题意:给两个DNA序列,在这两个DNA序列中插入若干个'-',使两段序列长度相等,对应位置的两个符号的得分规则给出,求最高得分。
解法:dp。dp[i][j]表示第一个字符串s1的前i个字符和第二个字符串s2的前j个字符对齐时的最高得分,转移方程:dp[i][j] = max{dp[i - 1][j - 1] + a[s1[i]][s2[j]], dp[i - 1] + a[s1[i]]['-'] + dp[i][j - 1] + a['-'][s2[j]]},第一项表示对齐时s1[i]和s2[j]作为结尾,第二项表示对齐时'-'和s2[j]作为结尾,第三项表示对齐时s1[i]和'-'作为结尾。
注意dp应该以1开始,但字符串一般直接读入的话是以0开始的,因为这个样例一直过不去……调了好久……
代码:
#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string>
#include<string.h>
#include<math.h>
#include<limits.h>
#include<time.h>
#include<stdlib.h>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<vector>
#define LL long long
using namespace std;
int a[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 main()
{
int T;
while(~scanf("%d", &T))
{
while(T--)
{
string s1, s2;
int len1, len2;
cin >> len1 >> s1 >> len2 >> s2;
for(int i = 0; i < len1; i++)
if(s1[i] == 'A') s1[i] = 0;
else if(s1[i] == 'C') s1[i] = 1;
else if(s1[i] == 'G') s1[i] = 2;
else if(s1[i] == 'T')s1[i] = 3;
for(int i = 0; i < len2; i++)
if(s2[i] == 'A') s2[i] = 0;
else if(s2[i] == 'C') s2[i] = 1;
else if(s2[i] == 'G') s2[i] = 2;
else if(s2[i] == 'T') s2[i] = 3;
int dp[105][105] = {0};
for(int i = 1; i <= len1; i++)
dp[i][0] = dp[i - 1][0] + a[s1[i - 1]][4];
for(int i = 1; i <= len2; i++)
dp[0][i] = dp[0][i - 1] + a[4][s2[i - 1]];
for(int i = 1; i <= len1; i++)
for(int j = 1; j <= len2; j++)
dp[i][j] = max(dp[i - 1][j - 1] + a[s1[i - 1]][s2[j - 1]], max(dp[i - 1][j] + a[s1[i - 1]][4], dp[i][j - 1] + a[4][s2[j - 1]]));
printf("%d\n", dp[len1][len2]);
}
}
return 0;
}