The following iterative sequence is defined for the set of positive integers:
n
n/2 (n is even)
n
3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
import java.util.HashMap;
public class CollatzProblem {
public static int flag = 0;
public static HashMap<Integer, Integer> hashMap = new HashMap<Integer, Integer>();
public static void main(String args[]) {
int sum=0;
for(int i=2;i<1000000;i++){
if(sum<collatzArg(i,i)){
sum=collatzArg(i, i);
}
}
for(int j=2;j<1000000;j++){
if(hashMap.get(j)==sum){
System.out.println(j);
}
}
}
public static int collatzArg(double d, int n) {
flag++;
if (d > 1.0) {
if (d % 2 == 0) {
collatzArg(d / 2, n);
} else {
collatzArg(d * 3 + 1, n);
}
}else{
hashMap.put(n, flag);
flag=0;
}
return hashMap.get(n);
}
}
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探究在一千万以下的正整数中,哪个起始数字可以产生最长的Collatz序列。Collatz序列的生成规则为:若数字n为偶数,则下一步为n/2;若n为奇数,则下一步为3n+1。实验结果显示,起始数字837799产生了最长的序列。
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