Longest common subsequence prolem

Question

What is longest common subsequence for these 2 strings {xaybadfeg, abcdefg}. Isn't it "abdeg"? I am using this algorithm (the dynamic programming technique) to find the solution. It returns "adeg" as the answer. Is my understanding of subsequence wrong? Is my algorithm wrong? Am I missing something? Should I corner case for this type of input?

Dynamic programming code

#include <iostream>
#include <stack>
using namespace std;

void LCS(string str1, string str2){
    int out[100][100] = {};
    for (int i = 0; i <= str1.size(); i++){
        for (int j = 0; j <= str2.size(); j++){
            if (i == 0 || j == 0)
                out[i][j] = 0;
            else{
                if (str1[i-1] == str2[j-1]){
                    if (out[i][j - 1] > out[i - 1][j])
                        out[i][j] = out[i][j - 1] + 1;
                    else
                        out[i][j] = out[i - 1][j] + 1;
                }
                else{
                    if (out[i][j - 1] > out[i - 1][j])
                        out[i][j] = out[i][j - 1];
                    else
                        out[i][j] = out[i - 1][j];
                }
            }
        }
    }

    //Backtracing to print the numbers
    int i = str1.size()-1, j = str2.size()-1;
    std::string subSeqStr="";
    while (i >= 0 || j >= 0){
        if (str2[j] != str1[i]){
            if (out[i][j - 1] > out[i - 1][j])
                j--;
            else
                i--;
        }
        else{
            subSeqStr.insert(subSeqStr.begin(), str2[j]);
            i--; j--;
        }
    }
    std::cout << "The least common subsequence is: " << subSeqStr<< std::endl;
}

int main(){
    string str1 = "xaybadfeg";
    string str2 = "abcdefg";
    LCS(str1,str2);
    getchar();
    return 0;
}

Any input is greatly appreciated. Thanks!

score 1 · Answer 1 · answered Jul 09 '16 at 20:37

"abdeg" is a longest common subsequence, but there are others like "abdfg".

The backtracking is wrong. If you output the values of i and j, then they are becoming negative, and then invalid string indexes are accessed.

Subtracting 1 from the string indexes should give the right answer. I've also change the || condition to an &&.

int i = str1.size(), j = str2.size();
std::string subSeqStr="";
while (i > 0 && j > 0){
    if (str2[j - 1] != str1[i - 1]) {
        if (out[i][j - 1] > out[i - 1][j])
            j--;
        else
            i--;
    }
    else{
        subSeqStr.insert(subSeqStr.begin(), str2[j - 1]);
        i--; j--;
    }
}

but doesn't it go out of range for these lines of code when i and j are str1.size and str2.size respectively? `if (str2[j - 1] != str1[i - 1]) { if (out[i][j - 1] > out[i - 1][j])` — sri_84, Jul 09 '16 at 21:00

score 0 · Answer 2 · answered Jul 09 '16 at 20:10

This looks wrong:

if (i == 0 || j == 0)
    out[i][j] = 0;

Your strings are indexed starting from 0, so you cannot apply the formula as it appears in most textbooks and tutorials, which consider the indexing to start from 1.

The easiest is probably to prepend something to your strings, so your indexing also starts from 1. Otherwise, you'll have to do some unsightly adaptations to the formula.

Longest common subsequence prolem

2 Answers2