Java 代码分享（第11篇）编程解决数学问题：“计算3个10以内的数字，与合计值相除后，商的第3位小数大于4，共有多少个数的组合满足条件”类似问题

求与合计相除，小数位大于4的数字组合

1 + 3 + 4 + 9 = 17
1 / 17 ≈ 0.05882
3 / 17 ≈ 0.17647
4 / 17 ≈ 0.23529
9 / 17 ≈ 0.52941
可以发现，每一个商的第三位都是大于等于5的数，四舍五入后会进位。
下面的程序可以生成符合这样条件的数据。

import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.Random;
import java.util.stream.IntStream;public class Calculator {private enum COMPAREMOD {DAYU, DENGYU, XIAOYU}public Calculator() {// 第几位小数int bdNum1 = 3;// 大于等于小于 数字几int bdNum2 = 4;// 计算100次，任意三个100以内的数，共有多少个数满足条件，与合计值相除后，商的第3位小数大于4// doHalfAdjustRandom(100, bdNum1, bdNum2, COMPAREMOD.DAYU);// 计算3个10以内的数字，共有多少个数满足条件，与合计值相除后，商的第3位小数大于4。int max = 9;int count = 0;for (int i = 1; i <= max; i++) {for (int j = 1; j <= max; j++) {for (int k = 1; k <= max; k++) {if (doHalfAdjustRecycle2(bdNum1, bdNum2, COMPAREMOD.DAYU, i, j, k)) {count += 1;}}}}if (count != 0) {System.out.println("恭喜你，找到了" + count + "个这样的数！");} else {System.out.println("很遗憾，没找到！");}count = 0;// 计算4个10以内的数字，共有多少个数满足条件，与合计值相除后，商的第3位小数大于4。for (int i = 1; i <= 32767; i++) {if (doHalfAdjustRecycle2(bdNum1, bdNum2, COMPAREMOD.DAYU, i, i + 1, i + 2, i + 3)) {count += 1;}}if (count != 0) {System.out.println("恭喜你，找到了" + count + "个这样的数！");} else {System.out.println("很遗憾，没找到！");}}/*** 通过targetRecycle次运算，任意三个随机数，计算它们分别与合计的值进行除算，得到的商中满足条件的组合。* * @param targetRecycle   随机循环次数* @param compareNumIndex 第几位小数* @param comparedNum     和哪个数字进行比较* @param mode            比较是大于等于还是等于* @return*/private boolean doHalfAdjustRandom(int targetRecycle, int compareNumIndex, int comparedNum, COMPAREMOD mode) {return doHalfAdjustRecycleRandom(targetRecycle, 0, compareNumIndex, comparedNum, mode);}/*** @param targetRecycle   随机循环次数* @param currentRecycle  随机循环当前次数* @param compareNumIndex 第几位小数* @param comparedNum     和哪个数字进行比较* @param mode            比较是大于等于还是等于* @return*/private boolean doHalfAdjustRecycleRandom(int targetRecycle, int currentRecycle, int compareNumIndex,int comparedNum, COMPAREMOD mode) {BigDecimal zero = new BigDecimal(0);BigDecimal num1 = null;BigDecimal num2 = null;BigDecimal num3 = null;try {Random r = new Random();num1 = new BigDecimal(r.nextInt(100));num2 = new BigDecimal(r.nextInt(100));num3 = new BigDecimal(r.nextInt(100));} catch (Exception e) {e.printStackTrace();}if (num1 == zero || num2 == zero || num3 == zero) {return false;}BigDecimal sum = num1.add(num2).add(num3);BigDecimal result1 = num1.divide(sum, 5, RoundingMode.UP);BigDecimal result2 = num2.divide(sum, 5, RoundingMode.UP);BigDecimal result3 = num3.divide(sum, 5, RoundingMode.UP);int locThreshold1 = Integer.parseInt(result1.toString().substring(compareNumIndex + 1, compareNumIndex + 2));int locThreshold2 = Integer.parseInt(result2.toString().substring(compareNumIndex + 1, compareNumIndex + 2));int locThreshold3 = Integer.parseInt(result3.toString().substring(compareNumIndex + 1, compareNumIndex + 2));if (compare(comparedNum, mode, locThreshold1, locThreshold2, locThreshold3)) {System.out.println(num1 + "+" + num2 + "+" + num3 + "=" + sum);System.out.println(num1 + "/" + sum + "=" + result1.toString().substring(0, compareNumIndex + 2));System.out.println(num2 + "/" + sum + "=" + result2.toString().substring(0, compareNumIndex + 2));System.out.println(num3 + "/" + sum + "=" + result3.toString().substring(0, compareNumIndex + 2));System.out.println("****************\n");// return true;}if (targetRecycle == currentRecycle) {System.out.println("计算结束");return false;} else {return doHalfAdjustRecycleRandom(targetRecycle, currentRecycle + 1, compareNumIndex, comparedNum, mode);}}/*** 指定任意个数的数字，计算它们分别与合计的值进行除算，得到的商中满足条件的组合。* * @param targetRecycle   随机循环次数* @param currentRecycle  随机循环当前次数* @param compareNumIndex 第几位小数* @param comparedNum     和哪个数字进行比较* @param mode            比较是大于等于还是等于* @return*/private boolean doHalfAdjustRecycle2(int compareNumIndex, int comparedNum, COMPAREMOD mode, int... numParamArray) {// numParamArray的合计BigDecimal sum = new BigDecimal(IntStream.of(numParamArray).sum());// 商的集合BigDecimal[] thres = new BigDecimal[numParamArray.length];for (int i = 0; i < thres.length; i++) {// 求每一个数除以合计的商，第compareNumIndex+3位小数四舍五入。thres[i] = new BigDecimal(numParamArray[i]).divide(sum, compareNumIndex + 3, RoundingMode.FLOOR);// 求第compareNumIndex位小数int locThreshold = Integer.parseInt(thres[i].toString().substring(compareNumIndex + 1, compareNumIndex + 2));// 如果第compareNumIndex位的小数值不满足要求，则返回false，终止程序if (!compare(comparedNum, mode, locThreshold)) {return false;}}for (int i = 0; i < numParamArray.length; i++) {System.out.println(numParamArray[i] + "/" + sum + "≈" + thres[i].toString().substring(0, compareNumIndex + 2));}System.out.println("****************\n");return true;}/*** num与comparedNum做比较* * @param comparedNum 正整数* @param mode        比较模式：大于，等于，小于* @param num         正整数* @return*/private boolean compare(int comparedNum, COMPAREMOD mode, int... numParamArray) {for (int i = 0; i < numParamArray.length; i++) {int compareSrc = numParamArray[i];if (mode == COMPAREMOD.DAYU) {if (compareSrc <= comparedNum)return false;} else if (mode == COMPAREMOD.DENGYU) {if (compareSrc != comparedNum)return false;} else {if (compareSrc >= comparedNum)return false;}}return true;}public static void main(String[] args) {Calculator c = new Calculator();}}

