Merge branch 'project_euler/problem_15' into project_euler/master

# Conflicts:
#	DIRECTORY.md

project_euler/Problem 15/sol1.c

@@ -0,0 +1,35 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+
+
+/**
+ * At every node, there are 2 possible ways to move -> down or right.
+ * Since it is a square grid, there are in all, 2N steps with N down 
+ * and N right options, without preference for order. 
+ * Hence, the path can be be traced in N out of 2N number of ways.
+ * This is the same as binomial coeeficient.
+ **/
+unsigned long long number_of_paths(int N)
+{
+    unsigned long long path = 1;
+    for (int i = 0; i < N; i++)
+    {
+        path *= (N << 1) - i;
+        path /= i + 1;
+    }
+    
+    return path;
+}
+
+int main(int argc, char **argv)
+{
+    int N = 20;
+
+    if (argc == 2)
+        N = atoi(argv[1]);
+
+    printf("Number of ways to traverse diagonal of %dx%d grid = %llu\n", N, N, number_of_paths(N));
+
+    return 0;
+}