Space/time tradeoffs; dynamic programming - Framingham State ...
Space/time tradeoffs; dynamic programming - Framingham State ...
Space/time tradeoffs; dynamic programming - Framingham State ...
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6. <strong>Space</strong>-<strong>time</strong> <strong>tradeoffs</strong> and <strong>dynamic</strong> <strong>programming</strong><br />
B trees<br />
• Each node has m children<br />
• All data is stored in leaves<br />
• All leaves are at same tree level<br />
• Used to store very large indexes for<br />
databases stored on disk<br />
• Advantage: extremely short paths to<br />
leaves (lgmn) • Disadvantage: Wasted space<br />
David Keil Analysis of Algorithms 1/11<br />
2. Dynamic <strong>programming</strong><br />
• Some problems (e.g., Fibonacci) have<br />
overlapping subproblems<br />
• Dynamic <strong>programming</strong> suggests solving each<br />
subproblem only once and storing solution in a<br />
table for later reference<br />
• Cases:<br />
– Fibonacci<br />
– Binomial i i l coefficient ffi i<br />
– Warshall’s and Floyd’s algorithms (graphs)<br />
– Optimal BSTs<br />
– Knapsack problem<br />
David Keil Analysis of Algorithms 1/11<br />
D. Keil Analysis of Algorithms 1/11<br />
7<br />
8
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