hdu 1503 LCS输出路径【dp】

hdu 1503

　　不知道最后怎么输出，因为公共部分只输出一次。有人说回溯输出，感觉好巧妙！其实就是下图，输出的就是那条灰色的路径，但是初始时边界一定要初始化一下，因为最第一列只能向上走，第一行只能向左走。我用1表示向上走，2向左上方走，3向左走。

　　刚开始输入字符串时有两种方法，直接输入；或从地址后一位输入，即此时数组起始编号为1。直接输入时，dp[i][j]表示的是以s1[i-1],s2[j-1]为结尾LCS，另一种则就是表示以s1[i],s2[j]为结尾的LCS。两者在路径输出时有些差别，以前感觉直接输出LCS长度后者方便，其实都一样。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 const int MAXN = ;
 char s1[MAXN], s2[MAXN];
 int dp[MAXN][MAXN], flag[MAXN][MAXN];
 int len1, len2;

 void LCS()
 {
     memset(dp, , sizeof(dp));
     for (int i = ; i <= len1; i++) flag[i][] = ;
     for (int i = ; i <= len2; i++) flag[][i] = ;
     for (int i = ; i <= len1; i++) {
         for (int j = ; j <= len2; j++) {
             if (s1[i - ] == s2[j - ]) {
                 dp[i][j] = dp[i - ][j - ] + ;
                 flag[i][j] = ;
             }
             else if (dp[i - ][j] >= dp[i][j - ]) {
                 dp[i][j] = dp[i - ][j];
                 flag[i][j] = ;
             }
             else {
                 dp[i][j] = dp[i][j - ], flag[i][j] = ;
             }
         }
     }
 }

 void Print(int x, int y)
 {
     if (x ==  && y == ) return;
     if (flag[x][y] == ) {
         Print(x - , y - );
         cout << s1[x-];
     }
     else if (flag[x][y] == ) {
         Print(x - , y);
         cout << s1[x - ];
     }
     else {
         Print(x, y - );
         cout << s2[y - ];
     }
 }

 int main()
 {
     while (cin>>s1>>s2)
     {
         len1 = strlen(s1), len2 = strlen(s2);
         LCS();
         Print(len1, len2);
         cout << endl;
     }
     return ;
 }

起始编号为1：

 #include<cstdio>
 #include<cstring>
 #include<iostream>
 using namespace std;
 const int MAXN = ;
 int dp[MAXN][MAXN], flag[MAXN][MAXN];
 char s1[MAXN], s2[MAXN];
 int len1, len2;

 void LCS()
 {
     for (int i = ; i <= len1; i++) flag[i][] = ;
     for(int i = ; i <= len2; i++) flag[][i] = ;
     for (int i = ; i <= len1; i++) {
         for (int j = ; j <= len2; j++) {
             if (s1[i] == s2[j])
                 dp[i][j] = dp[i - ][j - ] + , flag[i][j] = ;
             else if (dp[i - ][j] >= dp[i][j - ])
                 dp[i][j] = dp[i - ][j], flag[i][j] = ;
             else dp[i][j] = dp[i][j - ], flag[i][j] = ;
         }
     }
 }

 void Print(int x, int y)
 {
     if (x ==  && y == ) return;
     if (flag[x][y] == ) {
         Print(x - , y - );
         printf("%c", s1[x]);
     }
     else if (flag[x][y] == ) {
         Print(x - , y);
         printf("%c", s1[x]);
     }
     else {
         Print(x, y - );
         printf("%c", s2[y]);
     }
     return;
 }

 int main()
 {
     while (scanf("%s %s", s1 + , s2 + )==)
     {
         len1 = strlen(s1 + ), len2 = strlen(s2 + );
         memset(dp, , sizeof(dp));
         LCS();
         Print(len1, len2);
         printf("\n");
     }
     return ;
 }