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RecursionDemo.java
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497 lines (351 loc) · 9.92 KB
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import java.util.*;
public class RecursionDemo{
/**************************************** SubSequence **************************************/
public static HashSet<String> getSubSequence(String str){
HashSet<String> arr=new HashSet<String>();
subSeqProcess(str.toCharArray(),0,"",arr);
return arr;
}
public static void subSeqProcess(char[] str,int length,String path,HashSet<String> list){
if(str.length ==length){
list.add(path);
return ;
}
char ch = str[length];
subSeqProcess(str,length+1,path,list);
subSeqProcess(str,length+1,path+String.valueOf(ch),list);
}
/**************************************** Permutation *************************************/
public static HashSet<String> getPermutation(String str){
HashSet<String> arr=new HashSet<String>();
ArrayList<Character> strArr=new ArrayList<Character>();
for (int i=0; i<str.toCharArray().length; i++) {
strArr.add(str.toCharArray()[i]);
}
permuProcess(strArr,"",arr);
return arr;
}
public static void permuProcess(ArrayList<Character> str,String path,HashSet<String> list){
if(str.isEmpty()){
list.add(path);
}else{
int length = str.size();
for (int i=0; i<length;i++ ) {
char ch = str.get(i);
str.remove(i);
permuProcess(str,path+ch,list);
str.add(i,ch);
}
}
}
/**************************************** reboot1 *************************************/
public static int reboot(int size,int start,int aim,int rest){
return process(size,start,aim,rest);
}
public static int process(int size,int start,int aim,int rest){
int ans;
if(rest == 0){
ans= start==aim?1:0;
}
else if(start == 1){
ans= process(size,start+1,aim,rest-1);
}
else if(start == size){
ans= process(size,size-1,aim,rest-1);
}
else{
ans= process(size,start-1,aim,rest-1) + process(size,start+1,aim,rest-1);
}
return ans;
}
/**************************************** robot2 *************************************/
public static long reboot2(int size,int start,int aim,int rest){
long[][] dp = new long[size+1][rest+1];
for (int i=0; i<=size; i++) {
for (int j=0; j<=rest; j++) {
dp[i][j]=-1;
}
}
return process2(size,start,aim,rest,dp);
}
public static long process2(int size,int start,int aim,int rest,long[][] dp){
if(dp[start][rest]!=-1)
return dp[start][rest];
long ans;
if(rest == 0){
ans= start==aim?1:0;
}else if(start == 1){
ans= process2(size,start+1,aim,rest-1,dp);
}else if(start == size){
ans= process2(size,size-1,aim,rest-1,dp);
}
else{
ans= process2(size,start-1,aim,rest-1,dp) + process2(size,start+1,aim,rest-1,dp);
}
dp[start][rest]=ans;
return ans;
}
/**************************************** reboot3 *************************************/
public static long reboot3(int size,int start,int aim,int rest){
long[][] dp = new long[size+1][rest+1];
dp[aim][0]= 1;
for (int i=1; i<=rest; i++) {
dp[1][i] = dp[2][i - 1];
for (int j=2; j<size; j++) {
dp[j][i] = dp[j-1][i-1]+dp[j+1][i-1];
}
dp[size][i] = dp[size - 1][i - 1];
}
return dp[start][rest];
}
/**************************************** play *************************************/
// 根据规则，返回获胜者的分数
public static int win1(int[] arr) {
if (arr == null || arr.length == 0) {
return 0;
}
int N = arr.length;
int[][] fmap = new int[N][N];
int[][] gmap = new int[N][N];
for (int i=0;i<N ;i++ ) {
for (int j=0; j<N;j++ ) {
fmap[i][j]=gmap[i][j]=-1;
}
}
int first = f1(arr, 0, arr.length - 1,fmap,gmap);
int second = g1(arr, 0, arr.length - 1,fmap,gmap);
return Math.max(first, second);
}
// arr[L..R]，先手获得的最好分数返回
public static int f1(int[] arr, int L, int R,int[][] fmap,int[][] gmap) {
if (fmap[L][R] != -1) {
return fmap[L][R];
}
int ans = 0;
if (L == R) {
ans = arr[L];
} else {
int p1 = arr[L] + g1(arr, L + 1, R, fmap, gmap);
int p2 = arr[R] + g1(arr, L, R - 1, fmap, gmap);
ans = Math.max(p1, p2);
}
fmap[L][R] = ans;
return ans;
}
// // arr[L..R]，后手获得的最好分数返回
public static int g1(int[] arr, int L, int R,int[][] fmap,int[][] gmap) {
if (gmap[L][R] != -1) {
return gmap[L][R];
}
int ans = 0;
if (L != R) {
int p1 = f1(arr, L + 1, R, fmap, gmap); // 对手拿走了L位置的数
int p2 = f1(arr, L, R - 1, fmap, gmap); // 对手拿走了R位置的数
ans = Math.min(p1, p2);
}
gmap[L][R] = ans;
return ans;
}
public static int[] getArray(){
int max = 5;
int[] arr=new int[max];
for (int i=0; i<max; i++) {
arr[i] = (int)(Math.random()*100);
}
return arr;
}
public static int[][] getMatrix(int row,int clo){
int[][] arr=new int[row][clo];
for (int i=0; i<row; i++) {
for (int j=0; j<clo; j++) {
arr[i][j] = i==0&&j==0?0:(int)(Math.random()*2);
}
}
return arr;
}
