Given n coins and a pan balance,find the only counterfeit 3

最新推荐文章于 2025-11-27 10:55:11 发布

最新推荐文章于 2025-11-27 10:55:11 发布 · 138 阅读

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本文介绍了一种通过有限次称重来确定一组球中哪些球是标准重量的算法。该算法分为三种情况：1-ball、2-ball 和 3-ball，并详细阐述了每种情况下所需的称重次数及操作流程。

In the 1-ball case, if the status flag is already set, then we don't need to weight anymore. Otherwise, we need to find a good ball to compare.

java 代码

package solve;
import scale.Ball;
import scale.Scale;
import java.util.Set;
/**
* 1-ball case: we need a good reference ball and at most one trial
*/
public class OneBallCaseSolver
{
private Scale scale;
private Set originalBallSet;
public void findWeight(Set ballSet)
{
if (ballSet.size() != 1)
throw new IllegalArgumentException("scale.Ball set size is not 1: size=" + ballSet.size());
Ball ball = (Ball)ballSet.iterator().next();
if (!ball.getStatus().equals(Ball.UNKNOWN)) return;
// in order to figure it's good or bad, we need a good reference ball.
Ball goodBall = Utils.findGoodBall(originalBallSet);
if (goodBall == null)
{
throw new RuntimeException("can't findBallBall a good reference ball to use for the judgement");
}
// flag conversion
int result = scale.weigh(ball, goodBall);
ball.setStatus(Utils.convertToBallStatus(result));
}
public void setScale(Scale scale) { this.scale = scale; }
public void setOriginalBallSet(Set originalBallSet) { this.originalBallSet = originalBallSet; }
}

In the 2-ball case, we need to check whether the status flags for both are set. If not, then we need two weighings.

java 代码

package solve;
import scale.Scale;
import scale.Ball;
import java.util.Iterator;
import java.util.Set;
/**
* 2-ball case: we need a good reference ball and one or two weighings.
*/
public class TwoBallCaseSolver
{
private Scale scale;
private Set originalBallSet;
public void findWeight(Set ballSet)
{
if (ballSet.size() != 2)
throw new IllegalArgumentException("scale.Ball set size is not 2: size=" + ballSet.size());
Iterator it = ballSet.iterator();
Ball balla = (Ball)it.next();
Ball ballb = (Ball)it.next();
Ball goodBall = Utils.findGoodBall(originalBallSet);
int result = scale.weigh(balla, goodBall);
balla.setStatus(Utils.convertToBallStatus(result));
if (!balla.getStatus().equals(Ball.NORMAL))
{
ballb.setStatus(Ball.NORMAL);
}
else if (ballb.getStatus().equals(Ball.UNKNOWN))
{
result = scale.weigh(ballb, goodBall);
ballb.setStatus(Utils.convertToBallStatus(result));
}
}
public void setScale(Scale scale) { this.scale = scale; }
public void setOriginalBallSet(Set originalBallSet) { this.originalBallSet = originalBallSet; }
}

In the above two cases, whenever we need to weigh, we need a good ball as the reference. In the 3-ball case, we don't need a good ball.

java 代码

package solve;
import scale.Scale;
import scale.Ball;
import java.util.Set;
import java.util.Iterator;
/**
* 3-ball case: we need two trials if all of the balls are not marked, otherwise
* we need only one trial.
*/
public class ThreeBallCaseSolver
{
private Scale scale;
public void findWeight(Set ballSet)
{
if (ballSet.size() != 3)
throw new IllegalArgumentException("scale.Ball set size is not 3: size=" + ballSet.size());
// In the 3-ball case, we can figure out which one is good.
// Here, we assume there is only one bad ball.
Iterator it = ballSet.iterator();
Ball balla = (Ball)it.next();
Ball ballb = (Ball)it.next();
Ball ballc = (Ball)it.next();
if (balla.getStatus().equals(Ball.UNKNOWN)) // This means we start with 3 balls
{
// In this case we need two trials
int result = scale.weigh(balla, ballb);
if (result == Scale.EVEN)
{
// This means balla and ballb are good, ballc is bad.
balla.setStatus(Ball.NORMAL);
ballb.setStatus(Ball.NORMAL);
if (scale.weigh(balla, ballc) == Scale.HEAVIER)
ballc.setStatus(Ball.LIGHTER);
else
ballc.setStatus(Ball.HEAVIER);
}
else //if (result == Scale.HEAVIER)
{
// This means ballc is good
ballc.setStatus(Ball.NORMAL);
int result1 = scale.weigh(balla, ballc);
if (result1 == Scale.EVEN) // a is also good
{
balla.setStatus(Ball.NORMAL);
if (result == Scale.HEAVIER)
ballb.setStatus(Ball.LIGHTER);
else
ballb.setStatus(Ball.HEAVIER);
}
else if (result1 == Scale.HEAVIER) // b is good, a is heavier
{
balla.setStatus(Ball.HEAVIER);
ballb.setStatus(Ball.NORMAL);
}
else
{
balla.setStatus(Ball.LIGHTER);
ballb.setStatus(Ball.NORMAL);
}
}
}
else // This means we start with more than 3 balls and markWeight is marked.
{
// In this case we need only 1 trial with the marked info.
// At this stage, all 3 balls are marked with either lighter or heavier.
// From the Pigeon Principle, we can choose two balls with the same mark.
Ball w1;
Ball w2;
Ball w3;
if (balla.getStatus().equals(ballb.getStatus()))
{
w1 = balla;
w2 = ballb;
w3 = ballc;
}
else if (balla.getStatus().equals(ballc.getStatus()))
{
w1 = balla;
w2 = ballc;
w3 = ballb;
}
else if (ballb.getStatus().equals(ballc.getStatus()))
{
w1 = ballb;
w2 = ballc;
w3 = balla;
}
else
{
throw new RuntimeException("The balls are not marked properly");
}
int result = scale.weigh(w1, w2);
if (result == Scale.EVEN)
{
w1.setStatus(Ball.NORMAL);
w2.setStatus(Ball.NORMAL);
}
else if (result == Scale.HEAVIER)
{
w3.setStatus(Ball.NORMAL);
if (w1.getStatus().equals(Ball.HEAVIER)) // heavier is bad
{
w2.setStatus(Ball.NORMAL);
}
else // lighter is bad
{
w1.setStatus(Ball.NORMAL);
}
}
else
{
w3.setStatus(Ball.NORMAL);
if (w1.getStatus().equals(Ball.HEAVIER))
{
w1.setStatus(Ball.NORMAL);
}
else
{
w2.setStatus(Ball.NORMAL);
}
}
}
}
public void setScale(Scale scale) { this.scale = scale; }
}