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 = 107;
char s1[MAXN], s2[MAXN];
int dp[MAXN][MAXN], flag[MAXN][MAXN];
int len1, len2;

void LCS()
{
    memset(dp, 0, sizeof(dp));
    for (int i = 0; i <= len1; i++) flag[i][0] = 1;
    for (int i = 0; i <= len2; i++) flag[0][i] = 3;
    for (int i = 1; i <= len1; i++) {
        for (int j = 1; j <= len2; j++) {
            if (s1[i - 1] == s2[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1] + 1;
                flag[i][j] = 2;
            }
            else if (dp[i - 1][j] >= dp[i][j - 1]) {
                dp[i][j] = dp[i - 1][j];
                flag[i][j] = 1;
            }
            else {
                dp[i][j] = dp[i][j - 1], flag[i][j] = 3;
            }
        }
    }
}

void Print(int x, int y)
{
    if (x == 0 && y == 0) return;
    if (flag[x][y] == 2) {
        Print(x - 1, y - 1);
        cout << s1[x-1];
    }
    else if (flag[x][y] == 1) {
        Print(x - 1, y);
        cout << s1[x - 1];
    }
    else {
        Print(x, y - 1);
        cout << s2[y - 1];
    }
}

int main()
{
    while (cin>>s1>>s2)
    {
        len1 = strlen(s1), len2 = strlen(s2);
        LCS();
        Print(len1, len2);
        cout << endl;
    }
    return 0;
}

起始编号为1：

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
const int MAXN = 107;
int dp[MAXN][MAXN], flag[MAXN][MAXN];
char s1[MAXN], s2[MAXN];
int len1, len2;

void LCS()
{
    for (int i = 0; i <= len1; i++) flag[i][0] = 1;
    for(int i = 0; i <= len2; i++) flag[0][i] = 3;
    for (int i = 1; i <= len1; i++) {
        for (int j = 1; j <= len2; j++) {
            if (s1[i] == s2[j])
                dp[i][j] = dp[i - 1][j - 1] + 1, flag[i][j] = 2;
            else if (dp[i - 1][j] >= dp[i][j - 1])
                dp[i][j] = dp[i - 1][j], flag[i][j] = 1;
            else dp[i][j] = dp[i][j - 1], flag[i][j] = 3;
        }
    }
}

void Print(int x, int y)
{
    if (x == 0 && y == 0) return;
    if (flag[x][y] == 2) {
        Print(x - 1, y - 1);
        printf("%c", s1[x]);
    }
    else if (flag[x][y] == 1) {
        Print(x - 1, y);
        printf("%c", s1[x]);
    }
    else {
        Print(x, y - 1);
        printf("%c", s2[y]);
    }
    return;
}

int main()
{
    while (scanf("%s %s", s1 + 1, s2 + 1)==2)
    {
        len1 = strlen(s1 + 1), len2 = strlen(s2 + 1);
        memset(dp, 0, sizeof(dp));
        LCS();
        Print(len1, len2);
        printf("
");
    }
    return 0;
}