题意:给定字符串s,t.问s串删除k个字符后,最多有多少个互不相交的子序列和p相等.
解法:dp[i][j]:字符s[i]之前删除了j个字符后的答案.
对于s[i]的每一位设置一个转移位点to[i],表示以s[i]开始的串匹配t的最后一个位置加上1.
dp转移方程:
dp[i+1][j]=max(dp[i+1][j],dp[i][j])//这一步主要是为了那些不在to[]中的位点更新值.
dp[i+1][j+1]=max(dp[i+1][j+1],dp[i][j])//删除该点.
Next = j + to[i] - i - m;
dp[to[i]][Next] = max(dp[to[i]][Next], dp[i][j] + 1);#include <cstdio>
#include <cstring>
#include <set>
#include <vector>
#include <algorithm>
#include <string>
#include <map>
#include <iostream>
#include <iomanip>
#include <list>
using namespace std;
typedef long long ll;
int n, m;
char s[2005], t[505];
int to[2005];
int dp[2005][2005];
int MAIN()
{
scanf("%s%s", s, t);
n = (int)strlen(s);
m = (int)strlen(t);
for (int i = 0; i < n; ++ i) {
to[i] = n + 1;
int k = 0;
for (int j = i; j < n; ++ j) {
if (s[j] == t[k]) {
k ++;
if (k == m) {
to[i] = j + 1;
break;
}
}
}
}
for (int i = 0; i < n; ++ i) {
for (int j = 0; j <= i; ++ j) {
dp[i + 1][j] = max(dp[i + 1][j], dp[i][j]);
dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j]);
if (to[i] < n + 1) {
int Next = j + to[i] - i - m;
dp[to[i]][Next] = max(dp[to[i]][Next], dp[i][j] + 1);
}
}
}
for (int i = 0; i <= n; ++ i) {
printf("%d%c", dp[n][i], i == n ? '\n':' ');
}
return 0;
}
int main()
{
//ios::sync_with_stdio(false);
cout << fixed << setprecision(16);
return MAIN();
}