算法设计与分析——动态规划——最长公共子序列

蔚落 2022-11-16 15:17 126阅读 0赞

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 1]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 2]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 3]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 4]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 5]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 6]

#include<iostream>
    #include<stdio.h>
    #include<string.h>
    #include<bits/stdc++.h>
    #define MAXLEN 50
    using namespace std;
    
    void LCSlength(int m,int n,char *x,char *y,int c[][MAXLEN],int b[][MAXLEN])
    {
        
    	for(int i=0;i<=m;i++)//m为字符个数 
    	{
        
    		c[i][0]=0;
    	}
    	for(int i=1;i<=n;i++)
    	{
        
    		c[0][i]=0;
    	}
    	
    	for(int i=1;i<=m;i++)
    	{
        
    		for(int j=1;j<=n;j++)
    		{
        
    			if(x[i-1]==y[j-1])//因为字符串是在从第0位开始存储的
    			{
        
    				c[i][j]=c[i-1][j-1]+1;
    				b[i][j]=1;//本算法采用1,2,3三个整形作为标记
    			}
    			else if(c[i-1][j]>=c[i][j-1])//这个else if关键 
    			{
        
    				c[i][j]=c[i-1][j];
    				b[i][j]=2;
    			}
    			else
    			{
        
    				c[i][j]=c[i][j-1];
    				b[i][j]=3;
    			}
    		}
    	}
    }
    
    void LCS(int i,int j,char *x,int b[][MAXLEN])
    {
        
    	if(i==0||j==0)
    	{
        
    		return;
    	}
    	if(b[i][j]==1)
    	{
        
    		LCS(i-1,j-1,x,b);
    		cout<<x[i-1]<<" ";
    	}
    	else if(b[i][j]==2)//这个else if 很关键 
    	{
        
    		LCS(i-1,j,x,b); 
    	}
    	else
    	{
        
    		LCS(i,j-1,x,b);
    	}
     } 
    int main()
    {
        
    	
    	
    
     char x[MAXLEN] = {
        "*abcbdab"};
        char y[MAXLEN] = {
        "*bdcdba"};
    //传递二维数组必须知道列数，所以使用MAXLEN这个确定的数
        int  b[MAXLEN][MAXLEN];//b矩阵是用来存储这个问题是由那个子问题来解决的                       
        int  c[MAXLEN][MAXLEN];//c矩阵用来存储最长公共子串的长度 
    
        int m, n;
    
        m = strlen(x);
       // cout<<m<<endl;
        n = strlen(y);
        //cout<<n<<endl;
    
    
    	LCSlength(m,n,x,y,c,b);
    	cout<<"b矩阵是用来存储这个问题是由那个子问题来解决的"<<endl; 
    	 for(int i=0;i<=m;i++)
    	{
        
    		for(int j=0;j<=n;j++)
    		{
        
    			cout<<b[i][j];
    		}
    		cout<<endl;
    	 } 
    	 
    	 
    	 cout<<"c矩阵用来存储最长公共子串的长度 "<<endl;
    	  for(int i=0;i<=m;i++)
    	{
        
    		for(int j=0;j<=n;j++)
    		{
        
    			cout<<c[i][j];
    		}
    		cout<<endl;
    	 } 
    
    	LCS(m,n,x,b);
    	
    	
     }

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 7]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70]: /images/20221022/245b8b002cad416ea05281b6aca65673.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 1]: /images/20221022/3e14fd0e89d24eb4aceb8a185c5ca40e.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 2]: /images/20221022/665090dc406340cbbc44ce6d271dc4da.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 3]: /images/20221022/342195180082419d92c065e9d2ad85bb.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 4]: /images/20221022/b2809a0b28084260822dfbb26a8fe763.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 5]: /images/20221022/90a157c308cd4fd8ab334894bd5ada47.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 6]: /images/20221022/d47fd99297974f3182dbb08da821b75f.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzUwNjc1ODEz_size_16_color_FFFFFF_t_70 7]: /images/20221022/c3faed3b98d34f2aac36dd122e7b51a8.png