动态规划-3-RNA的二级结构

/*
状态转移方程：

OPT(i , j)= max(OPT(i , j − 1) , max( 1+OPT(i , t − 1)+OPT(t + 1, j − 1))),

where the  max is taken over t such that bt and bj are an allowable base pair

(under conditions (i) and (ii) from the definition of a secondary structure)

*/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
#define RNALEN 9
#define LEN(X) (sizeof (X) / sizeof (X[0]))
#define MAX(X,Y) ((X < Y) ? Y : X)

char base[] = {'A', 'U', 'C', 'G'};

typedef char *string;

string generateRNA(int size)
{
    string rna = (string) malloc((size + 1) * sizeof (char) );
    string start = rna;
    string stop = rna + size;
    int index;
    srand(time(NULL));

    for (; rna < stop; rna++) {
        index = rand() % 4;
        *rna = base[index];
    }
    *rna = '\0';
    return start;
}

void testgenerate()
{
    string rna = generateRNA(RNALEN);
    printf("%s\n", rna);
}

/*
void matrix_print(char (*m)[], int len)
{

}
*/

int isMatch(char a, char b)
{
    if (a == 'A' && b == 'U')
        return 1;
    else if (a == 'U' && b == 'A')
        return 1;
    else if (a == 'C' && b == 'G')
        return 1;
    else if (a == 'G' && b == 'C')
        return 1;
    else
        return 0;
}
//核心函数：实现了状态转移方程
int opt(int (*dp)[RNALEN+1], string rna, int i, int j)
{
    int  maxPair, tmp, t;
    maxPair = 0;

    for (t = i; t < j-4; t++) {
        tmp = 0;
        if(isMatch(rna[t], rna[j])) {
            tmp++;
            if (t > i + 5) { //compute leftPair
                tmp += dp[i][t-1];
            }
            if (t < j - 6) { //comput innerPair
                tmp += dp[t+1][j];
            }
        }
        if (tmp > maxPair)
            maxPair = tmp;
    }
    return MAX(dp[i][j-1], maxPair);
}

int rna2structure(string rna, int exlen)
{
    int i, j, k;

    int dp[exlen][exlen];
    int n = exlen - 1;
    memset(dp, 0, sizeof dp);//string.h
/*
    for (int i = 0; i < len; i++){
        for (int j = 0; j < len; j++) {
            if (j % len == 0)
                putchar('\n');
            printf("%d, ", dp[i][j]);
        }
    }
    putchar('\n');
*/
    for (k = 5; k < n; k++) {
        for (i = 1; i <= n-k; i++) {
            j = i + k;
            dp[i][j] = opt(dp, rna, i, j);
        }
    }

    for (int i = 0; i < exlen; i++){
        for (int j = 0; j < exlen; j++) {
            if (j % exlen == 0)
                putchar('\n');
            printf("%d, ", dp[i][j]);
        }
    }
    putchar('\n');

    return dp[1][n];
}

void testStructure()
{
    string rna1 = generateRNA(RNALEN);
    //头部插入空格符，使得碱基下标从1开始
    char rna2[] = {' ', 'A', 'C', 'C', 'G', 'G', 'U', 'A', 'G', 'U', '\0'};
    char rna3[] = " ACCGGUAGU";
//    printf("len of rna2 = %d\n", LEN(rna2));
//    int maxPair = rna2structure(rna1, RNALEN+1);
    int maxPair = rna2structure(rna2, RNALEN+1);
    printf("maxPair = %d\n", maxPair);
//    rna2structure(rna3, strlen(rna3));
    //rna2structure(rna1, RNALEN);
}

int main()
{
    testgenerate();
    testStructure();
//    printf("MAX(3, 5) = %d\n", MAX(3, 5));
    return 0;
}

实现自《Algorithm Design》

6.5 RNA Secondary Structure: Dynamic Programming over Intervals