project euler 26

Problem 26

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Reciprocal cycles

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2= 0.5
1/3= 0.(3)
1/4= 0.25
1/5= 0.2
1/6= 0.1(6)
1/7= 0.(142857)
1/8= 0.125
1/9= 0.(1)
1/10= 0.1

Where 0.1(6) means 0.166666…, and has a 1-digit recurring cycle. It can be seen that1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

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倒数的循环节

单位分数指分子为1的分数。分母为2至10的单位分数的十进制表示如下所示：

1/2= 0.5
1/3= 0.(3)
1/4= 0.25
1/5= 0.2
1/6= 0.1(6)
1/7= 0.(142857)
1/8= 0.125
1/9= 0.(1)
1/10= 0.1

这里0.1(6)表示0.166666…，括号内表示有一位循环节。可以看出，1/7有六位循环节。

找出正整数d < 1000，其倒数的十进制表示小数部分有最长的循环节。

package projecteuler;import java.util.ArrayList;import java.util.HashMap;import java.util.List;import java.util.Map;import java.util.Map.Entry;import org.junit.Test;public class Prj26 {/** * A unit fraction contains 1 in the numerator. The decimal representation * of the unit fractions with denominators 2 to 10 are given: *  * 1/2 = 0.5 1/3 = 0.(3) 1/4 = 0.25 1/5 = 0.2 1/6 = 0.1(6) 1/7 = 0.(142857) * 1/8 = 0.125 1/9 = 0.(1) 1/10 = 0.1 Where 0.1(6) means 0.166666..., and * has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit * recurring cycle. *  * Find the value of d < 1000 for which 1/d contains the longest recurring * cycle in its decimal fraction part. */@Testpublic void test() {Calculator.calculate();}public static class Calculator {public static void calculate() {Map<Integer, Integer> map = new HashMap<Integer, Integer>();map.put(1, 0);map.put(2, 0);IntegerDivisor div = new IntegerDivisor();for(int i = 3; i < 1000; i ++){div.divisor(i);long num = getNumExcept2Or5(div.primeMap);map.put(i,  getCycleLen(num));div.clear();}int maxId = 1;int maxVal = 0;for( Entry<Integer, Integer> entry : map.entrySet()){if( entry.getValue() > maxVal){maxId = entry.getKey();maxVal = entry.getValue();}}System.out.println("maxId=" + maxId + ", maxVal=" + maxVal);}public static long getNumExcept2Or5(Map<Long, Integer> primeMap) {long val = 1L;for (Entry<Long, Integer> entry : primeMap.entrySet()) {if (!entry.getKey().equals(5L) && !entry.getKey().equals(2L)) {val *= Math.pow(entry.getKey(), entry.getValue());}}return val;}public static int getCycleLen(long val) {if (val == 1L) {return 0;}int count = 1;int mod = (int) val;int modVal = 10;for (;;) {if (modVal % mod == 1) {break;}modVal = (modVal * 10) % mod;count++;}return count;}}/** * 因子分解 *  * @author 1440 *  */public static class IntegerDivisor {public Map<Long, Integer> primeMap = new HashMap<Long, Integer>();public List<Long> primeList = new ArrayList<Long>();public void clear() {primeMap.clear();primeList.clear();}public void divisor(long num) {if (num <= 1)return;long prime = getPrime(num,primeList.size() == 0 ? 2: primeList.get(primeList.size() - 1));if (prime < 0) {primeMap.put(num, 1);primeList.add(num);return;} else {primeList.add(prime);int count = 0;do {count += 1;num = num / prime;} while (num % prime == 0);primeMap.put(prime, count);divisor(num);}}private long getPrime(long num, long start) {for (long i = start; i <= Math.sqrt(num); i++) {if (num % i == 0) {return i;}}return -1;}@Overridepublic String toString() {return print_Map(this.primeMap);}public Long getLargestPrime() {return primeList.get(primeList.size() - 1);}}public static String print_Map(Map<?, ?> primeMap) {StringBuilder sb = new StringBuilder();for (Entry<?, ?> entry : primeMap.entrySet()) {sb.append(entry.getKey().toString() + "="+ entry.getValue().toString() + "\n");}return sb.toString();}public static void print_List(List<Integer> list) {for (int i = 0; i < list.size(); i++) {System.out.print(list.get(i) + ",");}System.out.println();}}