从M中选N C(M，N) Demo（参考）
import java.util.ArrayList;
import java.util.List;
import java.util.Objects;
public class MathUtil {
/// <summary>
/// 从n中 取出 m的组合个数
/// n!/(m!*(n-m)!)
/// </summary>
/// <param name="n"></param>
/// <param name="m"></param>
/// <returns></returns>
private static int combination(int n, int m) {
return factorial(n, n - m) / factorial(m, 0);
}
/// <summary>
/// 阶乘
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
private static int factorial(int n, int limit) {
int res = 1;
for (int i = n; i > limit; i--) {
res = res * i;
}
return res;
}
/**
* 从n个数字中选择m个数字
*/
public static List<int[]> combine(int[] a,int m){
int n = a.length;
if(m>n){
return null;
}
if(m==n){
ArrayList<int[]> ints = new ArrayList<>();
ints.add(a);
return ints;
}
List<int[]> result = new ArrayList<int[]>();
int[] bs = new int[n];
for(int i=0;i<n;i++){
bs[i]=0;
}
//初始化
for(int i=0;i<m;i++){
bs[i]=1;
}
boolean flag = true;
boolean tempFlag = false;
int pos ,sum;
//首先找到第一个10组合，然后变成01，同时将左边所有的1移动到数组的最左边
do{
sum = 0;
pos = 0;
tempFlag = true;
result.add(print(bs,a,m));
for(int i=0;i<n-1;i++){
if(bs[i]==1 && bs[i+1]==0 ){
bs[i]=0;
bs[i+1]=1;
pos = i;
break;
}
}
//将左边的1全部移动到数组的最左边
for(int i=0;i<pos;i++){
if(bs[i]==1){
sum++;
}
}
for(int i=0;i<pos;i++){
if(i<sum){
bs[i]=1;
}else{
bs[i]=0;
}
}
//检查是否所有的1都移动到了最右边
for(int i= n-m;i<n;i++){
if(bs[i]==0){
tempFlag = false;
break;
}
}
flag = tempFlag == false;
}while(flag);
result.add(print(bs,a,m));
return result;
}
public static List<String[]> combine(String[] a,int m){
int n = a.length;
if(m>n){
return null;
}
if(m==n){
ArrayList<String[]> ints = new ArrayList<>();
ints.add(a);
return ints;
}
List<String[]> result = new ArrayList<>();
String[] bs = new String[n];
for(int i=0;i<n;i++){
bs[i]="0";
}
//初始化
for(int i=0;i<m;i++){
bs[i]="1";
}
boolean flag = true;
boolean tempFlag = false;
int pos ,sum;
//首先找到第一个10组合，然后变成01，同时将左边所有的1移动到数组的最左边
do{
sum = 0;
pos = 0;
tempFlag = true;
result.add(print(bs,a,m));
for(int i=0;i<n-1;i++){
if(Objects.equals(bs[i], "1") && Objects.equals(bs[i + 1], "0")){
bs[i]="0";
bs[i+1]="1";
pos = i;
break;
}
}
//将左边的1全部移动到数组的最左边
for(int i=0;i<pos;i++){
if(Objects.equals(bs[i], "1")){
sum++;
}
}
for(int i=0;i<pos;i++){
if(i<sum){
bs[i]="1";
}else{
bs[i]="0";
}
}
//检查是否所有的1都移动到了最右边
for(int i= n-m;i<n;i++){
if(Objects.equals(bs[i], "0")){
tempFlag = false;
break;
}
}
flag = !tempFlag;
}while(flag);
result.add(print(bs,a,m));
return result;
}
private static int[] print(int[] bs,int[] a,int m){
int[] result = new int[m];
int pos= 0;
for(int i=0;i<bs.length;i++){
if(bs[i]==1){
result[pos]=a[i];
pos++;
}
}
return result ;
}
private static String[] print(String[] bs,String[] a,int m){
String [] result = new String[m];
int pos= 0;
for(int i=0;i<bs.length;i++){
if(Objects.equals(bs[i], "1")){
result[pos]=a[i];
pos++;
}
}
return result ;
}
/**
* 排列选择（从列表中选择n个排列）
* @param dataList 待选列表
* @param n 选择个数
*/
static void arrangementSelect(String[] dataList, int n, List<String[]> result) {
arrangementSelect(dataList, new String[n], 0,result);
}
/**
* 排列选择
* @param dataList 待选列表
* @param results 前面（resultIndex-1）个的排列结果
* @param resultIndex 选择索引，从0开始
*/
