Merge branch 'master' of https://github.com/williamfiset/algorithms

Author: William Fiset

src/main/java/com/williamfiset/algorithms/math/NChooseRModPrime.java

@@ -0,0 +1,61 @@
+/** @author Rohit Mazumder, mazumder.rohit7@gmai.com */
+package com.williamfiset.algorithms.math;
+
+import java.math.BigInteger;
+
+public class NChooseRModPrime {
+  /**
+   * Calculate the value of C(N, R) % P using Fermat's Little Theorem.
+   *
+   * @param N
+   * @param R
+   * @param P
+   * @return The value of N choose R Modulus P
+   */
+  public static long compute(int N, int R, int P) {
+    if (R == 0) return 1;
+
+    long[] factorial = new long[N + 1];
+    factorial[0] = 1;
+
+    for (int i = 1; i <= N; i++) {
+      factorial[i] = factorial[i - 1] * i % P;
+    }
+
+    return (factorial[N]
+            * ModularInverse.modInv(factorial[R], P)
+            % P
+            * ModularInverse.modInv(factorial[N - R], P)
+            % P)
+        % P;
+  }
+
+  // Method for testing output against the output generated by the compute(int,int,int) function
+  private static String bigIntegerNChooseRModP(int N, int R, int P) {
+    if (R == 0) return "1";
+    BigInteger num = new BigInteger("1");
+    BigInteger den = new BigInteger("1");
+    while (R > 0) {
+      num = num.multiply(new BigInteger("" + N));
+      den = den.multiply(new BigInteger("" + R));
+      BigInteger gcd = num.gcd(den);
+      num = num.divide(gcd);
+      den = den.divide(gcd);
+      N--;
+      R--;
+    }
+    num = num.divide(den);
+    num = num.mod(new BigInteger("" + P));
+    return num.toString();
+  }
+
+  public static void main(String args[]) {
+    int N = 500;
+    int R = 250;
+    int P = 1000000007;
+    int expected = Integer.parseInt(bigIntegerNChooseRModP(N, R, P));
+    long actual = compute(N, R, P);
+    System.out.println(expected); // 515561345
+    System.out.println(actual); // 515561345
+  }
+}