I was solving a simple DP problem ..
Given a string S and a string T, count the number of distinct subsequences of T in S.
A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).
Here is an example: S = "rabbbit", T = "rabbit"
Return 3.
I made a recursive code which is like this ..
I initialise the DP array with -1 and used one based indexing in DP matrix ..
int solve(string S,string T,int N,int M){
if( M <= 0)
return 1 ;
if( N <= 0 )
return 0 ;
int &ret = DP[N][M];
if(ret != -1)
return ret ;
ret = 0 ;
if(S[N-1] == T[M-1]){
ret += (solve(S,T,N-1,M-1)+solve(S,T,N-1,M)) ;
}else{
ret += (solve(S,T,N-1,M)) ;
}
ret ;
}
I was not getting correct answer then i changed my code and prepared a bottom up code which is this ..
int solve(string &S,string &T,int N,int M){
for(int i=0;i<=N;i++)
for(int j=0;j<=M;j++)
DP[i][j] = 0;
for(int i=0;i<=N;i++)
DP[i][0] = 1;
for(int i=1;i<=N;i++){
for(int j=1;j<=M;j++){
if(S[i-1] == T[j-1])
DP[i][j] += DP[i-1][j-1] ;
DP[i][j] += DP[i-1][j] ;
}
}
return DP[N][M] ;
}
I got AC with this solution ..Essentially the same as previous one ..
I am still unable to find a bug in my previous code so can anyone help me please ..
Thanx in advance