问题
这道题原理跟约瑟夫排序是相同的,不同之处在于约瑟夫排序输出的是数组,而这道题要求输出约瑟夫排序的最后一位数。
给定两个数组n,k。输出{1,2,3.。。,n}这个数组中约瑟夫排序的最后一个数。不知道什么是约瑟夫排序?请看约瑟夫排序
例子
josephus_survivor(7,3) => means 7 people in a circle;
one every 3 is eliminated until one remains
[1,2,3,4,5,6,7] - initial sequence
[1,2,4,5,6,7] => 3 is counted out
[1,2,4,5,7] => 6 is counted out
[1,4,5,7] => 2 is counted out
[1,4,5] => 7 is counted out
[1,4] => 5 is counted out
[4] => 1 counted out, 4 is the last element - the survivor!
我的代码
package codewars;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
public class JosephusSurvivor {
public static int josephusSurvivor(final int n, final int k) {
List<Integer> list = IntStream.range(1, n+1).boxed().collect(Collectors.toList());
int position = 0;
while (list.size() > 1) {
position = (position + k -1)%list.size();
list.remove(position);
}
return list.get(0);
}
public static void main(String[] args) {
System.out.println(JosephusSurvivor.josephusSurvivor(7,3));
}
}
高手的代码
public class JosephusSurvivor {
public static int josephusSurvivor(final int n, final int k) {
int remaining = 0;
for (int i = 2; i <= n; i++) {
remaining = (remaining + k) % i;
}
return remaining + 1;
}
}
分析
约瑟夫环算法的推导见约瑟夫环问题详解