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Dynamic Programming

2. Overlapping Subproblems.

$\psfig{figure=figures/f7-3.ps,width=3.5in,height=2in}$

Define: c[i,j] = length of LCS for X_i and Y_j.

c[i,j] = $\left\{ \begin{array}{ll} 0 & {\rm if} \;i=0 \; {\rm or} \; j = 0 \\ c[i-1,... ...i-1,j]) & {\rm if} \;i,j > 0 \; {\rm and} \; x_i \neq y_j \end{array} \right.$

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