计算结果

1/6≈0.166

1/6≈0.166

4/6≈0.666

---

1/6≈0.166

4/6≈0.666

1/6≈0.166

---

1/13≈0.076

4/13≈0.307

8/13≈0.615

---

1/15≈0.066

7/15≈0.466

7/15≈0.466

---

1/13≈0.076

8/13≈0.615

4/13≈0.307

---

2/7≈0.285

2/7≈0.285

3/7≈0.428

---

2/12≈0.166

2/12≈0.166

8/12≈0.666

---

2/7≈0.285

3/7≈0.428

2/7≈0.285

---

2/12≈0.166

5/12≈0.416

5/12≈0.416

---

2/16≈0.125

7/16≈0.437

7/16≈0.437

---

2/12≈0.166

8/12≈0.666

2/12≈0.166

---

3/7≈0.428

2/7≈0.285

2/7≈0.285

---

3/16≈0.187

6/16≈0.375

7/16≈0.437

---

3/16≈0.187

7/16≈0.437

6/16≈0.375

---

4/6≈0.666

1/6≈0.166

1/6≈0.166

---

4/13≈0.307

1/13≈0.076

8/13≈0.615

---

4/14≈0.285

4/14≈0.285

6/14≈0.428

---

4/15≈0.266

4/15≈0.266

7/15≈0.466

---

4/17≈0.235

4/17≈0.235

9/17≈0.529

---

4/14≈0.285

5/14≈0.357

5/14≈0.357

---

4/14≈0.285

6/14≈0.428

4/14≈0.285

---

4/15≈0.266

7/15≈0.466

4/15≈0.266

---

4/13≈0.307

8/13≈0.615

1/13≈0.076

---

4/17≈0.235

9/17≈0.529

4/17≈0.235

---

5/12≈0.416

2/12≈0.166

5/12≈0.416

---

5/14≈0.357

4/14≈0.285

5/14≈0.357

---

5/12≈0.416

5/12≈0.416

2/12≈0.166

---

5/14≈0.357

5/14≈0.357

4/14≈0.285

---

6/16≈0.375

3/16≈0.187

7/16≈0.437

---

6/14≈0.428

4/14≈0.285

4/14≈0.285

---

6/19≈0.315

6/19≈0.315

7/19≈0.368

---

6/21≈0.285

6/21≈0.285

9/21≈0.428

---

6/16≈0.375

7/16≈0.437

3/16≈0.187

---

6/19≈0.315

7/19≈0.368

6/19≈0.315

---

6/21≈0.285

9/21≈0.428

6/21≈0.285

---

7/15≈0.466

1/15≈0.066

7/15≈0.466

---

7/16≈0.437

2/16≈0.125

7/16≈0.437

---

7/16≈0.437

3/16≈0.187

6/16≈0.375

---

7/15≈0.466

4/15≈0.266

4/15≈0.266

---

7/16≈0.437

6/16≈0.375

3/16≈0.187

---

7/19≈0.368

6/19≈0.315

6/19≈0.315

---

7/15≈0.466

7/15≈0.466

1/15≈0.066

---

7/16≈0.437

7/16≈0.437

2/16≈0.125

---

8/13≈0.615

1/13≈0.076

4/13≈0.307

---

8/12≈0.666

2/12≈0.166

2/12≈0.166

---

8/13≈0.615

4/13≈0.307

1/13≈0.076

---

8/26≈0.307

9/26≈0.346

9/26≈0.346

---

9/17≈0.529

4/17≈0.235

4/17≈0.235

---

9/21≈0.428

6/21≈0.285

6/21≈0.285

---

9/26≈0.346

8/26≈0.307

9/26≈0.346

---

9/26≈0.346

9/26≈0.346

8/26≈0.307

---

恭喜你，找到了51个这样的数！

很遗憾，没找到！

连续数字的验证

使用下面的程序，可以使用更大的数据去验证，是否存在连续的数字符合这样的计算方式。**
执行结果是没有找到，大概率是不存在的。

import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.Random;
