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Widest One-Degree Sample

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Trains the technique from

LeetCode 594Longest Harmonious Subsequence

This is an original problem, written from a brief that listed the technique, the difficulty, the topics, the function shape and the input bounds — none of that problem's wording, examples, hints or editorials. The link is there so you can map your practice onto the standard set.

Same function shape, different story and different numbers.

A cold-store probe logs whole-degree temperatures into the list readings. Values may be below zero.

A technician wants to pull out a sample: any collection of readings taken from the log, chosen freely and without regard to where they sat in the log. A sample is tight when the difference between its largest and its smallest reading is exactly one degree.

Return the number of readings in the largest tight sample. If no tight sample exists, return 0.

Examples

Example 1

Input: readings = [-1, 0, 0, -1, 3]
Output: 4

Taking both readings of -1 and both readings of 0 gives a sample of four whose smallest is -1 and whose largest is 0, one degree apart.

Example 2

Input: readings = [4, 4, 5, 5, 5, 6]
Output: 5

The two 4s together with the three 5s make a sample of five running from 4 to 5. Adding the 6 as well would stretch the spread to two degrees.

Example 3

Input: readings = [12, 14, 10]
Output: 0

No two of these readings differ by exactly one degree, so no tight sample can be formed and the answer is 0.

Constraints

1 <= readings.length <= 2 * 10^4
-10^9 <= readings[i] <= 10^9

The signature

The editor is preloaded with this. It matches the parent problem's shape, so a solution that works here transfers to a judge unchanged.

Python

def longest_paired_sample(readings: list[int]) -> int:

Java

public int longestPairedSample(int[] readings)

The intended approach

Time O(n): one pass to tally and one pass over the distinct values.Space O(n) for the tally, which holds one entry per distinct reading.

Because only the smallest and largest reading of a sample matter, a tight sample is built from exactly two values, some `v` and `v + 1`, and it may take every copy of both. So tally how often each value occurs, then for each tallied value check whether the next degree up was also logged and add the two tallies. The largest such total is the answer, and `0` stands when no value has a neighbour one degree above it.

Pythonentry point: longest_paired_sample

def longest_paired_sample(readings):
    # Tally every reading, then look at each value together with the value one
    # degree above it. O(n) time, O(n) space.
    tally = {}
    for r in readings:
        tally[r] = tally.get(r, 0) + 1
    best = 0
    for v in tally:
        if v + 1 in tally:
            width = tally[v] + tally[v + 1]
            if width > best:
                best = width
    return best

The obvious version

Take each logged reading as the low end of the sample, then rescan the whole log counting how many readings equal it and how many are one degree above. Keep the largest total from a low end that actually has a partner.

This is not filler. It was written independently of the fast solution and the two were run against thousands of random inputs to confirm they agree — which is how the answer above is known to be right. Read it when the intended approach feels like a rabbit pulled out of a hat.

Python

def bf_longest_paired_sample(readings):
    best = 0
    for v in readings:
        low = 0
        high = 0
        for x in readings:
            if x == v:
                low += 1
            elif x == v + 1:
                high += 1
        if high > 0 and low + high > best:
            best = low + high
    return best

How this problem was checked

Reference solution executed against 10 test cases — 10 passed
3 worked examples confirmed by running the code
0 eight-word sequences shared with the parent problem's text
Agrees with an independent brute-force implementation on random inputs
Test set proven to catch deliberately broken solutions
Reviewed by a separate quality pass
Function arity matches the parent problem's

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