hdoj1080 Human Gene Functions(DP解决LCS问题!)

来源:http://acm.hdu.edu.cn/showproblem.php?pid=1080

类似于求最长公共字串，在dp的初始化和状态转移方程的书写上有少许差别。

dp[i][j] = dp[i-1,j] + dist[s1[i],'-'];s1[i]对上'-'

dp[i][j] = dp[i,j-1] + dist['-',s2[j]];'-'对上s2[j]

dp[i][j] = dp[i-1,j-1] + dist[s1[i],s2[j]];s1[i]对上s2[j]
dp[i,j]=max( dp[i-1,j] + dist[s1[i],'-'], dp[i,j-1]+dist['-',s2[j]], dp[i-1,j-1]+dist[s1[i],s2[j]]);

有关LCS问题的讲解链接:http://blog.csdn.net/rrrfff/article/details/7523437

本题的另外讲解链接:http://blog.sina.com.cn/s/blog_93ced90c01016rjv.html

代码如下:

#include<stdio.h>#include<string>#include<iostream>using namespace std;int max3(int a,int b,int c){int x;x=(a>b)?a:b;x=(c>x)?c:x;return x;}int score[5][5]={5, -1, -2, -1, -3,-1, 5, -3, -2, -4,-2, -3, 5, -2, -2,-1, -2, -2, 5, -1,-3, -4, -2, -1, 0};int dp[105][105];int a1[105],a2[105];int main(){char s1[105],s2[105];int t,i,j,l1,l2;scanf("%d",&t);while(t--){scanf("%d%s%d%s",&l1,s1+1,&l2,s2+1);for(i=1;i<=l1;i++){if(s1[i]=='A')a1[i]=0;if(s1[i]=='C')a1[i]=1;if(s1[i]=='G')a1[i]=2;if(s1[i]=='T')a1[i]=3;}for(i=1;i<=l2;i++){if(s2[i]=='A')a2[i]=0;if(s2[i]=='C')a2[i]=1;if(s2[i]=='G')a2[i]=2;if(s2[i]=='T')a2[i]=3;}memset(dp,0,sizeof(dp));for(i=0;i<=l1;i++)for(j=0;j<=l2;j++){if (i==0&&j==0) dp[i][j]=0;            else if (j==0&&i>0) dp[i][j]=dp[i-1][j]+score[a1[i]][4];            else if (i==0&&j>0) dp[i][j]=dp[i][j-1]+score[4][a2[j]];            else            dp[i][j] = max3(dp[i-1][j-1]+score[a1[i]][a2[j]],dp[i][j-1]+score[4][a2[j]],dp[i-1][j]+score[a1[i]][4]);}printf("%d\n",dp[l1][l2]);}return 0;}