最长公共子串和最长公共子序列。。。傻傻烦不清楚

最长公共子串和最长公共子序列。。。傻傻烦不清楚

 

    举个栗子：

 

    str1="123ABCD456" str2 ="ABE12345D"

 

    最长公共子串是：123

 

    最长公共子序列是：12345

 

 

    这两个都可以用动态规划，只是状态转移方程有点区别

 

    最长公共子序列是：

 

    dp[i][j] -- 表示子串str1[0...i]和子串str[0...j]的最长公共子序列

 

    当str1[i] == str2[j]时，dp[i][j] = dp[i-1][j-1] +1;

 

    否则，dp[i][j] = max(dp[i-1][j], dp[i][j-1]);

 

    最优解为dp[len1-1][len2-1];

 

      

 

    最长公共子串是： dp[i][j] -- 表示以str1[i]和str2[j]为结尾的最长公共子串 当str1[i] == str2[j]时，dp[i][j] = dp[i-1][j-1] +1; 否则，dp[i][j] =0;

 

    最优解为max(dp[i][j]),其中0<=i<len1,0<=j<len2;

 




代码如下：

 

   //求最长公共子串

 

import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner scanner=new Scanner(System.in);
while(scanner.hasNext()){
String str1=scanner.next();
String str2=scanner.next();
System.out.println(getCommonStrLength(str1,str2));
}
scanner.close();
}


private static int getCommonStrLength(String str1, String str2) {
str1=" "+str1;
str2=" "+str2;
char[] a=str1.toCharArray();
char[] b=str2.toCharArray();
int m=a.length;
int n=b.length;
int[][]c=new int[m][n];
int max=0;
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
if (a[i]==b[j]) {
c[i][j]=c[i-1][j-1]+1;
}else {
c[i][j]=0;
}
if (max<c[i][j]) {
max=c[i][j];//记录最长子串
}
}
}
return max;
}

}

 //求最长公共子序列

import java.util.Scanner;


public class Main {
public static void main(String[] args) {
Scanner scanner=new Scanner(System.in);
while(scanner.hasNext()){
String str1=scanner.next();
String str2=scanner.next();
System.out.println(getCommonStrLength(str1,str2));
}
scanner.close();
}


private static int getCommonStrLength(String str1, String str2) {
str1=" "+str1;
str2=" "+str2;
char[] a=str1.toCharArray();
char[] b=str2.toCharArray();
int m=a.length;
int n=b.length;
int[][]c=new int[m][n];
int max=0;
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
if (a[i]==b[j]) {
c[i][j]=c[i-1][j-1]+1;
}else {
c[i][j]=Math.max(c[i-1][j], c[i][j-1]);
}
}
}
return c[m-1][n-1];
}
}