Problem 015

git-svn-id: file:///srv/svn/euler@40 e5f4c3ec-3c0c-11df-b522-21efaa4426b5

e015.py

@@ -0,0 +1,33 @@
+"""
+Calculate the number of possible paths from the top left corner to the bottom
+right, without backtracking (no moving up or left)
+
+i.e., for a 2x2 grid:
+     _ _
+    |_|_|
+    |_|_|
+    
+Paths to each point, forming a Pascal Triangle:
+    1 1 1
+    1 2 3
+    1 3 6
+
+    001 001 001 001
+    001 002 003 004
+    001 003 006 010
+    001 004 010 020
+"""
+def pascal(row, col):
+    val = 1
+    r = row + 1
+    for c in range(1, col + 1):
+        val = (val * ((r - c) / float(c)))
+    return int(val)
+def paths(size):
+    return pascal(size + (size - 2), size - 1)
+
+if __name__ == '__main__':
+    # 20x20 grid
+    # Points = cubes + 1
+    size = 21
+    print 'Paths: ', paths(size)