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 />
1. <strong>Space</strong>/<strong>time</strong> <strong>tradeoffs</strong><br />
• Time efficiency can some<strong>time</strong>s be<br />
gained by making use of storage space<br />
• Tables or larger tree nodes may be used<br />
to obtain improved running <strong>time</strong>s<br />
• Cases:<br />
– Sorting by counting<br />
– String matching<br />
– Hashing<br />
– B trees<br />
David Keil Analysis of Algorithms 1/11<br />
Sorting by counting<br />
• Suppose problem is to sort an array composed<br />
only of values in 1..m<br />
• Then a solution is to count the occurrences of<br />
each value in 1..m and store in a table T<br />
• Then write to the array T[1] 1’s,<br />
T[2] 2’s, etc.<br />
• RRunning i <strong>time</strong> ti O(n) O( )i is better b tt than th any comparison-based<br />
sort, provided that m ≤ O(n)<br />
• 2 5 1 2 8 7 5 1 5 ⇒ 1 1 2 2 5 5 7 8<br />
David Keil Analysis of Algorithms 1/11<br />
D. Keil Analysis of Algorithms 1/11<br />
3<br />
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