Dynamic programming interleaving matching problem __ Dynamic programming

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Topic Analysis

The dynamic planning of the topic of understanding is not particularly deep, so read someone else's blog to learn, give a blog address staggered matching blog, said very good also very detailed, but the pretreatment is not very good written, I think of the way I wrote out, clear point.

#include <cstdio> #include <cstring> #include <iostream> #include <algorithm> using namespace
Std
const int MAXN = 2005;
int A[MAXN],B[MAXN];

int DP1[MAXN][MAXN],DP2[MAXN][MAXN],F[MAXN][MAXN];
    void init (int n,int m) {memset (DP1, 0, sizeof (DP1));
    memset (DP2, 0, sizeof (DP2));
        for (int i = 1; I <= n; i++)//dp1 the element position {for (int j = 2; J <= M; j + +) that is closest to J and equal to A[i] in the first and first J elements of column A;
            {if (a[i] = = B[j-1]) dp1[i][j] = j-1;
        else dp1[i][j] = dp1[i][j-1];  for (int j = 1; j <= m; j)//dp2 Store the element position {for (int i = 2; I <=) in the first and J Elements of column A, the nearest position to I and equal to B[j] N
            i++) {if (b[j] = = A[i-1]) dp2[i][j] = i-1;
        else dp2[i][j] = dp2[i-1][j];
    int main () {int n,m; while (scanf ("%d%d", &n, &m)!= EOF) {for (int i = 1; I <= n; i++) scanf ("%d", &Amp;a[i]);
        for (int j = 1; j <= M; j +) scanf ("%d", &b[j]);
        Init (n, m);
        memset (f, 0, sizeof (f));  for (int i = 2; I <= n; i++) {for (int j = 2; J <= m; j) {F[i][j]   = F[i-1][j-1]; I and J do not participate in matching f[i][j] = max (F[i][j], f[i-1][j]); I do not participate in matching f[i][j] = max (F[i][j], f[i][j-1]);
                    J does not participate in the match if (A[i]!= b[j])//Front has the number that can match, at the same time found is the closest to the i,j, because this must be the best {
                    int ip = DP2[I][J],JP = Dp1[i][j];
                if (IP && jp) f[i][j] = max (F[i][j], f[ip-1][jp-1] + 2);
    } printf ("%d\n", F[n][m]);
return 0;
 }