C++ Programming Code Examples
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Generate All the Set Partitions of n Numbers Beginning from 1 and so on
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/* Generate All the Set Partitions of n Numbers Beginning from 1 and so on
- This algorithm generates all the possible partition can be generated by breaking the given integer value.
- The time complexity of this algorithm is O(n*n!).
- This algorithm takes the input of a natural number and prints all the possible partition of each number less than or equal to it.
- For each number, it starts with the number and breaks it by 1, at a time.
- Exit. */
#include<iostream>
using namespace std;
// A function to print the generated partition.
void printArray(int p[], int n)
{
cout<<"\t";
for (int i = 0; i < n; i++)
cout<<p[i]<<" ";
cout<<"\n";
}
// A function to print all the possible partition.
void PrintAllUniqueParts(int n)
{
int p[n], k = 0;
p[k] = n;
// Loop until all the array elements converted to 1 mean no further partition can be generated.
while(1)
{
printArray(p, k + 1);
int rem_val = 0;
// Move the pointer to the index so that p[k] > 1.
while (k >= 0 && p[k] == 1)
{
rem_val += p[k];
k--;
}
// If k < 0 then the all the element are broken down to 1.
if (k < 0)
return;
// If value greater than 1 is found then decrease it by 1 and increase rem_val to add it to other elements.
p[k]--;
rem_val++;
// Loop until the number of 1's are greater than the value at k index.
while (rem_val > p[k])
{
p[k+1] = p[k];
// Decrease the rem_val value.
rem_val = rem_val - p[k];
k++;
}
// Assign the remaining value to the index next to k.
p[k+1] = rem_val;
k++;
}
}
int main()
{
int n;
cout<<"Enter natural numbers for creating partitions: ";
cin>>n;
if (value <= 0)
{
cout<<"Wrong input!!";
break;
}
cout<<"All Unique Partitions of "<<n<<" are:-\n";
PrintAllUniqueParts(n);
return 0;
}
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