SemiPerfectNumbers.cpp

Author: geekboi777

SemiPerfect Numbers/SemiPerfect Numbers.cpp

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+// C++ program to check if the number
+// is semi-perfect or not
+#include <bits/stdc++.h>
+using namespace std;
+
+// code to find all the factors of
+// the number excluding the number itself
+vector<int> factors(int n)
+{
+	// vector to store the factors
+	vector<int> v;
+	v.push_back(1);
+
+	// note that this loop runs till sqrt(n)
+	for (int i = 2; i <= sqrt(n); i++) {
+
+		// if the value of i is a factor
+		if (n % i == 0) {
+			v.push_back(i);
+
+			// condition to check the
+			// divisor is not the number itself
+			if (n / i != i) {
+				v.push_back(n / i);
+			}
+		}
+	}
+	// return the vector
+	return v;
+}
+
+// Function to check if the
+// number is semi-perfect or not
+bool check(int n)
+{
+	vector<int> v;
+
+	// find the divisors
+	v = factors(n);
+
+	// sorting the vector
+	sort(v.begin(), v.end());
+
+	int r = v.size();
+
+	// subset to check if no is semiperfect
+	bool subset[r + 1][n + 1];
+
+	// initialising 1st column to true
+	for (int i = 0; i <= r; i++)
+		subset[i][0] = true;
+
+	// initializing 1st row except zero position to 0
+	for (int i = 1; i <= n; i++)
+		subset[0][i] = false;
+
+	// loop to find whether the number is semiperfect
+	for (int i = 1; i <= r; i++) {
+		for (int j = 1; j <= n; j++) {
+
+			// calculation to check if the
+			// number can be made by summation of divisors
+			if (j < v[i - 1])
+				subset[i][j] = subset[i - 1][j];
+			else {
+				subset[i][j] = subset[i - 1][j] ||
+							subset[i - 1][j - v[i - 1]];
+			}
+		}
+	}
+
+	// if not possible to make the
+	// number by any combination of divisors
+	if ((subset[r][n]) == 0)
+		return false;
+	else
+		return true;
+}
+
+// driver code to check if possible
+int main()
+{
+	int n;
+	cin >> n;
+	for(int i =0 ; i <n ; i++){
+	    if (check(i))
+	        cout << i << " ";
+	}
+	return 0;
+	
+}
+