title: Given a string S and a string T, count the number of distinct subsequences of T in S
body: <p>Hi All: can someone explain to me how this algorithm works? I fail to understand the mechanism. Thanks.</p>
  
  <p>Problem: Given a string S and a string T, count the number of distinct subsequences of T in S.</p>
  
  <p>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).</p>
  
  <p>Here is an example:
  S = "rabbbit", T = "rabbit"</p>
  
  <p>Return 3.</p>
  
  <p>Solution:</p>
  
  <pre><code>public int numDistincts(String S, String T)
  {
    int[][] table = new int[S.length() + 1][T.length() + 1];
  
    for (int i = 0; i &lt; S.length(); i++)
        table[i][0] = 1;
  
    for (int i = 1; i &lt;= S.length(); i++) {
        for (int j = 1; j &lt;= T.length(); j++) {
            if (S.charAt(i - 1) == T.charAt(j - 1)) {
                table[i][j] += table[i - 1][j] + table[i - 1][j - 1];
            } else {
                table[i][j] += table[i - 1][j];
            }
        }
    }
  
    return table[S.length()][T.length()];
  }
  </code></pre>