414. Third Maximum Number
Problem type - Array
🧩 Problem
🎯 Strategy
Understand the concept
In this problem, we are going to compare the array's value and find the third biggest number.
As we did with other problems, we will approach this in two different ways to achieve the same goal.
Regular approach
max() approach
Let's approach this by setting and comparing each number as we loop through the array.
We will set the first array item as the first maximum and two other variables to -inf. By doing so, we can satisfy the constraints(-2^31 <= n <= 2^31 - 1).
def thirdMax(self, nums: List[int]) -> int:
max1 = nums[0]
max2 = float('-inf')
max3 = float('-inf')
...Then, set the edge case checker that checks if the array length is less than three. If the array length is three or longer, we iterate through the array. If the array length is less than three, we return the max number of the array.
def thirdMax(self, nums: List[int]) -> int:
max1 = nums[0]
max2 = float('-inf')
max3 = float('-inf')
if len(nums) < 3:
return max(nums)
for i in range(len(nums)):
...Inside the loop, we set the temporary variable num to track the current nums[i] value. If the current value num is bigger than max1, we set max3 = max2, max2 = max1, and max1 = num. What happens here is the new biggest number pushes other values.
If the number satisfies the max2 < num < max1 condition, we have to set max3 = max2, max2 = num.
Otherwise, if the num is between num2 and num3, we set the num to num3.
def thirdMax(self, nums: List[int]) -> int:
...
for i in range(len(nums)):
num = nums[i]
if num > max1:
max3 = max2
max2 = max1
max1 = num
elif num > max2 and num < max1:
max3 = max2
max2 = num
elif num > num3 and num < num2:
max3 = num
...Lastly, return the max3, if the max3 is not the initial value -inf. In the case of max3 == -inf, we will return max1.
def thirdMax(self, nums: List[int]) -> int:
...
for i in range(len(nums)):
num = nums[i]
if num > max1:
max3 = max2
max2 = max1
max1 = num
elif num > max2 and num < max1:
max3 = max2
max2 = num
elif num > num3 and num < num2:
max3 = num
return max3 if max3 != float('-inf') else max1The time complexity is O(n) because the function iterates through the array only once with a single loop.
The space complexity is O(1), as the code uses a constant amount of extra space regardless of the input size. The variables max1, max2, and max3 are integers, and the function doesn't use any additional data structure.
Pythonic approach
set() approach
In Python, we have a set function to deduct duplicated values.
Similar to the previous solution, we will set the space for the -inf value and make a variable for a new list with a set() function.
def thirdMax(self, nums: List[int]) -> int:
n = list(set(nums))
T = [float('-inf')] * 3
...Then, we will loop through the new array n, to compare three values.
This time, we will compare the value from the back. No matter how long the array is, the T[2] is always the right-most number, which is the largest number.
def thirdMax(self, nums: List[int]) -> int:
n = list(set(nums))
T = [float('-inf')] * 3
for i in n:
if i > T[2]:
T = [T[1], T[2], i]
...Then, we check if i is greater than T[1]. If i is bigger than T[1], The list order will change.
If the i is greater than T[0], we set the i's position at the first place of the array.
Lastly, we return T[0] if it is not -inf, where the -inf is the initial value. If T[0] is -inf, it means the array length is less than three. Otherwise, we will return T[0], which is the third max.
def thirdMax(self, nums: List[int]) -> int:
n = list(set(nums))
T = [float('-inf')] * 3
for i in n:
if i > T[2]:
T = [T[1], T[2], i]
elif i > T[1]:
T = [T[1], i, T[2]]
elif i > T[0]:
T = [i, T[1], T[2]]
return T[0] if T[0] != float('-inf') else T[2]The time complexity is O(n) because the n = list(set(nums)) part has a time complexity of O(n) in the worst case. Therefore, the overall time complexity is linear with respect to the size of the input array.
The space complexity is O(n) where the n is the length of the input array nums. The set() operation creates a new list with distinct elements. In the worst case, where all elements are distinct, the space complexity is O(n). The additional space used by the list T is constant and doesn't depend on the input size.
📌 Thoughts
I couldn't solve this problem due to the float('-inf'). The concept of float('-inf') was new to me, and I applied the swap technique I learned previously, but it didn't work well.
Learning new concepts is always good; after two more questions, the first chapter will be done. I will finish the first chapter in the next post and move forward.
💻 Solution
max() approach
def thirdMax(self, nums: List[int]) -> int:
max1 = nums[0]
max2 = float('-inf')
max3 = float('-inf')
if len(nums) < 3:
return max(nums)
for i in nums:
num = nums[i]
if num > max1:
max3 = max2
max2 = max1
max1 = num
elif num > max2 and num < max1:
max3 = max2
max2 = num
elif num > max3 and num < max2:
max3 = num
return max3 if max3 != float('-inf') else max1set() approach
def thirdMax(self, nums: List[int]) -> int:
n = list(set(nums))
T = [float('-inf')] * 3
for i in n:
if i > T[2]:
T = [T[1], T[2], i]
elif i > T[1]:
T = [T[1], i, T[2]]
elif i > T[0]:
T = [i, T[1], T[2]]
return T[0] if T[0] != float('-inf') else T[2]