algorithm             size    calls made      distinct subs   ratio       
Merge Sort            8       15              15              1.00        
Merge Sort            16      31              31              1.00        
Merge Sort            24      47              47              1.00        
naive Fibonacci       8       67              9               7.44        
naive Fibonacci       16      3193            17              187.82      
naive Fibonacci       24      150049          25              6001.96     
matrix chain (plain)  4       27              10              2.70        
matrix chain (plain)  8       2187            36              60.75       
matrix chain (plain)  12      177147          78              2271.12     

A ratio near 1 means no subproblem is ever revisited: divide and conquer.
A ratio that grows without bound means the recursion is redoing work: use DP.
