Added an algorithm that calculates derangement numbers D(n) mod m using principle of inclusion-exclusion

CPP/algorithms/mathematical/derangements.cpp

@@ -0,0 +1,26 @@
+/*
+ * Derangements Calculation using Inclusion-Exclusion Principle
+ * Time Complexity: O(n)
+ * Space Complexity: O(1)
+ */
+#include <iostream>
+using namespace std;
+
+int main() {
+    int n, m;
+    cin >> n >> m;  // Read n (limit) and m (modulus)
+
+    long long c = 1;  // Initialize c = 1 (use long long to avoid overflow before mod)
+    for (int i = 1; i <= n; i++) {
+        // Multiply c by i under modulo m
+        c = (c * i) % m;
+
+        // Add or subtract 1 depending on whether i is odd or even
+        if (i % 2 == 1) c = (c - 1 + m) % m;  // subtract 1 safely under mod
+        else c = (c + 1) % m;                 // add 1 safely under mod
+
+        cout << c << ' ';
+    }
+    cout << endl;
+    return 0;
+}