Advent Of Code 2021 Day 7 solutions

import kotlin.math.abs
import kotlin.math.ceil
import kotlin.math.floor

// assuming the input has already been parsed

// the optimal position is the one at the index which corresponds to the median of the sorted list
fun part1(positions: List<Int>): Int {
    val sorted = positions.sorted()
    val medianPosition = positions.size / 2

    return positions.sumOf { abs(sorted[medianPosition] - it) }
}

fun Double.gauss() = this * (this + 1) / 2

fun List<Int>.solve(roundedMean: Double) = this.sumOf { abs(roundedMean - it).gauss() }

// the mean approximates the optimal position but there's a variation of +/- 0.5, so the calculation
// must be performed once with the minimum between the floor and the ceiling of the mean, and once
// with the maximum. the solution is the lower of the two results
fun part2(positions: List<Int>): Int {
    val mean = positions.sum().toDouble() / positions.size
    val meanFloor = floor(mean)
    val meanCeil = ceil(mean)
    val roundedLow = positions.solve(minOf(meanFloor, meanCeil))
    val roundedHigh = positions.solve(maxOf(meanFloor, meanCeil))

    return minOf(roundedLow, roundedHigh).toInt()
}