Catalan numbers: Difference between revisions
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Implement at least one of these algorithms and print out the first 15 Catalan numbers with each. [[Memoization]] is not required, but may be worth the effort when using the second method above. |
Implement at least one of these algorithms and print out the first 15 Catalan numbers with each. [[Memoization]] is not required, but may be worth the effort when using the second method above. |
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;Cf.: |
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* [[Pascal's triangle]] |
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* [http://milan.milanovic.org/math/english/fibo/fibo4.html Catalan Numbers and the Pascal Triangle] |
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=={{header|Ada}}== |
=={{header|Ada}}== |
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C(14) = 2674440 |
C(14) = 2674440 |
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C(15) = 9694845 |
C(15) = 9694845 |
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</pre> |
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===An Alternative Approach=== |
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<lang cpp>// Generate Catalan Numbers |
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// |
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// Nigel Galloway: June 9th., 2012 |
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// |
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#include <iostream> |
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int main() { |
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const int N = 15; |
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int t[N+2] = {0,1}; |
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for(int i = 1; i<=N; i++){ |
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for(int j = i; j>1; j--) t[j] = t[j] + t[j-1]; |
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t[i+1] = t[i]; |
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for(int j = i+1; j>1; j--) t[j] = t[j] + t[j-1]; |
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std::cout << t[i+1] - t[i] << " "; |
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} |
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return 0; |
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}</lang> |
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{{out|Produces}} |
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<pre> |
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1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 |
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</pre> |
</pre> |
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