public static int[][] copyMatrix(int[][] m){
int[][] arr=new int[m.length][m[0].length];
for (int i=0; i<m.length; i++) {
for (int j=0; j<m[0].length; j++) {
arr[i][j] = m[i][j];
}
}
return arr;
}
/**************************************** Bag *************************************/
public static int bag2(int[] w,int[] v,int bag){
int N = w.length;
int[][] dp = new int[N+1][bag+1];
for (int i=N-1; i>=0; i--) {
for (int rest=0; rest<=bag;rest++ ) {
int p1 = dp[i+1][rest];
int p2=0;
int next = rest-w[i]<0?-1:dp[i+1][rest-w[i]];
if(next != -1){
p2 = v[i]+next;
}
dp[i][rest] = Math.max(p1,p2);
}
}
return dp[0][bag];
}
public static int bag1(int[] w,int[] v,int bag){
return process3(w,v,0,bag);
}
public static int process3(int[] w,int[] v,int index,int rest){
if(rest<0){
return -1;
}
if(index == w.length){
return 0;
}
int p1 = process3(w,v,index+1,rest);
int p2=0;
int next = process3(w,v,index+1,rest-w[index]);
if(next != -1){
p2 = v[index]+next;
}
return Math.max(p1,p2);
}
/**************************************** Cut *************************************/
public static int cut1(int[]w,int[] v,int restLength){
int[] dp = new int[restLength+1];
for (int i=1; i<=restLength; i++) {
int max=0;
for (int j=1; j<=i&&j<v.length;j++ ) {
int r = restLength- w[j-1];
if(r>=0){
max= Math.max(v[j-1]+dp[i-j],max);
}
}
dp[i]=max;
}
System.out.println();
for (int i=0; i<=restLength; i++) {
System.out.print(dp[i]+",");
}
System.out.println();
return dp[restLength];
}
public static int cut(int[]w,int[] v,int restLength){
List<String> list= new ArrayList<String>();
int[] dp = new int[restLength+1];
for (int i=0; i<=restLength; i++) {
dp[i]=-1;
}
int max= process4(w,v,restLength,"",list,dp);
for (String str:list ) {
System.out.println(str);
}
System.out.println();
for (int i=0; i<=restLength; i++) {
System.out.print(dp[i]+",");
}
System.out.println();
return max;
}
public static void f(String path,List<String> list){
if(list.isEmpty()){
list.add(path);
}else{
int x=0;
for (String str: path.split(",") ) {
x+=Integer.valueOf(str);
}
int y=0;
for (String str:list.get(0).split(",") ) {
y+=Integer.valueOf(str);
}
if(x>y){
list.clear();
list.add(path);
}
}
}
public static int process4(int[]w,int[] v,int rest,String path,List<String> list,int[] dp){
if(dp[rest]!=-1){
return dp[rest];
}
if(rest == 0 ){
f(path,list);
return 0;
}
int max=0;
for (int i=1; i<=v.length; i++) {
int r = rest-w[i-1];
if(r>=0){
String p=path+v[i-1]+",";
// System.out.println("path = "+p+"$r="+r);
int p1=v[i-1]+process4(w,v,rest-w[i-1],p,list,dp);
max= Math.max(max,p1);
}
}
dp[rest]= max;
return max;
}
/**************************************** 迷宫 *************************************/
public static boolean migong(int[][] arr,int[] start,int[] end){
int curRow=start[0];
int curClo=start[1];
boolean[] result = new boolean[]{false};
migongProcess(arr,end,curRow,curClo,result);
return result[0];
}
public static void migongProcess(int[][] arr,int[] end,int curRow,int curClo,boolean[] result){
if(result[0]) return;
if(curRow<0 ||curClo<0 || curRow==arr.length || curClo==arr[0].length) return;
if(curRow == end[0] && curClo == end[1] && arr[curRow][curClo] == 0){
result[0]=true;
}
if(arr[curRow][curClo] == 0){
arr[curRow][curClo]=8;
migongProcess(arr,end,curRow,curClo+1,result); //right
migongProcess(arr,end,curRow,curClo-1,result); //left
migongProcess(arr,end,curRow+1,curClo,result); //bottom
migongProcess(arr,end,curRow-1,curClo,result); //top
}
}
public static void migongPrint(){
for (int w=0; w<1000;w++ ) {
int[][] arr= getMatrix(20,20);
int[] start = new int[]{0,0};
int[] end = new int[]{arr.length-1,arr[0].length-1};
boolean r=migong(arr,start,end);
if(r){
for (int i=0;i<arr.length;i++) {
System.out.println();
for (int j=0; j<arr[0].length;j++ ) {
System.out.print(arr[i][j]+",");
}
}
System.out.println();
System.out.println("result="+r);
return;
}
}
}
public static void main(String[] args){
// HashSet<String> arr = getSubSequence("acccddeeffccc");
// for (String str : arr ) {
// System.out.println("\""+str+"\"");
// }
// HashSet<String> arr = getPermutation("1114");
// for (String str : arr ) {
// System.out.println("\""+str+"\"");
// }
// System.out.println("count = "+reboot2(5,2,4,100));
// System.out.println("count = "+reboot3(5,2,4,100));
// int[] _arr = getArray();
// int result=win1(_arr);
int[] w=new int[]{1,2,3,4,5};
int[] v=new int[]{1,5,8,9,10};
System.out.println(bag1(w,v,4));
System.out.println(bag2(w,v,4));
// 1 2 3 4 5 6
// int[] w=new int[]{1,2,3,4,5};
// int[] v1=new int[]{2,5,1,9,4};
// System.out.println("max="+cut(w,v1,140));
// System.out.println("max="+cut1(w,v1,140));
//migongPrint();
}
}