project euler 31

Problem 31

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Coin sums

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p), £2 (200p)

It is possible to make £2 in the following way:

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

How many different ways can £2 be made using any number of coins?

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硬币求和

英国的货币单位包括英镑£和便士p，在流通中的硬币一共有八种：

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p), £2 (200p)

以下是组成£2的其中一种可行方式：

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

不限定使用的硬币数目，组成£2有多少种不同的方式？

package projecteuler;import java.io.BufferedWriter;import java.io.File;import java.io.FileNotFoundException;import java.io.FileOutputStream;import java.io.IOException;import java.io.OutputStreamWriter;import java.util.Arrays;import org.junit.Test;public class Prj31 {/** * In England the currency is made up of pound, £, and pence, p, and there * are eight coins in general circulation: *  * 1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p). It is possible to * make £2 in the following way: *  * 1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p How many different ways can £2 * be made using any number of coins? */@Testpublic void test() {Calculator cal = new Calculator();int[] val = new int[8];cal.calculate(0, 200, val);System.out.println(cal.getCount());}public static class Calculator {private static final String FILE_PATH = "C:\\Users\\1440\\Desktop\\prj31.txt";static {File f = new File(FILE_PATH);f.delete();}private int count = 0;private int[] values = { 1, 2, 5, 10, 20, 50, 100, 200 };public void calculate(int index, int total, int[] val) {int len = val.length;if (total < 0) {return;}if (total == 0) {if (checkSum(val, 200, values)) {count++;print_arr(val);}return;}if (index == len - 1) {if (total % values[len - 1] == 0) {val[len - 1] = total / values[len - 1];if (checkSum(val, 200, values)) {count++;print_arr(val);}} else {}return;}for (int i = 0; i <= total / values[index]; i++) {int[] copy = Arrays.copyOf(val, val.length);copy[index] = i;int totalCopy = total - i * values[index];calculate(index + 1, totalCopy, copy);}}private boolean checkSum(int[] arr, int sum, int[] _values) {int sum1 = 0;for (int i = 0; i < arr.length; i++) {sum1 += arr[i] * _values[i];}return sum1 == sum;}public int getCount() {return count;}public void print_arr(int[] arr) {for (int i = 0; i < arr.length; i++) {System.out.print(arr[i] + ",");}System.out.println();//saveArr(FILE_PATH, arr);}private void saveArr(String path, int[] arr) {File file = new File(path);try {BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(file, true)));for (int i = 0; i < arr.length; i++) {writer.append(String.valueOf(arr[i]) + ",");}writer.write("\t\n");writer.close();} catch (FileNotFoundException e) {e.printStackTrace();} catch (IOException e) {e.printStackTrace();}}}}