry Run:
Complexity Analysis:
Time Complexity: The function makes “n” recursive calls, where each call performs a constant amount of work (printing and updating parameters).
- Time Complexity: O(n)
Space Complexity: Each recursive call adds a frame to the call stack. For “n” recursive calls, the space complexity is proportional to “n”.
- Space Complexity: O(n)
Advantages of Using Recursion:
- Eliminates Loops: This approach adheres to the problem’s requirement of avoiding loops.
- Simplicity: The recursive function mirrors the iterative logic, making it easy to understand and implement.
Disadvantages:
- Stack Usage: Recursive solutions consume more memory due to stack usage, making them less efficient for very large “n”.
- Risk of Stack Overflow: For extremely large “n”, the solution may exceed the recursion depth limit, causing a stack overflow.
Learn Extraction of Digits in Python | Explained Step-by-Step.
2.Recursion Solution (With Backtracking)
This solution uses backtracking to print numbers from 1 to N without using loops. Unlike the standard recursive approach, where numbers are printed during the forward recursion phase, this method delays printing until the recursion starts “backtracking.”
This technique ensures numbers are printed in the correct order while adhering to the problem’s constraints.
Key Steps in the Approach:
- Recursive Functionality:
- Start with the largest number (N)
- Recursively call the function with the next smaller number (i−1)
- When the base case is reached, the recursion stops
- Print numbers while backtracking, ensuring they are printed in ascending order
- Base Case:
- The recursion stops when i<1, ensuring no further function calls are made
- Wrapper Function:
- A wrapper function (printNos) initializes the process by calling the recursive function (func) with i=N
Code:
class Solution:
def func(self, i, n):
if i < 1: # Base case: stop recursion when i is less than 1
return
self.func(i - 1, n) # Recursive call with the next smaller number
print(i, end=" ") # Print the number during backtracking
def printNos(self, n):
self.func(n, n) # Start recursion with n
Code Explanation:
- Recursive Function (func):
- Parameters:
- i: The current number being processed
- n: The original upper limit of the range (not used actively in the logic but passed for consistency)
- Logic:
- If i<1, the function terminates (base case)
- Otherwise, the function calls itself with i−1 (moves toward the base case)
- After the recursive call, the current number iii is printed during the backtracking phase
- Parameters:
- Wrapper Function (printNos):
- Initializes the recursion by calling func(n, n), starting the process with i=N
Dry Run:
Complexity Analysis:
- Time Complexity: The function makes “n” recursive calls, where each call performs a constant amount of work (printing or making a recursive call).
- Time Complexity: O(n)
- Space Complexity: Each recursive call adds a frame to the call stack. For “n” recursive calls, the space complexity is proportional to “n”.
- Space Complexity: O(n)
Advantages of Using Backtracking:
- Order Control: By printing during backtracking, the order of output (1 to n) is maintained naturally.
- Adheres to Constraints: The solution avoids loops while ensuring correctness.
- Logical Clarity: Separating the recursive phase (function calls) from the backtracking phase (printing) improves code readability.
Disadvantages:
- Stack Usage: Similar to standard recursion, this method uses additional memory for the call stack, making it less efficient for very large “n”.
- Risk of Stack Overflow: For extremely large “n”, exceeding the recursion depth limit may lead to stack overflow errors.