My needleman-wunsch global alignment scoring matrix:

        G    C    A   T    G   C    U
    0   -1  -2   -3  -4   -5  -6   -7
G  -1   1    0   -1  -2   -3  -4   -5
A  -2   0    0    1   0   -1  -2   -3
T  -3  -1   -1    0   2    1   0   -1
T  -4  -2   -2   -1   1    1   0   -1
A  -5  -3   -3   -1   0    0   0   -1
C  -6  -4   -2   -2  -1   -1   1    0
A  -7  -5   -3   -1  -2   -2   0    0

I want traceback algorithm and find best alignment sequence.

I try for this code.

Astring <- strsplit(A, "")[[1]]
Bstring <- strsplit(B, "")[[1]]

n=length(Astring) #seq1
m=length(Bstring) #seq2

s=matrix(data = 0, nrow = m, ncol =n, dimnames = list(Bstring,Astring))

for (i in seq_len(m)) {
    for (j in seq_len(n)) {
        if (Astring[j]==Bstring[i])
            s[i,j]<- 1
        else
            s[i,j]<- -1
    }
}

fmatrix = matrix(0, nrow = (nchar(A)+1) , ncol = nchar(B)+1)
d = -1  #this is gap penalty
for(i in 0 : nchar(B)) {
    fmatrix[i+1,1] = d * I  #populates initial row with gap penalty
}

for(j in 0 : nchar(A)) {
    fmatrix[1,j+1] = d * j
}

for(i in 1 : nchar(B)) {
    for(j in 1 : nchar(A)) {
        #get me sccore for the pair of aa or nt
        match  =  fmatrix[i,j] + s[i,j]
        delete = fmatrix[i,j+1] + d
        insert = fmatrix[i+1,j] + d
        fmatrix[i+1,j+1] = max(match,delete,insert)
    }
}

colnames(fmatrix) = strsplit( paste(" " , A, sep=""), "")[[1]];
rownames(fmatrix) = strsplit( paste(" " , B, sep=""), "")[[1]];
#return(fmatrix)

AlignmentA = ""
AlignmentB = ""

i = nchar(B) +1
j = nchar(A) +1

maxscore=numeric(length=0)

while(i > 1 && j > 1) {
    CurrentScore= fmatrix[i,j]
    ScoreDiag= fmatrix[i-1,j-1]
    ScoreLeft=fmatrix[i,j-1]
    ScoreUp=fmatrix[i-1,j]
    maxscore= max(CurrentScore,ScoreDiag,ScoreLeft,ScoreUp)

    if( CurrentScore <= ScoreDiag ) {
        AlignmentA=paste(substr(A,j-1,j-1),AlignmentA, sep="")
        AlignmentB=paste(substr(B,i-1,i-1),AlignmentB, sep="")
        j=j-1
        i=i-1
    } else if (ScoreLeft >= CurrentScore) {
        AlignmentA=paste(substr(A,j-1,j-1),AlignmentA, sep="")
        AlignmentB=paste("-",AlignmentB, sep="")
        j=j-1
    } else if (CurrentScore>=ScoreUp+d) {
        AlignmentA=paste("-",AlignmentA, sep="")
        AlignmentB=paste(substr(B,i-1,i-1),AlignmentB, sep="")            
        i=i-1
    }
    ans <- matrix(c(al1=paste(AlignmentA, collapse=""), al2=paste(AlignmentB, collapse="")))
    print(ans)
}

But I don't find best alignment. The best alignments :

GCATG-CU      GCA-TGCU      GCAT-GCU
G-ATTACA      G-ATTACA      G-ATTACA

Can you help this topic please?