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C++ Program to Perform integer Partition for a Specific Case
This is a C++ program to perform integer partition for a specific case. In this program, a positive integer n is given, and shall have to generate all possible unique ways to represent n as sum of positive integers.
Algorithm
Begin function displayAllUniqueParts(int m): 1) Set Index of last element k in a partition to 0 2) Initialize first partition as number itself, p[k]=m 3) Create a while loop which first prints current partition, then generates next partition. The loop stops when the current partition has all 1s. 4) Display current partition as displayArray(p, k + 1) 5) Generate next partition: 6) Initialize val = 0. Find the rightmost non-one value in p[]. Also, update the val so that we know how much value can be ccommodated. If k < 0, All the values are 1 so there are no more partitions Decrease the p[k] found above and adjust the val. 7) If val is more, then the sorted order is violated. Divide val in different values of size p[k] and copy these values at different positions after p[k]. Copy val to next position and increment position. End
Example
#include<iostream>
using namespace std;
void displayArray(int p[], int m) { //to print the array
for (int i = 0; i < m; i++)
cout << p[i] << " ";
cout << endl;
}
void displayAllUniqueParts(int m) {
int p[m];
int k = 0;
p[k] = m;
while (true) {
displayArray(p, k + 1);
int val = 0; // initialize val
while (k >= 0 && p[k] == 1) {
val += p[k]; // update val
k--;
}
if (k < 0)
return;
p[k]--;
val++;
//if val is more
while (val > p[k]) {
p[k + 1] = p[k];
val = val - p[k];
k++;
}
p[k + 1] = val;
k++;
}
}
int main() {
cout << "Display All Unique Partitions of integer:7\n";
displayAllUniqueParts(7);
return 0;
}Output
Display All Unique Partitions of integer:7 7 6 1 5 2 5 1 1 4 3 4 2 1 4 1 1 1 3 3 1 3 2 2 3 2 1 1 3 1 1 1 1 2 2 2 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
Updated on: 30-Jul-2019
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