@ashish: AAA is the prefix of the string and it is valid as a prefix and it's only used for strings with length >= 6 (where it is a valid prefix) actually only dp[i][j] where i==j counts the number of such strings and otherwise there is no string where i!=j and it that case dp[i][j] counts the number of valid prefixes for string dp[0][0]=1 does satisfy both properties because 0=0 so the number of As & Bs are the same the logic behind n/2 is that if the length of the string is n this means that it has n/2 As and n/2 Bs (n must be even) the dp for n=4 doesn't look like that! this is how it looks (i just compiled the code and checked values of dp): 1 0 0 1 1 0 1 2 2 so dp[2][2]=2 which means the number of strings with 2 As and 2 Bs is 2
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