From f6df24a589fa26cf147e1da226c67bf366c7b94d Mon Sep 17 00:00:00 2001
From: KaustubhDamania <kaustubh.damania@gmail.com>
Date: Thu, 22 Oct 2020 12:06:10 +0530
Subject: [PATCH] Added all functions inside a class + added more asserts

---
 math/ncr_modulo_p.cpp | 164 ++++++++++++++++++++++++------------------
 1 file changed, 94 insertions(+), 70 deletions(-)

diff --git a/math/ncr_modulo_p.cpp b/math/ncr_modulo_p.cpp
index 5f31b90a7..5f4f61d46 100644
--- a/math/ncr_modulo_p.cpp
+++ b/math/ncr_modulo_p.cpp
@@ -8,72 +8,103 @@
 #include <iostream>
 #include <vector>
 
-/** Finds the value of x, y such that a*x + b*y = gcd(a,b)
+
+/** Class which contains all methods required for calculating nCr mod p
  *
- * @params[in] the numbers 'a', 'b' and address of 'x' and 'y' from above
- * equation
- * @returns the gcd of a and b
  */
-int64_t gcdExtended(int64_t a, int64_t b, int64_t *x, int64_t *y) {
-    if (a == 0) {
-        *x = 0, *y = 1;
-        return b;
+class NCRModuloP {
+private:
+    std::vector<int64_t> fac;
+    int64_t p;
+public:
+    /** Constructor which precomputes the values of n! % mod from n=0 to size
+     *  and stores them in vector 'fac'
+     *  @params[in] the numbers 'size', 'mod'
+    */
+    NCRModuloP(int64_t size, int64_t mod){
+        p = mod;
+        fac = std::vector<int64_t>(size);
+        fac[0] = 1;
+        for (int i = 1; i <= size; i++) {
+            fac[i] = (fac[i - 1] * i) % p;
+        }
     }
 
-    int64_t x1 = 0, y1 = 0;
-    int64_t gcd = gcdExtended(b % a, a, &x1, &y1);
+    /** Finds the value of x, y such that a*x + b*y = gcd(a,b)
+     *
+     * @params[in] the numbers 'a', 'b' and address of 'x' and 'y' from above
+     * equation
+     * @returns the gcd of a and b
+     */
+    int64_t gcdExtended(int64_t a, int64_t b, int64_t *x, int64_t *y) {
+        if (a == 0) {
+            *x = 0, *y = 1;
+            return b;
+        }
 
-    *x = y1 - (b / a) * x1;
-    *y = x1;
-    return gcd;
+        int64_t x1 = 0, y1 = 0;
+        int64_t gcd = gcdExtended(b % a, a, &x1, &y1);
+
+        *x = y1 - (b / a) * x1;
+        *y = x1;
+        return gcd;
+    }
+
+    /** Find modular inverse of a with m i.e. a number x such that (a*x)%m = 1
+     *
+     * @params[in] the numbers 'a' and 'm' from above equation
+     * @returns the modular inverse of a
+     */
+    int64_t modInverse(int64_t a, int64_t m) {
+        int64_t x = 0, y = 0;
+        int64_t g = gcdExtended(a, m, &x, &y);
+        if (g != 1) {  // modular inverse doesn't exist
+            return -1;
+        }
+        else {
+            int64_t res = (x % m + m) % m;
+            return res;
+        }
+    }
+
+    /** Find nCr % p
+     *
+     * @params[in] the numbers 'n', 'r' and 'p'
+     * @returns the value nCr % p
+     */
+    int64_t ncr(int64_t n, int64_t r, int64_t p) {
+        // Base cases
+        if (r > n) {
+            return 0;
+        }
+        if (r == 1) {
+            return n % p;
+        }
+        if (r == 0 || r == n){
+            return 1;
+        }
+        // fac is a global array with fac[r] = (r! % p)
+        int64_t denominator = modInverse(fac[r], p);
+        if (denominator < 0) {  // modular inverse doesn't exist
+            return -1;
+        }
+        denominator = (denominator * modInverse(fac[n - r], p)) % p;
+        if (denominator < 0) {  // modular inverse doesn't exist
+            return -1;
+        }
+        return (fac[n] * denominator) % p;
+    }
+};
+
+void tests(NCRModuloP ncrObj) {
+    // (52323 C 26161) % (1e9 + 7) = 224944353
+    assert(ncrObj.ncr(52323, 26161, 1000000007) == 224944353);
+    // 6 C 2 = 30, 30%5 = 0
+    assert(ncrObj.ncr(6,2,5) == 0);
+    // 7C3 = 35, 35 % 29 = 8
+    assert(ncrObj.ncr(7,3,29) == 6);
 }
 
-/** Find modular inverse of a with m i.e. a number x such that (a*x)%m = 1
- *
- * @params[in] the numbers 'a' and 'm' from above equation
- * @returns the modular inverse of a
- */
-int64_t modInverse(int64_t a, int64_t m) {
-    int64_t x = 0, y = 0;
-    int64_t g = gcdExtended(a, m, &x, &y);
-    if (g != 1) {  // modular inverse doesn't exist
-        return -1;
-    }
-    else {
-        int64_t res = (x % m + m) % m;
-        return res;
-    }
-}
-
-std::vector<int64_t> fac;
-
-/** Find nCr % p
- *
- * @params[in] the numbers 'n', 'r' and 'p'
- * @returns the value nCr % p
- */
-int64_t ncr(int64_t n, int64_t r, int64_t p) {
-    // Base cases
-    if (r > n) {
-        return 0;
-    }
-    if (r == 1) {
-        return n % p;
-    }
-    if (r == 0 || r == n){
-        return 1;
-    }
-    // fac is a global array with fac[r] = (r! % p)
-    int64_t denominator = modInverse(fac[r], p);
-    if (denominator < 0) {  // modular inverse doesn't exist
-        return -1;
-    }
-    denominator = (denominator * modInverse(fac[n - r], p)) % p;
-    if (denominator < 0) {  // modular inverse doesn't exist
-        return -1;
-    }
-    return (fac[n] * denominator) % p;
-}
 
 /**
  * @brief Main function
@@ -82,19 +113,12 @@ int64_t ncr(int64_t n, int64_t r, int64_t p) {
 int main() {
     // populate the fac array
     const int64_t size = 1e6 + 1;
-    fac = std::vector<int64_t>(size);
-    fac[0] = 1;
     const int64_t p = 1e9 + 7;
-    for (int i = 1; i <= size; i++) {
-        fac[i] = (fac[i - 1] * i) % p;
-    }
-
+    NCRModuloP ncrObj = NCRModuloP(size, p);
     // test 6Ci for i=0 to 7
     for (int i = 0; i <= 7; i++) {
-        std::cout << 6 << "C" << i << " = " << ncr(6, i, p) << "\n";
+        std::cout << 6 << "C" << i << " = " << ncrObj.ncr(6, i, p) << "\n";
     }
-
-    // (52323 C 26161) % (1e9 + 7) = 224944353
-    assert(ncr(52323, 26161, p) == 224944353);
-    std::cout << "Assertion passed, (52323 C 26161) % (1e9 + 7) = 224944353\n";
+    tests(ncrObj);
+    std::cout << "Assertions passed\n";
 }