《Java数据结构和算法》Six 递归
递归是一种自己调用自己的编程技术。
1、三角数字
1、3、6、10、15、21……第n项=n-1项的值+n
package Structure;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
public class triangleD {
static int theNumber;
public static void main(String[] args)throws IOException{
System.out.print("Enter a number: ");
theNumber = getInt();
int theAnswer = triangle(theNumber);
System.out.println("Trangle=" + theAnswer);
}
//三角数
//递归实现
public static int triangle(int n){
if(n==0)
return 1;
else
return(n+triangle(n-1));//将+变*为求阶乘
}
public static String getString() throws IOException{
InputStreamReader isr = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(isr);
String s = br.readLine();
return s;
}/*从键盘读入*/
public static int getInt()throws IOException{
String s = getString();
//Parses the string argument as a signed decimal integer.
return Integer.parseInt(s);
}
}
2、递归算法：
1）、调用自身
2）、解决比本步更小的问题
3）、存在足够简单的不需要调用自身就能得到的值，如n=1时三角数的第一项值为1。
package Structure;
/*全排列*/
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
public class TwoQuanPaiLie {
static int size;
static int count;
static char[] arrChar = new char[100];
public static void main(String[] args) throws IOException{
System.out.print("Enter a word :");
String input = getString();
size = input.length();
count = 0;
for(int j=0;j<size;j++){
arrChar[j] = input.charAt(j);
}
doAnagram(size);
}
public static void doAnagram(int newSize){
if(newSize==1)
return;
for(int j=0;j<newSize;j++){
doAnagram(newSize-1);
if(newSize==2)
displayWord();
rotate(newSize);
}
public static void rotate(int newSize){
int j;
int position = size-newSize;
char temp = arrChar[position];
for(j=position+1;j<size;j++)
arrChar[j-1] = arrChar[j];
arrChar[j-1] = temp;
}
public static void displayWord(){
if(count<99)
System.out.print(" ");
if(count<9)
System.out.print(" ");
System.out.print(++count+" ");
for(int j=0;j<size;j++)
System.out.print(arrChar[j]);
System.out.print(" ");
System.out.flush();
if(count%6==0)
System.out.println("");
}
public static String getString()throws IOException{
InputStreamReader isr = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(isr);
String s = br.readLine();
return s;
}
}}/*Outputs:
Enter a word :cat
1 cat 2 cta 3 atc 4 act 5 tca 6 tac
*/
3、递归实现二分查找
package Structure;
class OrdArray{
private long[] a;
private int nElems;
public OrdArray(int max){
a = new long[max];
nElems = 0;
}
public int size(){
return nElems;
}
/*public int find(long searchKey){
int lowerBound = 0;
int upperBound = nElems - 1;
int curIn;
while(true){
curIn = (lowerBound + upperBound) / 2;
if(a[curIn]==searchKey)
return curIn;
else if(lowerBound>upperBound)
return nElems;
else{
if(a[curIn]<searchKey)
lowerBound = curIn + 1;
else
upperBound = curIn - 1;
}
}
}*///end find
//递归实现二分查找
public int find(long searchKey,int lowerBound,int upperBound){
int curIn;
curIn = (lowerBound + upperBound) / 2;
if(a[curIn]==searchKey)
return curIn;
else if(lowerBound > upperBound)
return nElems;
else{
if(a[curIn]<searchKey)
return find(searchKey,curIn+1,upperBound);
else
return find(searchKey,lowerBound,curIn-1);
}
}//end find
public void insert(long value){
int j;
for(j=0;j<nElems;j++)
if(a[j]>value)
break;
for(int k=nElems;k>j;k--)
a[k] = a[k-1];
a[j] = value;
nElems++;
}//end insert
public boolean delete(long value ){
int j = find(value, 0, nElems - 1);
if(j==nElems)
return false;
else{
for(int k=j;k<nElems;k++)
a[k] = a[k+1];
nElems--;
return true;
}
}//end delete
public void display(){
for(int j=0;j<nElems;j++)
System.out.print(a[j]+" ");
System.out.println("");
}
}
public class TwoDiGuiOrderedArray {
public static void main(String[] args){
int maxSize = 100;
OrdArray arr;
arr = new OrdArray(maxSize);
arr.insert(12);
arr.insert(103);
arr.insert(131);
arr.insert(113);
arr.insert(123);
arr.insert(133);
int searchKey = 55;
if(arr.find(searchKey,0,(arr.size()-1))!=arr.size())
System.out.println("find " + searchKey);
else
System.out.println("Can't find " + searchKey);
arr.display();
arr.delete(13);
arr.delete(103);
arr.display();
}
}
4、汉诺塔问题
将第一个柱子上的盘子按现在同样的顺序移到最后一个柱子上，可以使用中间的柱子。
package Structure;
public class SixTowers {
static int nDisks = 3;
public static void doTowers(int topN,char from,char inter,char to){
if(topN==1)
System.out.println("Disk 1 from "+from+" to "+to);
else{
doTowers(topN-1,from,to,inter);
System.out.println("Disk "+topN+" from "+from+" to "+to);
doTowers(topN-1,inter,from,to);
}
}
public static void main(String[] args){
doTowers(nDisks,'A','B','C');
}
} /*Outputs:
Disk 1 from A to C
Disk 2 from A to B
Disk 1 from C to B
Disk 3 from A to C
Disk 1 from B to A
Disk 2 from B to C
Disk 1 from A to C*/
5、归并排序
归并两个已经有序的数组。
package Structure;
/*归并排序，注意待归并的两个数组都是有序的*/
public class SixGuiBing {
public static void guiBing(int[] arrA,int sizeA,int[]
arrB,int sizeB,int arrC[]){
int aDex = 0,bDex = 0,cDex = 0;
while(aDex < sizeA && bDex < sizeB){
if(arrA[aDex] < arrB[bDex])
arrC[cDex++] = arrA[aDex++];
else
arrC[cDex++] = arrB[bDex++];
}/*复制小的到arrC*/
while(aDex < sizeA)
arrC[cDex++] = arrA[aDex++];//arrB排空了，arrA未空
while(bDex < sizeB)
arrC[cDex++] = arrB[bDex++];//arrA排空了，arrB未空
}
public static void display(int[] theArr,int size){
for(int j=0;j<size;j++)
System.out.print(theArr[j]+" ");
System.out.println("");
}
public static void main(String[] args){
int[] arrA = {10,12,20,21,30};
int[] arrB = {0,2,3,11,23};
int[] arrC = new int[10];
guiBing(arrA,5,arrB,5,arrC);
display(arrC,10);
}
}/*Output:0 2 3 10 11 12 20 21 23 30 */