private static void arrangementSelect(String[] dataList, String[] results, int resultIndex, List<String[]> result) {
int resultLen = results.length;
if (resultIndex >= resultLen) { // 全部选择完时，输出排列结果
String [] temps = new String[resultLen];
System.arraycopy(results, 0, temps, 0, results.length);
result.add(temps);
// System.out.println(Arrays.asList(temps));
return;
}
// 递归选择下一个
for (String aDataList : dataList) {
// 判断待选项是否存在于排列结果中
boolean exists = false;
for (int j = 0; j < resultIndex; j++) {
if (aDataList.equals(results[j])) {
exists = true;
break;
}
}
if (!exists) { // 排列结果不存在该项，才可选择
results[resultIndex] = aDataList;
arrangementSelect(dataList, results, resultIndex + 1, result);
}
}
}
/**
* 组合选择（从列表中选择n个组合）
* @param dataList 待选列表
* @param n 选择个数
*/
public static void combinationSelect(String[] dataList, int n, List<String[]> result) {
combinationSelect(dataList, 0, new String[n], 0,result);
}
/**
* 组合选择
* @param dataList 待选列表
* @param dataIndex 待选开始索引
* @param resultList 前面（resultIndex-1）个的组合结果
* @param resultIndex 选择索引，从0开始
*/
private static void combinationSelect(String[] dataList, int dataIndex, String[] resultList, int resultIndex,List<String[]> result) {
int resultLen = resultList.length;
int resultCount = resultIndex + 1;
if (resultCount > resultLen) { // 全部选择完时，输出组合结果
String [] temps = new String[resultLen];
System.arraycopy(resultList, 0, temps, 0, resultList.length);
result.add(temps);
// System.out.println(Arrays.asList(temps));
return;
}
// 递归选择下一个
for (int i = dataIndex; i < dataList.length + resultCount - resultLen; i++) {
resultList[resultIndex] = dataList[i];
combinationSelect(dataList, i + 1, resultList, resultIndex + 1,result);
}
}
/**
* 计算阶乘数，即n! = n * (n-1) * ... * 2 * 1
*/
public static long factorial(int n) {
return (n > 1) ? n * factorial(n - 1) : 1;
}
/**
* 计算排列数，即A(n, m) = n!/(n-m)!
*/
private static long arrangement(int n, int m) {
return (n >= m) ? factorial(n) / factorial(n - m) : 0;
}
public static void main(String[] args) {
/* Date date1 = new Date();
int [] initNum = new int[]{1,2,3,4,5,6,7,8,9,10,11};
System.out.println(combine(initNum,8).size());
Date date2 = new Date();
System.out.println("毫秒："+(date2.getTime()-date1.getTime()));
Date date3 = new Date();
String [] strInit = new String[]{"1","2","3","4","5","6","7","8","9","10","11"};
System.out.println(combine(strInit,8).size());
Date date4 = new Date();
System.out.println("毫秒："+(date4.getTime()-date3.getTime()));*/
String [] dataList = new String[] {
"01", "02", "03", "04", "05", "06", "07", "08", "09", "10", "11"
};
Integer n = 2;
List<String[]> result = new ArrayList<>();
arrangementSelect(dataList, n,result);
System.out.println(result.size());
for(int i = 0; i < result.size(); i++){
System.out.println("第"+(i+1)+"个组合："+result.get(i)[0]+" "+result.get(i)[1]);
}
System.out.println(String.format("A(%d, %d) = %d", dataList.length, n, arrangement(dataList.length, n)));
combinationSelect(dataList, 3,result);
System.out.println(result.size());
System.out.println(String.format("C(%d, %d) = %d", dataList.length, n, combination(dataList.length, n)));
}
}
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