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yanglbme
2019-08-21 10:10:08 +08:00
parent abc0d365de
commit 69ddc9fc52
101 changed files with 3154 additions and 2984 deletions
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38
Dynamic Programming/Catalan-Numbers.cpp
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@@ -13,7 +13,7 @@ int *cat; // global array to hold catalan numbers
unsigned long int catalan_dp(int n)
{
/** Using the tabulation technique in dynamic programming,
/** Using the tabulation technique in dynamic programming,
this function computes the first `n+1` Catalan numbers
Parameter
@@ -26,39 +26,39 @@ unsigned long int catalan_dp(int n)
*/
// By definition, the first two Catalan numbers are 1
cat[0] = cat[1] = 1;
cat[0] = cat[1] = 1;
// Compute the remaining numbers from index 2 to index n, using tabulation
for (int i = 2; i <= n; i++)
{
cat[i] = 0;
for (int j = 0; j < i; j++)
cat[i] += cat[j] * cat[i-j-1]; // applying the definition here
}
for (int i = 2; i <= n; i++)
{
cat[i] = 0;
for (int j = 0; j < i; j++)
cat[i] += cat[j] * cat[i - j - 1]; // applying the definition here
}
// Return the result
return cat[n];
return cat[n];
}
int main(int argc, char *argv[])
{
int n;
cout << "Enter n: ";
cin >> n;
int n;
cout << "Enter n: ";
cin >> n;
cat = new int[n+1];
cat = new int[n + 1];
cout << "Catalan numbers from 0 to " << n << " are:\n";
for (int i = 0; i <= n; i++)
cout << "Catalan numbers from 0 to " << n << " are:\n";
for (int i = 0; i <= n; i++)
{
cout << "catalan (" << i << ") = " << catalan_dp(i) << endl;
// NOTE: Since `cat` is a global array, calling `catalan_dp`
cout << "catalan (" << i << ") = " << catalan_dp(i) << endl;
// NOTE: Since `cat` is a global array, calling `catalan_dp`
// repeatedly will not recompute the the values already computed
// as in case of pre-computed values, the array will simply return them,
// as in case of pre-computed values, the array will simply return them,
// instead of recomputing them.
}
return 0;
return 0;
}
/** Sample Test Case: