Largest Number

 

Problem Statement: Given a list of non-negative integers nums, arrange them such that they form the largest number.

Note:

  • The result may be very large, so you need to return a string instead of an integer.

1. Clarify the problem:

  • Can the input list contain duplicate numbers?
  • Can the input list be empty?
  • Can the input list contain negative numbers?

2. Analyze the problem:

  • Input: List of non-negative integers nums
  • Output: String representing the largest number formed from nums
  • Constraints:
    • The input list can contain duplicate numbers.
    • The input list can be empty.
    • The input list will only contain non-negative integers.

3. Design an algorithm:

  • Convert each number in the input list to a string.
  • Sort the list of strings using a custom comparison function.
    • The comparison function should compare two numbers by concatenating them in different orders and comparing the resulting strings. The larger string should be considered greater.
  • Join the sorted list of strings into a single string.
  • Return the resulting string.

4. Explain your approach:

  • We will convert each number in the input list to a string and then sort the list of strings using a custom comparison function.
  • The comparison function will compare two numbers by concatenating them in different orders and comparing the resulting strings. This will ensure that we get the largest number formed by the list of integers.
  • Finally, we join the sorted list of strings into a single string and return it.

5. Write clean and readable code:

python
class Solution:
    def largestNumber(self, nums: List[int]) -> str:
        def compare(x: str, y: str) -> int:
            return int(y + x) - int(x + y)
        
        nums = list(map(str, nums))
        nums.sort(key=functools.cmp_to_key(compare))
        
        if nums[0] == '0':
            return '0'
        
        return ''.join(nums)

6. Test your code: I will test the code with the following test cases:

  • Test case 1: nums = [10, 2]
  • Test case 2: nums = [3, 30, 34, 5, 9]
  • Test case 3: nums = [1]
  • Test case 4: nums = [0, 0, 0]
  • Test case 5: nums = [9, 99, 999, 9999]
python
solution = Solution()
print(solution.largestNumber([10, 2]))  # Expected output: "210"
print(solution.largestNumber([3, 30, 34, 5, 9]))  # Expected output: "9534330"
print(solution.largestNumber([1]))  # Expected output: "1"
print(solution.largestNumber([0, 0, 0]))  # Expected output: "0"
print(solution.largestNumber([9, 99, 999, 9999]))  # Expected output: "99999999999"

7. Optimize if necessary: The given solution is already efficient with a time complexity of O(n log n), where n is the length of the input list.

8. Handle error cases:

  • If the input list is empty, we can return an empty string.

9. Discuss complexity analysis:

  • The time complexity of the solution is O(n log n), where n is the length of the input list. This is because we sort the list of strings using the custom comparison function.
  • The space complexity is O(n) since we create a new list of strings to store the converted numbers.
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