Sorting the digits ascending is the obvious move and I got there fast.
Convert the integer to a string, sort its digits in ascending order, and then join them back to form the smallest number. Since leading zeros are allowed, the result may have leading zeros, which is acceptable. This approach is straightforward and efficient with O(n log n) time complexity due to sorting.
Pro tip: Clarify that leading zeros are allowed, so no special handling is needed; if they weren't, you'd need to find the smallest non-zero digit to place first. Also, mention that the result might be a string if leading zeros are present, but if an integer is required, you can convert it back (though leading zeros would be lost).
Confirm that the input is a non-negative integer and that leading zeros are permitted in the output. Ask if the output should be an integer or a string, as leading zeros affect representation.
Convert the integer to a string or list of characters to easily manipulate individual digits. Sorting is the key operation.
Sort the digits in ascending order. This places the smallest digits first, which minimizes the overall number when concatenated.
Join the sorted digits to form the smallest number. If leading zeros are allowed, simply return the string; otherwise, handle the first non-zero digit.
State that the time complexity is O(n log n) due to sorting, where n is the number of digits, and space complexity is O(n) for the string/list.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I started second-guessing myself.
First, clarify the problem constraints and edge cases, then propose an algorithm that finds the smallest permutation of the digits that is strictly greater than the lower bound. A common efficient approach is to sort the digits and use backtracking with pruning, or to generate permutations in lexicographic order and pick the first that exceeds the bound.
Pro tip: Mention that if the number of digits is large, generating all permutations is infeasible, so pruning based on the lower bound is crucial. Also, consider if the lower bound has more digits than the integer, then no rearrangement can be greater, so return 'none'.
Ask about the range of the integer, the lower bound, and whether the rearrangement must use all digits exactly once. Discuss cases like leading zeros, negative numbers, and when the lower bound has more digits.
Decide between generating all permutations and sorting, or using a more efficient approach like backtracking with pruning. Consider time and space complexity trade-offs.
Write code to generate permutations in lexicographic order, compare with the lower bound, and return the first valid one. Ensure to handle duplicates if digits repeat.
Walk through examples like integer=123, lowerBound=200 (answer: 213) and integer=123, lowerBound=321 (answer: none). Also test edge cases like single digit, repeated digits, and leading zeros.
Discuss the time complexity (e.g., O(n! * n) for brute force) and suggest optimizations like pruning branches that cannot exceed the bound, or using next permutation algorithm.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.