I have written Longest Common SubSequence in Python using recursion with memoization:
def print2d(table):
print '\n'.join([''.join(['{:4}'.format(item) for item in row]) for row in table])
a="123"
b="213"
m = [[-1]*len(b)]*len(a)
def lcs(i,j):
print i, j
print2d(m)
if i== -1 or j == -1:
return 0;
if m[i][j] != -1:
return m[i][j]
res = 0
res = max(res, lcs(i, j-1))
res = max(res, lcs(i-1, j))
if a[i] == b[j]:
res = max(res, 1 + lcs(i-1,j-1))
m[i][j]=res
return res
print lcs(len(a)-1,len(b)-1)
print2d(m)
All those print statements are there because I didn't get the correct result and decided to take a look at how the algorithm works. What I found surprised me. If you run it yourself you can see the tables printed and they look ok until:
0 -1
-1 -1 -1
-1 -1 -1
-1 -1 -1
-1 0
-1 -1 -1
-1 -1 -1
-1 -1 -1
0 -1
0 -1 -1
0 -1 -1
0 -1 -1
1 1
1 -1 -1
1 -1 -1
1 -1 -1
1 0
1 -1 -1
1 -1 -1
1 -1 -1
0 1
1 -1 -1
1 -1 -1
1 -1 -1
Why all of a sudden on the step 0 -1 the whole first column became 0 ?
So, I quickly created C++ program doing exactly the same thing the same way:
#include <iostream>
#include <iomanip>
#include <string>
#include <cstring>
using namespace std;
string a = "123",
b = "213";
int mem[1000][1000];
int lcs(int i, int j) {
cout << i << " " << j << "\n";
for(auto i = 0; i < a.length(); i++){
for(auto j = 0; j < b.length(); j++){
cout << setw(4) << right << mem[i][j];
}
cout << "\n";
}
if (i == -1 || j == -1) {
return 0;
}
if (mem[i][j] != -1) {
return mem[i][j];
}
int res = 0;
res = max(res, lcs(i, j - 1));
res = max(res, lcs(i - 1, j));
if (a[i] == b[j]) {
res = max(res, 1 + lcs(i - 1, j - 1));
}
mem[i][j] = res;
return res;
}
int main(){
memset(mem, -1, sizeof mem );
int r = lcs(a.length()-1, b.length()-1);
cout << r << "\n";
return 0;
}
And it works as expected. Corresponding tables look like this:
0 -1
-1 -1 -1
-1 -1 -1
-1 -1 -1
-1 0
-1 -1 -1
-1 -1 -1
-1 -1 -1
0 -1
0 -1 -1
-1 -1 -1
-1 -1 -1
1 1
0 -1 -1
1 -1 -1
1 -1 -1
1 0
0 -1 -1
1 -1 -1
1 -1 -1
0 1
0 -1 -1
1 -1 -1
1 -1 -1
I am puzzled why Python and C++ code that are not that different produce such drastically different results.
Am I missing something about how recursive functions in Python work? Or is it because in Python I use list of lists and not 2D array as in C++?