import java.util.stream.IntStream;public class Calculator2 {private enum COMPAREMOD {DAYU, DENGYU, XIAOYU}public Calculator2() {// 第几位小数int bdNum1 = 3;// 大于等于小于 数字几int bdNum2 = 4;boolean blrst = false;int count = 0;// 计算4个10以内的数字，共有多少个数满足条件，与合计值相除后，商的第3位小数大于4。for (BigDecimal i = new BigDecimal(1); i.compareTo(new BigDecimal("1000000000000")) != -1; i.add(new BigDecimal(1))) {BigDecimal n0 = i.add(new BigDecimal(0));BigDecimal n1 = i.add(new BigDecimal(1));BigDecimal n2 = i.add(new BigDecimal(2));BigDecimal n3 = i.add(new BigDecimal(3));BigDecimal n4 = i.add(new BigDecimal(4));BigDecimal n5 = i.add(new BigDecimal(5));BigDecimal n6 = i.add(new BigDecimal(6));BigDecimal n7 = i.add(new BigDecimal(7));BigDecimal n8 = i.add(new BigDecimal(8));BigDecimal n9 = i.add(new BigDecimal(9));if (doHalfAdjustRecycle2(bdNum1, bdNum2, COMPAREMOD.DAYU, n0, n1, n2, n3, n4, n5, n6, n7, n8, n9)) {count += 1;blrst = true;}}if (blrst) {System.out.println("恭喜你，找到了" + count + "个这样的数！");} else {System.out.println("计算结束，没找到！");}}/*** 指定任意个数的数字，计算它们分别与合计的值进行除算，得到的商中满足条件的组合。* * @param targetRecycle   随机循环次数* @param currentRecycle  随机循环当前次数* @param compareNumIndex 第几位小数* @param comparedNum     和哪个数字进行比较* @param mode            比较是大于等于还是等于* @return*/private boolean doHalfAdjustRecycle2(int compareNumIndex, int comparedNum, COMPAREMOD mode,BigDecimal... numParamArray) {// numParamArray的合计// BigDecimal sum = new BigDecimal(IntStream.of(numParamArray).sum());BigDecimal sum = new BigDecimal(0);for (int i = 0; i < numParamArray.length; i++) {sum = sum.add(numParamArray[i]);}// 商的集合BigDecimal[] thres = new BigDecimal[numParamArray.length];for (int i = 0; i < thres.length; i++) {// 求每一个数除以合计的商，第compareNumIndex+3位小数四舍五入。thres[i] = numParamArray[i].divide(sum, compareNumIndex + 3, RoundingMode.FLOOR);// 求第compareNumIndex位小数BigDecimal locThreshold = new BigDecimal(thres[i].toString().substring(compareNumIndex + 1, compareNumIndex + 2));// 如果第compareNumIndex位的小数值不满足要求，则返回false，终止程序if (!compare(new BigDecimal(comparedNum), mode, locThreshold)) {return false;}}for (int i = 0; i < numParamArray.length; i++) {System.out.println(numParamArray[i] + "/" + sum + "≈" + thres[i].toString().substring(0, compareNumIndex + 2));}System.out.println("****************\n");return true;}/*** num与comparedNum做比较* * @param comparedNum 正整数* @param mode        比较模式：大于，等于，小于* @param num         正整数* @return*/private boolean compare(BigDecimal comparedNum, COMPAREMOD mode, BigDecimal... numParamArray) {for (int i = 0; i < numParamArray.length; i++) {BigDecimal compareSrc = numParamArray[i];if (mode == COMPAREMOD.DAYU) {if (compareSrc.compareTo(comparedNum) != 1)return false;} else if (mode == COMPAREMOD.DENGYU) {if (compareSrc.compareTo(comparedNum) != 0)return false;} else {if (compareSrc.compareTo(comparedNum) != -1)return false;}}return true;}public static void main(String[] args) {Calculator2 c = new Calculator2();}}