project euler 52

Problem 52

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Permuted multiples

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.

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重排的倍数

可以看出，125874和它的两倍251748拥有同样的数字，只是排列顺序不同。

有些正整数x满足2x、3x、4x、5x和6x都拥有相同的数字，求其中最小的正整数。

import java.util.ArrayList;import java.util.Arrays;import java.util.HashSet;import java.util.List;import java.util.Set;import junit.framework.TestCase;public class Prj52 extends TestCase {/** * It can be seen that the number, 125874, and its double, 251748, contain * exactly the same digits, but in a different order. *  * Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, * contain the same digits. */public void test() {List<int[]> choose = new Comb(9, 6).calculateComb();List<int[]> allCbs = new Combination(6, 0).generateCom();for (int[] cb : choose) {int[] arr = new int[6];for (int j = 0, k = 0; j < cb.length; j++) {if (cb[j] == 1) {arr[k++] = j + 1;}}if (arr[0] != 1) {continue;}Set<Integer> allVals = getAllVals(allCbs, arr);for (int val : allVals) {if (allVals.contains(val) && allVals.contains(val * 2)&& allVals.contains(val * 3)&& allVals.contains(val * 4)&& allVals.contains(val * 5)&& allVals.contains(val * 6)) {System.out.println("val=" + val);return;}}}}private Set<Integer> getAllVals(List<int[]> allCbs, int[] arr) {Set<Integer> ret = new HashSet<Integer>();for (int i = 0; i < allCbs.size(); i++) {int[] val = new int[arr.length];int[] id = allCbs.get(i);for (int j = 0; j < arr.length; j++) {val[j] = arr[id[j]];}ret.add((int) Combination.getIntVal(val));}return ret;}public static class Combination {private int[] startArr;public Combination(int size) {this(size, 1);}public Combination(int size, int startNum) {startArr = new int[size];for (int i = 0; i < size; i++) {startArr[i] = i + startNum;}}public List<int[]> generateCom() {List<int[]> ret = new ArrayList<int[]>();ret.add(Arrays.copyOf(startArr, startArr.length));while (true) {int lastAsc = findLastAsc(startArr);if (lastAsc == -1) {break;}int lasBigThanAsc = findBigThanAsc(startArr, lastAsc);exchangeEach(lastAsc, lasBigThanAsc, startArr);ret.add(Arrays.copyOf(startArr, startArr.length));}return ret;}private int findBigThanAsc(int[] startArr2, int lastAsc) {int i = 0;for (i = startArr2.length - 1; i > lastAsc; i--) {if (startArr2[i] > startArr2[lastAsc]) {return i;}}assert (i > lastAsc);return i;}private void exchangeEach(int lastAsc, int lasBigThanAsc,int[] startArr2) {int temp = startArr2[lastAsc];startArr2[lastAsc] = startArr2[lasBigThanAsc];startArr2[lasBigThanAsc] = temp;int[] sortArr = getCopyArr(lastAsc + 1, startArr2);for (int i = 0; i < sortArr.length / 2; i++) {temp = sortArr[sortArr.length - 1 - i];sortArr[sortArr.length - 1 - i] = sortArr[i];sortArr[i] = temp;}for (int i = lastAsc + 1; i < startArr2.length; i++) {startArr2[i] = sortArr[i - lastAsc - 1];}}private int[] getCopyArr(int start, int[] startArr2) {int[] ret = new int[startArr2.length - start];for (int i = start; i < startArr2.length; i++) {ret[i - start] = startArr2[i];}return ret;}private int findLastAsc(int[] startArr2) {for (int i = startArr2.length - 1; i > 0; i--) {if (startArr2[i] > startArr2[i - 1]) {return i - 1;}}return -1;}public static long getIntVal(int[] arr) {long sum = arr[0];for (int i = 1; i < arr.length; i++) {sum = sum * 10 + arr[i];}return sum;}}public static class Comb {private int n;private int p;public Comb(int n, int p) {this.n = n;this.p = p;}public List<int[]> calculateComb() {assert (p < n && p > 0);List<int[]> ret = new ArrayList<int[]>();int[] arrs = new int[n];for (int i = 0; i < p; i++) {arrs[i] = 1;}ret.add(Arrays.copyOf(arrs, arrs.length));for (;;) {boolean find = findNext(arrs);ret.add(Arrays.copyOf(arrs, arrs.length));if (!find) {break;}}return ret;}private boolean findNext(int[] arrs) {int count = 0;int find = -1;for (int i = 0; i < arrs.length - 1; i++) {if (arrs[i] == 1) {count++;}if (arrs[i] == 1 && arrs[i + 1] == 0) {int tmp = arrs[i + 1];arrs[i + 1] = arrs[i];arrs[i] = tmp;find = i;break;}}count--;for (int i = 0; i < find; i++) {if (i < count) {arrs[i] = 1;} else {arrs[i] = 0;}}return !(find == -1);}}}