Program to check whether list is strictly increasing or strictly decreasing in Python

Suppose we have a list of numbers; we have to check whether the list is strictly increasing or strictly decreasing. A list is strictly increasing if each element is larger than the previous one, and strictly decreasing if each element is smaller than the previous one.

So, if the input is like nums = [10, 12, 23, 34, 55], then the output will be True, as all elements are distinct and each element is larger than the previous one, so this is strictly increasing.

Algorithm

To solve this, we will follow these steps ?

• If size of nums <= 2, then return True (trivially strictly ordered)
• If all elements in nums are not distinct, then return False
• Create a sorted version of the list
• Return True when nums is same as sorted list or nums is same as sorted list in reverse order, otherwise False

Implementation

Let us see the following implementation to get better understanding ?

class Solution:
    def solve(self, nums):
        if len(nums) <= 2:
            return True
        if len(set(nums)) != len(nums):
            return False
        ordered = sorted(nums)
        return nums == ordered or nums == ordered[::-1]

ob = Solution()
print(ob.solve([10, 12, 23, 34, 55]))
print(ob.solve([55, 34, 23, 12, 10]))
print(ob.solve([10, 20, 15, 30]))
print(ob.solve([5, 5, 6]))

True
True
False
False

Alternative Approach Using Direct Comparison

We can also check directly by comparing adjacent elements ?

def is_strictly_ordered(nums):
    if len(nums) <= 2:
        return True
    
    # Check if strictly increasing
    increasing = all(nums[i] < nums[i + 1] for i in range(len(nums) - 1))
    
    # Check if strictly decreasing
    decreasing = all(nums[i] > nums[i + 1] for i in range(len(nums) - 1))
    
    return increasing or decreasing

# Test cases
test_cases = [
    [10, 12, 23, 34, 55],  # Strictly increasing
    [55, 34, 23, 12, 10],  # Strictly decreasing
    [10, 20, 15, 30],      # Neither
    [5, 5, 6],             # Not strict (duplicate)
    [1, 2]                 # Trivial case
]

for case in test_cases:
    print(f"{case} ? {is_strictly_ordered(case)}")

[10, 12, 23, 34, 55] ? True
[55, 34, 23, 12, 10] ? True
[10, 20, 15, 30] ? False
[5, 5, 6] ? False
[1, 2] ? True

Comparison

Conclusion

Both approaches work effectively to check if a list is strictly increasing or decreasing. The direct comparison method is more efficient with O(n) time complexity, while the sorting approach offers cleaner logic but requires O(n log n) time.