0585MediumArraySortingPrefix SumOrdered Set

Brightest Spot on the Walkway

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Trains the technique from

LeetCode 2021Brightest Position on Street

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 walkway is marked off with whole-number coordinates that run in both directions from zero. Lamps are described by lights, where lights[i] = [position_i, range_i] means lamp i stands at coordinate position_i and throws light on every whole-number coordinate from position_i - range_i through position_i + range_i, both ends included.

The brightness of a coordinate is the number of lamps whose light reaches it. Return the coordinate with the greatest brightness. If several coordinates share the greatest brightness, return the smallest of them.

Examples

Example 1

Input: lights = [[4, 2], [6, 2], [5, 0]]
Output: 5

The first lamp lights 2 through 6, the second lights 4 through 8 and the third lights only 5. Coordinate 5 is reached by all three, so its brightness is 3 and no coordinate can beat that.

Example 2

Input: lights = [[0, 2], [4, 2]]
Output: 2

One lamp lights -2 through 2 and the other lights 2 through 6. Coordinate 2 is the only one reached by both, so its brightness is 2.

Example 3

Input: lights = [[0, 1], [3, 1]]
Output: -1

The lamps light -1 through 1 and 2 through 4, and they never overlap, so the greatest brightness is 1 and it is shared by six coordinates. The smallest of them is -1.

Constraints

1 <= lights.length <= 10^5
lights[i].length == 2
-10^8 <= position_i <= 10^8
0 <= range_i <= 10^8

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 brightest_position(lights: list[list[int]]) -> int:

Java

public int brightestPosition(int[][] lights)

The intended approach

Time O(n log n) — sorting the 2n events dominates.Space O(n) for the event list.

Brightness only changes where a lamp's reach begins or has just ended, so record two events per lamp: plus one at the first lit coordinate and minus one at the coordinate one step past the last lit coordinate. Sort the events by coordinate and sweep through them, applying every event that shares a coordinate before reading the running count, because that count then holds for the whole stretch starting at that coordinate. Keeping a record only on a strict improvement makes the smallest coordinate win any tie.

Pythonentry point: brightest_position

def brightest_position(lights):
    # O(n log n) time, O(n) space: turn each lamp into a pair of events, one
    # where its glow switches on and one just past the point where it switches
    # off, sort the events by coordinate, and sweep. The running count is the
    # brightness of every point from the current event coordinate up to the next
    # one, so the first coordinate that sets a new record is the answer.
    events = []
    for position, reach in lights:
        events.append((position - reach, 1))
        events.append((position + reach + 1, -1))
    events.sort()
    best_count = -1
    best_spot = 0
    running = 0
    i = 0
    total = len(events)
    while i < total:
        coord = events[i][0]
        while i < total and events[i][0] == coord:
            running += events[i][1]
            i += 1
        if running > best_count:
            best_count = running
            best_spot = coord
    return best_spot

The obvious version

Brightness can only rise where some lamp's reach begins, so the smallest brightest coordinate is one of those. Collect the first lit coordinate of every lamp, sort them, and for each one count the lamps whose reach covers it with a full scan, keeping the first coordinate that sets a record.

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_brightest_position(lights):
    candidates = sorted(position - reach for position, reach in lights)
    best_count = -1
    best_spot = 0
    for spot in candidates:
        count = 0
        for position, reach in lights:
            if position - reach <= spot <= position + reach:
                count += 1
        if count > best_count:
            best_count = count
            best_spot = spot
    return best_spot

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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