// Package q3296 implements a solution for https://leetcode.com/problems/minimum-number-of-seconds-to-make-mountain-height-zero/
package q3296

import (
	"math"
	"slices"
)

func canFinishIn(mHeight int, wTimes []int, secs int) bool {
	decHeight := 0

	for _, t := range wTimes {
		h := int(math.Sqrt(float64(secs) * 2 / float64(t)))
		if t*h*(h+1)/2 > secs {
			h--
		}
		decHeight += h
	}
	return decHeight >= mHeight
}

func minNumberOfSeconds(mountainHeight int, workerTimes []int) int64 {
	worse := slices.Max(workerTimes) * (mountainHeight + 1) * mountainHeight / 2
	l, r := 0, worse+1

	for l < r {
		m := (l + r) / 2
		if canFinishIn(mountainHeight, workerTimes, m) {
			r = m
		} else {
			l = m + 1
		}
	}
	return int64(l)
}

var _ = minNumberOfSeconds