皮带碰撞时间计算

Question

Mr. Dis and Mr. Aster are mechanical engineers at Fiasco Iron Works. They were assigned to design roadways for automated trolleys to carry the iron ores across the smelting plants. They were supposed to make two circular roadways for the automated trolleys. However, by mistake Mr Dis and Mr Aster made the circular roadways tangential to each other (i.e. the two circular paths touch each other at a point).
Every morning at 0800 hrs the trolleys start at the point of tangency and move clockwise in their respective tracks. It is quite obvious that at some point the trolleys would collide at the point from where they started. In a desperate attempt to save the trolleys and the damage caused to the operations of the plant, the Chief Engineer of the plant has requested you to write a program that will sound a hooter 10 seconds before the collision such that the foreman can stop the trolleys in order to avoid the collision. Write a program to find out the time lapsed (in seconds) before the hooter should go off.

public static int timeLapsed(int perimeter1, int speed1, int perimeter2, int speed2) {
    int greater,smaller;
    int result = 0;
    if(perimeter1 >  perimeter2)    {
        greater = perimeter1;
        smaller = perimeter2;
    }   else    {
        greater = perimeter2;
        smaller = perimeter1;
    }
    for(int i=1;i<=smaller;i++)     {
        if(((greater*i)%smaller)==0)    {
            result = greater*i;
            break;
        }
    }

    return result/speed1-10;
}

在这里，我试图计算碰撞前的距离，这基本上是 LCM 操作，然后除以速度。但这对一些人来说是失败的 cases.Please 帮助我理解为什么。

Answer 1

在计算碰撞前的距离时，会考虑周长较大的皮带。所以速度不能随意选择，应该选择周长较大的皮带。

变化

public static int timeLapsed(int perimeter1, int speed1, int perimeter2, int speed2) {
    int greater,smaller;
    int speed, result = 0;
    if(perimeter1 >  perimeter2)    {
        greater = perimeter1;
        smaller = perimeter2;
        speed = speed1;
    }   else    {
        greater = perimeter2;
        smaller = perimeter1;
        speed = speed2;
    }
    for(int i=1;i<=smaller;i++)     {
        if(((greater*i)%smaller)==0)    {
            result = greater*i;
            break;
        }
    }

    return result/speed-10;
}

Answer 2

另一种替代方法，计算两条皮带所用时间的 LCM，即碰撞时间。

    public static int timeLapsed(int perimeter1, int speed1, int perimeter2, int speed2) {
    int timeForTrolley1 = perimeter1/speed1,timeForTrolley2 = perimeter2/speed2;
    int greater,smaller;
    int result = 0;
    if(timeForTrolley1 >  timeForTrolley2)  {
        greater = timeForTrolley1;
        smaller = timeForTrolley2;
    }   else    {
        greater = timeForTrolley2;
        smaller = timeForTrolley1;
    }
    for(int i=1;i<=smaller;i++)     {
        if(((greater*i)%smaller)==0)    {
            result = greater*i;
            break;
        }
    }

    return result-10;
}

皮带碰撞时间计算

Belt Collision Time Calculation

java

algorithm

numbers

lcm