Merge pull request matthewsamuel95#692 from MatheusMiranda/master

Add calculation of binomial coefficients

Author: matthewsamuel95

Math/binomial_coefficients/binomial_coefficients.py

@@ -0,0 +1,33 @@
+# Complexity: O(n^2)
+# Computes the lines of Pascal's triangle.
+# Pascal's triangle gives us result of binom(n,p), which is equivalent to combination(n,p).
+
+import fileinput
+
+binomial_coefficients = []
+line = []
+line.append(1)
+binomial_coefficients.append(line)
+
+# Element at line x and column y(binom[x][y]) of Pascal's triangle can be calculated as (binom[x-1][y] + binom[x-1][y-1]).
+def precomp(n):
+    for i in range(1,n):
+        line = []
+        line.append(1)
+
+        for j in range(1,i):
+            line.append(binomial_coefficients[i - 1][j] + binomial_coefficients[i - 1][j - 1])
+
+        line.append(1)
+
+        binomial_coefficients.append(line)
+
+precomp(40)
+
+for line in fileinput.input():
+    n,p = line.strip().split()
+    n = int(n)
+    p = int(p)
+
+    print(binomial_coefficients[n][p])
+

README.md

@@ -150,6 +150,7 @@ ACM-ICPC Algorithms is a collection of important algorithms and data structures
    * [Tower Of Hanoi](/Math/TowerofHanoi)
    * [Truncated Square Root](/Math/truncated_square_root)
    * [Calculate And Print All Permutations](/Math/AllPermutations)
+   * [Calculate the result of binom(n,p)](/Math/binomial_coefficients)
 * [Network Flow](/NetworkFlow)
    * [Dinic](/NetworkFlow/Dinic)
    * [Edmund Karp](/NetworkFlow/EdmundKarp)
@@ -162,7 +163,7 @@ ACM-ICPC Algorithms is a collection of important algorithms and data structures
    * [Jump Search](/Search/JumpSearch)
    * [Linear Search](/Search/LinearSearch)
    * [Ternary Search](/Search/TernarySearch)
-   * [Interpolation Search](/Search/InterpolationSearch) 
+   * [Interpolation Search](/Search/InterpolationSearch)
 * [Sorting Algorithms](/Sorting)
    * [Bubble Sort](/Sorting/bubble%20sort)
    * [Cocktail Shaker Sort](/Sorting/CocktailShakerSort)