project euler 118

Pandigital prime sets

Using all of the digits 1 through 9 and concatenating them freely to form decimal integers, different sets can be formed. Interestingly with the set {2,5,47,89,631}, all of the elements belonging to it are prime.

How many distinct sets containing each of the digits one through nine exactly once contain only prime elements?

---

全数字素数集合

使用1至9的全部数字，并自由连接起来组成十进制整数，可以构造不同的集合。其中一个集合{2,5,47,89,631}非常有趣，因为它的所有元素都是素数。

有些集合包含数字1至9恰好各一次，且所有元素都是素数，这样的集合有多少个？

package projecteuler;import java.util.ArrayList;import java.util.Arrays;import java.util.Collections;import java.util.HashMap;import java.util.List;import java.util.Map;import junit.framework.TestCase;public class Prj118 extends TestCase {public static final int LIMIT = (int) Math.pow(10, 9);public void testPandigitalPrimeSets() {Map<Integer, List<Integer>> dataMap = new HashMap<Integer, List<Integer>>();List<Integer> set1 = new ArrayList<Integer>();List<Integer> set2 = new ArrayList<Integer>();List<Integer> set3 = new ArrayList<Integer>();List<Integer> set4 = new ArrayList<Integer>();List<Integer> set5 = new ArrayList<Integer>();List<Integer> set6 = new ArrayList<Integer>();List<Integer> set7 = new ArrayList<Integer>();List<Integer> set8 = new ArrayList<Integer>();List<Integer> set9 = new ArrayList<Integer>();// set1.add(13);// set2.add(2);// set3.add(3);// set4.add(47);// set5.add(5);// set6.add(631);// set7.add(7);// set8.add(89);// set9.add(91);set1 = getSet(1);set2 = getSet(2);set3 = getSet(3);set4 = getSet(4);set5 = getSet(5);set6 = getSet(6);set7 = getSet(7);set8 = getSet(8);set9 = getSet(9);dataMap.put(1, set1);dataMap.put(2, set2);dataMap.put(3, set3);dataMap.put(4, set4);dataMap.put(5, set5);dataMap.put(6, set6);dataMap.put(7, set7);dataMap.put(8, set8);dataMap.put(9, set9);int[] arr = new int[9];List<int[]> resultList = new ArrayList<int[]>();dfSearch(arr, 0, dataMap, resultList, 0);System.out.println("count=" + count);}static long count = 0;/** * [a1,a2,...,an], a1<a2<a3<...<an; * @param arr * @param depth * @param dataMap * @param resultList * @param digitSize */void dfSearch(int[] arr, int depth, Map<Integer, List<Integer>> dataMap,List<int[]> resultList, int digitSize) {if (digitSize >= 9 && isFind(arr, depth)) {int[] tp = Arrays.copyOfRange(arr, 0, depth);String str = "";for (int i = 0; i < tp.length; i++) {System.out.print(tp[i] + ",");str += Integer.toString(tp[i]);}System.out.println("=" + str);count++;return;}if (depth >= arr.length) {return;}for (int i = 1; i <= 9; i++) {if (depth == 0) {List<Integer> dataList = dataMap.get(i);for (int j = 0; j < dataList.size(); j++) {arr[depth] = dataList.get(j);dfSearch(arr, depth + 1, dataMap, resultList, Integer.toString(arr[depth]).length());}continue;}if (isCandidateId(arr, depth, i)) {List<Integer> dataList = dataMap.get(i);for (int j = 0; j < dataList.size(); j++) {int intVal = dataList.get(j);int digit = Integer.toString(intVal).length() + digitSize;if (digit <= 9 && isCandidateVal(arr, depth, intVal)) {arr[depth] = intVal;dfSearch(arr, depth + 1, dataMap, resultList, digit);}if (digit > 9) {break;}}}}}boolean isCandidateId(int[] arr, int depth, int id) {String str = "";for (int i = 0; i < depth; i++) {str += Integer.toString(arr[i]);}return !str.contains(Integer.toString(id));}boolean isCandidateVal(int[] arr, int depth, int intVal) {if (intVal < arr[depth - 1]) {return false;}String str = "";for (int i = 0; i < depth; i++) {str += Integer.toString(arr[i]);}String valStr = Integer.toString(intVal);for (int i = 0; i < valStr.length(); i++) {if (str.contains(String.valueOf(valStr.charAt(i)))) {return false;}}return true;}boolean isFind(int[] arr, int depth) {String str = "";for (int i = 0; i < depth; i++) {str += Integer.toString(arr[i]);}return str.length() == 9 && str.contains("1") && str.contains("2")&& str.contains("3") && str.contains("4") && str.contains("5")&& str.contains("6") && str.contains("7") && str.contains("8")&& str.contains("9");}List<Integer> getSet(int init0) {List<Integer> set = new ArrayList<Integer>();int[] arr = new int[9];dfs(arr, 0, init0, set);Collections.sort(set);// System.out.println(Arrays.toString(set.toArray()));System.out.println("id=" + init0 + ",size=" + set.size());return set;}void dfs(int[] arr, int startIndex, int init0, List<Integer> set) {if (startIndex >= 9) {int[] tmp = Arrays.copyOfRange(arr, 0, startIndex);int v = arr2Int(tmp);if (isPrime(v) && !set.contains(v)) {set.add(v);System.out.println(Arrays.toString(tmp));}return;}for (int i = 1; i <= 9; i++) {if (startIndex == 0) {arr[0] = init0;dfs(arr, startIndex + 1, init0, set);} else {if (isValid(arr, startIndex, i)) {int[] tmp = Arrays.copyOfRange(arr, 0, startIndex);int v = arr2Int(tmp);if (isPrime(v) && !set.contains(v)) {set.add(v);}arr[startIndex] = i;dfs(arr, startIndex + 1, init0, set);} else {continue;}}}}int arr2Int(int[] arr) {int v = 0;for (int i = 0; i < arr.length; i++) {v = v * 10 + arr[i];}return v;}boolean isValid(int[] arr, int startIndex, int v) {for (int i = 0; i < startIndex; i++) {if (v == arr[i]) {return false;}}return true;}boolean isPrime(int v) {if (v <= 10) {if (v == 2 || v == 3 || v == 5 || v == 7) {return true;}return false;}if (v % 2 == 0) {return false;}for (int i = 3; i * i <= v; i++) {if (v % i == 0) {return false;}}return true;}}