求排列组合的小技巧

求解组合数方法：

public class Combination {public List<List<Integer>> combination(int[] a,int m){ dfs(-1,0,m,a); return re; }List<List<Integer>> re=new ArrayList<List<Integer>>();List<Integer> trace=new ArrayList<Integer>();public void dfs(int k,int level,int m,int[] a){if(level==m){re.add(new ArrayList<Integer>(trace));return;}for(int i=k+1;i<a.length;i++){trace.add(a[i]);dfs(i,level+1,m,a);trace.remove(trace.size()-1);}}public static void main(String[] args) {Combination c=new Combination();System.out.println(c.combination(new int[]{1,2,3,4},2));}}

组合数去重两种做法：

做法1：

public class Combination2 {//去重public List<List<Integer>> combination(int[] a,int m){ Arrays.sort(a);//组合数的去重一定要先排序 dfs(-1,0,m,a); return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();List<Integer> trace=new ArrayList<Integer>();public void dfs(int k,int level,int m,int[] a){if(level==m){re.add(new ArrayList<Integer>(trace));return;}HashSet<Integer> set=new HashSet<Integer>();for(int i=k+1;i<a.length;i++){if(set.contains(a[i])) continue;set.add(a[i]);trace.add(a[i]);dfs(i,level+1,m,a);trace.remove(trace.size()-1);}}public static void main(String[] args) {Combination2 c=new Combination2();System.out.println(c.combination(new int[]{1,2,1,4},2));}}

做法2：

public class Combination3 {//去重public List<List<Integer>> combination(int[] a,int m){ Arrays.sort(a);//组合数的去重一定要先排序 dfs(-1,0,m,a); return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();List<Integer> trace=new ArrayList<Integer>();public void dfs(int k,int level,int m,int[] a){if(level==m){re.add(new ArrayList<Integer>(trace));return;}for(int i=k+1;i<a.length;i++){if(i!=k+1&&a[i]==a[i-1]) continue;trace.add(a[i]);dfs(i,level+1,m,a);trace.remove(trace.size()-1);}}public static void main(String[] args) {Combination3 c=new Combination3();System.out.println(c.combination(new int[]{1,2,1,4},2));}}

求解排列数：

两种做法：

1 通过swap的方式

2 通过boolean flag[] 数组标记已取得 数组的方法

方法1：

public class Permutation {public List<List<Integer>> permutatation(int[] a,int m){if(a.length==0) return re;dfs(0,a,m);return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();public void dfs(int k,int[] a,int m){if(k==m){List<Integer> temp=new ArrayList<Integer>();for(int i=0;i<m;i++) temp.add(a[i]);re.add(temp);return;}for(int i=k;i<a.length;i++){swap(a,k,i);dfs(k+1,a,m);swap(a,k,i);}}private void swap(int[] a, int i, int j) {int temp=a[i]; a[i]=a[j]; a[j]=temp;}public static void main(String[] args) {Permutation s=new Permutation();System.out.println(s.permutatation(new int[]{1,2,3,4},2));}}

针对这种方法的去重：

public class Permutation2 {public List<List<Integer>> permutatation(int[] a,int m){if(a.length==0) return re;dfs(0,a,m);return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();public void dfs(int k,int[] a,int m){if(k==m){List<Integer> temp=new ArrayList<Integer>();for(int i=0;i<m;i++) temp.add(a[i]);re.add(temp);return;}for(int i=k;i<a.length;i++){if(!isSwap(k,i,a)) continue;swap(a,k,i);dfs(k+1,a,m);swap(a,k,i);}}public boolean isSwap(int start,int end,int[] a){for(int i=start;i<end;i++){if(a[i]==a[end]) return false;}return true;}private void swap(int[] a, int i, int j) {int temp=a[i]; a[i]=a[j]; a[j]=temp;}public static void main(String[] args) {Permutation2 s=new Permutation2();System.out.println(s.permutatation(new int[]{1,1,1,4},2));}}

方法二：

public class Permutation3 {public List<List<Integer>> permutatation(int[] a,int m){if(a.length==0) return re;flag=new boolean[a.length];dfs(0,a,m);return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();List<Integer> trace=new ArrayList<Integer>();boolean[] flag;public void dfs(int k,int[] a,int m){if(k>m) return;if(k==m){re.add(new ArrayList<Integer>(trace));return;}for(int i=0;i<a.length;i++){if(flag[i]) continue;trace.add(a[i]);flag[i]=true;dfs(k+1,a,m);flag[i]=false;trace.remove(trace.size()-1);}}public static void main(String[] args) {Permutation3 s=new Permutation3();System.out.println(s.permutatation(new int[]{1,2,3,4},2));}}

方法二的去重：

去重1：

public class Permutation4 {//去重public List<List<Integer>> permutatation(int[] a,int m){if(a.length==0) return re;flag=new boolean[a.length];dfs(0,a,m);return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();List<Integer> trace=new ArrayList<Integer>();boolean[] flag;public void dfs(int k,int[] a,int m){if(k>m) return;if(k==m){re.add(new ArrayList<Integer>(trace));return;}HashSet<Integer> set=new HashSet<Integer>();for(int i=0;i<a.length;i++){if(flag[i]) continue;if(set.contains(a[i])) continue;set.add(a[i]);trace.add(a[i]);flag[i]=true;dfs(k+1,a,m);flag[i]=false;trace.remove(trace.size()-1);}}public static void main(String[] args) {Permutation4 s=new Permutation4();System.out.println(s.permutatation(new int[]{1,2,1,4},2));}}

去重2：

public class Permutation5 {//去重public List<List<Integer>> permutatation(int[] a,int m){if(a.length==0) return re;Arrays.sort(a);flag=new boolean[a.length];dfs(0,a,m);return re;}List<List<Integer>> re=new ArrayList<List<Integer>>();List<Integer> trace=new ArrayList<Integer>();boolean[] flag;public void dfs(int k,int[] a,int m){if(k>m) return;if(k==m){re.add(new ArrayList<Integer>(trace));return;}for(int i=0;i<a.length;i++){if(flag[i]) continue;if(i!=0&&!flag[i-1]&&a[i]==a[i-1]) continue;trace.add(a[i]);flag[i]=true;dfs(k+1,a,m);flag[i]=false;trace.remove(trace.size()-1);}}public static void main(String[] args) {Permutation5 s=new Permutation5();System.out.println(s.permutatation(new int[]{1,2,1,4},2));}}