Luo Gu P2543 [AHOI2004] strange string (LCS template)

Portal


Problem-solving ideas

It is clear that the board of the longest common subsequence (LCS) of.

Definition: represents the longest common subsequence S1 and the first j bits before i S2 with bits dp [i] [j].

State transition:

  • 当s1[i]==s2[j]时,dp[i][j]=dp[i-1][j-1]+1;
  • 当s1[i]!=s2[j]时,dp[i][j]=max(dp[i-1][j],dp[i][j-1];

Obviously right.

Bold conjecture without proof!

Plus one equal in time, the results will not be poor than without, so can be a plus.

Time complexity: O (n- 2 ).

AC Code

 1 #include<iostream>
 2 #include<cstring>
 3 using namespace std;
 4 string s1,s2; 
 5 int l1,l2,dp[10005][10005];
 6 int main()
 7 {
 8     cin>>s1>>s2;
 9     l1=s1.length();
10     l2=s2.length();
11     for(int i=1;i<=l1;i++){
12         for(int j=1;j<=l2;j++){
13             if(s1[i-1]==s2[j-1]) dp[i][j]=dp[i-1][j-1]+1;
14             else dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
15         }
16     }
17     cout<<dp[l1][l2];;
18     return 0;
19 }

//AHOI2004 Day1t1

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Origin www.cnblogs.com/yinyuqin/p/12142825.html