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| contest_2011-09-13 [2011/09/11 08:18] – jtkorb | contest_2011-09-13 [2011/09/20 14:31] – jtkorb |
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| * A: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=33&page=show_problem&problem=1143|Pairsumonious Numbers]] | * A: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=33&page=show_problem&problem=1143|Pairsumonious Numbers]] |
| | * B: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=32&page=show_problem&problem=1132|Longest Nap]] |
| | * C: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=32&page=show_problem&problem=967|Shoemaker's Problem]] |
| | * D: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=34&page=show_problem&problem=1154|How Many Pieces of Land?]] |
| | * E: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=34&page=show_problem&problem=990|Self-describing Sequence]] |
| | * F: [[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=34&page=show_problem&problem=787|Steps]] |
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| If you've already solved one or more of these problems, try (1) solving again without referring to your old solution, and/or (2) using a different language (Java or C++). If you want to work on an additional problem from this chapter, let [[jtk@purdue.edu|me]] know. | //Remember:// If you've already solved one or more of these problems, try (1) solving again without referring to your old solution, and/or (2) using a different language (Java or C++). If you want to work on an additional problem from the book, let [[jtk@purdue.edu|me]] know. |
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| **Hints:** | **Hints:** |
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| * A: Solve [[prelude_to_pairsumonious_numbers|Prelude to Pairsumonious Numbers]] first. An exhaustive search of all possible sums works. Create a candidate vector by seeding the first location with 1/2 of the first (lowest) sum. Extend the vector by subtracting the current vector element from one of the sums. Each time the vector fills, check to see if it is a solution. If not, backtrack by selecting a different sum value at each of the extension steps. Tricky bits: watch for sums less than 0 and only extend the current candidate solution vector if the entries are non-decreasing. The check solution procedure verifies that the pair-wise sum of every pair of values has been found. | * A: Solve [[prelude_to_pairsumonious_numbers|Prelude to Pairsumonious Numbers]] first. An exhaustive search of all possible sums works. Create a candidate vector by seeding the first location with 1/2 of the first (lowest) sum. Extend the vector by subtracting the current vector element from one of the sums. Each time the vector fills, check to see if it is a solution. If not, backtrack by selecting a different sum value at each of the extension steps. Tricky bits: watch for sums less than 0 and only extend the current candidate solution vector if the entries are non-decreasing. The check solution procedure verifies that the pair-wise sum of every pair of values has been found. |
| | * B: This problem is from the chapter on sorting. Comparators help here. |
| | * C: See B. |
| | * D: Once you see the trick, the solution is easy with big integers (are they required?). |
| | * E: Pre-compute a run-length encoded array to represent f, then do a binary search to find f(n). |
| | * F: |
