(Solved): 1. Dynamic Programming. 1. Explain the general principle of dynamic programming. 2. Explain the pro ...

1. Dynamic Programming. 1. Explain the general principle of dynamic programming. 2. Explain the problem of the matrix chain product. 3. Explain the meaning of the following formula in the context of the matrix chainproduct. \\[ \\begin{array}{c} N_{\\mathrm{i}, \\mathrm{i}}=0 \\\\ N_{\\mathrm{i}, \\mathrm{j}}=\\min _{\\mathrm{i} \\leq \\mathrm{k}<\\mathrm{j}}\\left(N_{\\mathrm{i}, \\mathrm{k}}+N_{\\mathrm{k}+1, \\mathrm{j}}+d_{\\mathrm{i}} d_{\\mathrm{k}+1} d_{\\mathrm{j}+1}\\right) . \\end{array} \\] 4. Find the optimal parenthetization of the matrix product \\( A_{0} \\times A_{1} \\times A_{2} \\times A_{3} \\), where the matrices have the following dimensions: