Basically a base conversion problem once you see it.
Treat the license plate as a mixed-radix number where the first three characters are base-26 digits (A-Z) and the last three are base-10 digits (0-9). Convert the 1-indexed N to a 0-indexed value, then extract each character by dividing and taking remainders, handling the letter and digit parts separately. This yields an O(1) time and space solution.
Pro tip: Clarify whether N is 1-indexed or 0-indexed and confirm the lexicographic ordering (e.g., 'AAA000' is first). Mentioning edge cases like N=1 and the maximum N=26^3 * 10^3 shows attention to detail.
Confirm the format: 3 uppercase letters followed by 3 digits. Determine if N is 1-indexed and what the lexicographic order means (e.g., 'AAA000' is the first plate).
Recognize that the plate can be viewed as a number in base 26 for the letters and base 10 for the digits. The total number of plates is 26^3 * 10^3 = 17,576,000.
Subtract 1 from N to make it 0-indexed. Compute the letter part by dividing by 1000 (since there are 1000 digit combinations) and the digit part by taking N modulo 1000.
For the letter part, extract each of the three letters by repeatedly dividing by 26 and mapping remainders to 'A'-'Z'. For the digit part, extract each digit by dividing by 10 and mapping remainders to '0'-'9'.
Combine the three letters and three digits into a string. Verify with a small example (e.g., N=1 gives 'AAA000') to ensure correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the 3x3 grid as a graph where edges represent valid moves, precomputing the intermediate dots that must be visited for each pair. Use backtracking to explore all paths of length 4 to 9, marking visited dots and checking the intermediate condition before each move. Count and return the total number of valid patterns.
Pro tip: Precompute the intermediate dot for every pair of dots (including 'none' when no dot lies between) to avoid repeated geometric checks during backtracking, and consider symmetry to reduce redundant exploration if optimizing.
Label dots 1-9 in a 3x3 grid. Precompute a 10x10 table where table[i][j] gives the dot that must be visited before moving from i to j, or 0 if no such dot exists.
Use a visited array to track which dots are currently in the pattern, and a counter for the current pattern length. Start from each dot as the first element.
From the current dot, iterate over all unvisited dots. For each, check if the intermediate dot (if any) is already visited. If valid, mark it visited, recurse, then unmark.
At each recursion depth between 4 and 9, increment a global counter. Continue until all paths are explored.
After backtracking completes, return the total number of valid patterns.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use a two-pointer technique to traverse both interval lists simultaneously, comparing current intervals to find overlaps. At each step, add the intersection if it exists, then advance the pointer of the interval that ends first. Continue until one list is exhausted.
Pro tip: Clarify edge cases upfront, such as empty lists or intervals that just touch (e.g., [1,2] and [2,3] intersect at [2,2]). Also, discuss time and space complexity: O(m+n) time and O(1) extra space (excluding output).
Restate the problem in your own words and ask clarifying questions about interval inclusivity, input constraints, and expected output format.
Explain that you'll use two pointers, one for each list, and iterate while both have intervals left.
For current intervals A and B, compute the overlap as [max(A.start, B.start), min(A.end, B.end)]. If start <= end, add to result.
Move the pointer of the interval with the smaller end time, because it cannot overlap with any future interval in the other list.
State time complexity O(m+n) and space O(1) extra. Mention edge cases: empty lists, no intersections, touching intervals, and single-point intersections.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.