project euler 41

Problem
41

Pandigital prime

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

全数字的素数

如果一个n位数恰好使用了1至n每个数字各一次，我们就称其为全数字的。例如，2143就是一个4位全数字数，同时它恰好也是一个素数。

最大的全数字的素数是多少？

@Test
public void test() {
for (int i = 9; i >= 2; i--) {

Combination comb = new Combination(i);
List<int[]> combinations = comb.generateCom();
for (int j = combinations.size() - 1; j >= 0; j--) {
int val = comb.getIntVal(combinations.get(j));
if (isPrime(val)) {
System.out.println("maxVal=" + val + ",bits=" + i);
return;
}
}

}
}

public static boolean isPrime(int val) {

int num = Math.abs(val);

if (num < 10) {

if (num == 2 || num == 3 || num == 5 || num == 7) {
return true;
}
return false;

} else {

for (int i = 2; i * i <= num; i++) {
if (num % i == 0) {
return false;
}
}

return true;
}

}

public static class Combination {
private int[] startArr;

public Combination(int size) {
startArr = new int[size];
for (int i = 0; i < size; i++) {
startArr[i] = i + 1;
}
}

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 int getIntVal(int[] arr) {
int sum = arr[0];

for (int i = 1; i < arr.length; i++) {
sum = sum * 10 + arr[i];
}

return sum;

}
}