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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.
[Solution]
Let W(i, j) stand for the number of subsequences of S(0, i) in T(0, j). If S.charAt(i) == T.charAt(j), W(i, j) = W(i-1, j-1) + W(i-1,j); Otherwise, W(i, j) = W(i-1,j).
1 int numDistinct(string S, string T) 2 { 3 int m = S.size(), n = T.size(), i, j, result; 4 int **table = new int* [m + 1]; 5 for (i = 0; i <= m; i++) 6 table[i] = new int[n + 1]; 7 8 for (j = 0; j <= n; j++) // S is empty 9 table[0][j] = 0; 10 for (i = 0; i <= m; i++) // T is empty 11 table[i][0] = 1; 12 13 for (i = 1; i <= m; i++) 14 { 15 for (j = 1; j <= n; j++) 16 { 17 if (S[i - 1] != T[j - 1]) 18 table[i][j] = table[i - 1][j]; 19 else 20 table[i][j] = table[i - 1][j] + table[i - 1][j - 1]; 21 } 22 } 23 result = table[m][n]; 24 25 for (i = 0; i <= m; i++) 26 delete[] table[i]; 27 delete[] table; 28 29 return result; 30 }
leetcode 115. Distinct Subsequences
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原文地址：http://www.cnblogs.com/ym65536/p/4287013.html
