The Race

Problems and Contests
#1

Is there any better way to do this problem?

// Question: http://www.usaco.org/index.php?page=viewproblem2&cpid=989

#include <bits/stdc++.h>
using namespace std;

long long MaxToDistance(int MaxSpeed)
{
	double e = (MaxSpeed-1) % 2;
	return (1 + e/2)*MaxSpeed + MaxSpeed*((MaxSpeed-e-1)/2);
}

int DistanceToMax(long long Distance)
{
	return floor((sqrt(Distance*2)+((0.125*sqrt(2))/sqrt(0.25))));
}

int FindSolution(long long MaxSpeed, long long RaceLength)
{

	int SpedUpDistance = 0; 
	int RequiredSlowPeriod = 0;
	int time = 0;

	long long InitialDistance = MaxToDistance(MaxSpeed);

	if (InitialDistance < RaceLength)
	{
		time = MaxSpeed;
		SpedUpDistance = InitialDistance;
	} else 
	{
		return DistanceToMax(RaceLength);
	}

	for (int CurrentSpeed = time + 1;; CurrentSpeed++) {

		SpedUpDistance += CurrentSpeed;
		time++;

		if (SpedUpDistance + RequiredSlowPeriod >= RaceLength) { return time; }
		if (CurrentSpeed >= MaxSpeed) {
			RequiredSlowPeriod += CurrentSpeed;
			time++;
			if (SpedUpDistance + RequiredSlowPeriod >= RaceLength) { return time; }
		}

	}

}


int main()
{
	long long RaceLength, MaxSpeedAmount;
	cin >> RaceLength >> MaxSpeedAmount;

	for (int Index = 0; Index < MaxSpeedAmount; Index++)
	{

		//int MaxSpeed;
		//cin >> MaxSpeed;
		cout << FindSolution(Index,RaceLength) << "\n";

	}

	return 0;
}

The edits are updates to the program that improved efficiency & accuracy. It currently is 2000% faster than the provided solution at returning a solution when the distance traveled to reach the max speed is greater than the race length (see DistanceToMax), and about 150-200% faster when doing all other equations.

(Benchmark, the input should be RaceDistance\tAmountOfMaxSpeed\nRaceDistance\tAmountOfMaxSpeed)