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本文介绍了一种最长公共子序列(LCS)的变种算法实现，通过动态规划方法求解两个字符串之间的最大匹配得分。文章详细展示了如何利用预定义的匹配得分矩阵来更新状态转移方程，并给出完整的C语言实现代码。

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LCS变种

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define inf 0x3f3f3f3f
#define len 105
char a[len], b[len];
int dp[len][len], mat[len][len];

int Max(int a, int b){
    return a > b ? a : b;
}
int main(){
    int T, i, j;
    mat['A']['A'] = mat['C']['C'] = mat['G']['G'] = mat['T']['T'] = 5;
    mat['A']['C'] = mat['C']['A'] = mat['A']['T'] = mat['T']['A'] = mat['-']['T'] = -1;
    mat['A']['G'] = mat['G']['A'] = mat['C']['T'] = mat['T']['C'] = mat['G']['T'] = mat['T']['G'] = mat['-']['G'] = -2;
    mat['-']['A'] = mat['C']['G'] = mat['G']['C'] = -3;
    mat['-']['C'] = -4;
    scanf("%d", &T);
    int len1, len2;
    while(T--){
        scanf("%d%s%d%s", &len1, a, &len2, b);
        dp[0][0] = 0;
        for(i = 1; i <= len1; i++)
            dp[i][0] = dp[i-1][0] + mat['-'][a[i-1]];
        for(j = 1; j <= len2; j++)
            dp[0][j] = dp[0][j-1] + mat['-'][b[j-1]];
        for(i = 1; i <= len1; i++){
            for(j = 1; j <= len2; j++){
                dp[i][j] = Max(dp[i-1][j-1] + mat[a[i-1]][b[j-1]], Max(dp[i-1][j] + mat['-'][a[i-1]], dp[i][j-1] + mat['-'][b[j-1]]));
            }
        }
        printf("%d\n", dp[len1][len2]);
    }
    return 0;
}