Arrange Nonnegative Integers to Form the Largest Number

Question

The question asks the candidate to arrange a list of nonnegative integers to form the largest possible number when concatenated.

Codemia · Accepted Answer

The goal is to arrange a list of nonnegative integers such that when concatenated, they form the largest possible number. For example, given the input [3, 30, 34, 5, 9], the output should be '9534330'.

To solve this problem, we can use a custom sorting approach. We need to define a comparison function that determines the order of two numbers based on their concatenated results. For two numbers x and y, we compare the concatenated strings xy and yx. If xy is greater than yx, then x should come before y.

We can implement this in Python using the following steps:

1. Convert all integers to strings.
2. Sort the list using a custom comparator.
3. Join the sorted strings into a single result.
4. Handle the edge case where the largest number is '0'.

Here is the Python code implementing this logic:
```python
from functools import cmp_to_key

def largestNumber(nums):
    # Convert integers to strings
    nums_str = list(map(str, nums))
    # Custom comparator function
    def compare(x, y):
        return (y + x > x + y) - (y + x < x + y)
    # Sort numbers based on the custom comparator
    nums_str.sort(key=cmp_to_key(compare))
    # Join the sorted strings
    result = ''.join(nums_str)
    # Handle the case where the result is all zeros
    return result if result[0] != '0' else '0'
```

The time complexity of this solution is O(n log n) due to the sorting step, where n is the number of integers in the input list. The space complexity is O(n) for storing the string representations of the integers.

It's important to consider edge cases, such as when the input list contains only zeros. In such cases, the output should be '0' instead of '000'. Additionally, we should ensure that the solution handles large inputs efficiently.

Arrange Nonnegative Integers to Form the Largest Number

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