Largest Number Leetcode Problem 179 [Python Solution]
Welcome to another coding session!
Today, we're going to tackle the Largest Number problem.
In this LeetCode challenge, we are presented with a list of non-negative integers and our goal is to arrange them in such a way that they form the largest number.
The catch is that the result might be too large for standard integer representation, so we need to return it as a string.
Let's begin by examining the problem statement and understanding its constraints.
Problem Overview
Given a list of non-negative integers nums, we are tasked with arranging them to create the largest possible number and returning it as a string.
Example 1:
– Input: nums = [10, 2]
– Output: "210"
Example 2:
– Input: nums = [3, 30, 34, 5, 9]
– Output: "9534330"
Understanding Constraints
Before diving into the solution, it's crucial to understand the constraints of the problem.
This helps us optimize our approach.
In this case, the constraints are as follows:
– 1 <= nums.length <= 100
– 0 <= nums[i] <= 10^9
Largest Number LeetCode Problem Solution
To solve this problem efficiently, we need to devise a plan.
The key idea here is to implement a custom comparison function to sort the numbers.
We want the numbers with the highest significance to appear first, creating the largest possible number.
Let's break down the solution into steps.
1. Bruteforce Approach
The naive approach is to generate all possible permutations of the given numbers and find the one that results in the largest number.
However, this approach is impractical for larger inputs as it leads to an enormous number of permutations.
for each permutation of nums:
convert each number to a string
concatenate them
convert the result to an integer
track the maximum result
return the maximum result as a string
While the bruteforce approach is conceptually simple, it's highly inefficient for larger inputs.
2. Efficient Approach with Custom Comparison Function
A more efficient approach is to use a custom comparison function during the sorting process.
The idea is to compare two numbers as strings, determining which combination would result in a larger number.
Here's the efficient Python code solution:
def largestNumber(self, nums: List[int]) -> str:
# Convert integers to strings
for i, n in enumerate(nums):
nums[i] = str(n)
# Custom comparison function
def compare(n1, n2):
if n1 + n2 > n2 + n1:
return -1
else:
return 1
# Sort the numbers based on the custom comparison
nums = sorted(nums, key=cmp_to_key(compare))
# Concatenate and return the result as a string
return str(int("".join(nums)))
In this code, we first convert the integers to strings, as we'll be working with string representations to create the largest number.
The custom comparison function, compare, determines which order of concatenation results in a larger number.
We sort the numbers using this comparison, ensuring that the largest digits appear first.
Finally, we concatenate the sorted strings and return the result as a string.
Time and Space Complexity
Let's analyze the time and space complexity of our efficient approach.
Time Complexity: The most time-consuming operation is the sorting step.
Using an efficient sorting algorithm (like QuickSort or MergeSort), the time complexity is O(n log n), where n is the number of integers in the input list nums.
Space Complexity: The space complexity is O(n) to store the string representations of the numbers.
Reasoning Behind Our Approach
The reasoning behind this efficient approach lies in recognizing that to form the largest number, we need to place the numbers with the highest significance (leading to a larger digit) first.
This idea is implemented through a custom comparison function, which ensures that during the sorting process, the numbers are arranged in a way that maximizes the resulting number's value.
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Conclusion
In this coding session, we successfully solved the Largest Number problem on LeetCode.
By implementing a custom comparison function and sorting the numbers as strings, we were able to efficiently arrange the numbers to create the largest possible number.
To further optimize our solution, we utilized a sorting algorithm with a time complexity of O(n log n).
The result was a clean and effective Python solution to the problem.
I hope you found this guide helpful in understanding the problem and the thought process behind the solution.
If you have any questions, suggestions, or comments, please feel free to share them.
Happy coding!
