Solved problem 18

0018-triangle-path.py

@@ -0,0 +1,82 @@
+"""
+Problem 18
+
+By starting at the top of the triangle below and moving to adjacent numbers
+on the row below, the maximum total from top to bottom is 23.
+
+3
+7 4
+2 4 6
+8 5 9 3
+
+That is, 3 + 7 + 4 + 9 = 23.
+
+Find the maximum total from top to bottom of the triangle below:
+
+75
+95 64
+17 47 82
+18 35 87 10
+20 04 82 47 65
+19 01 23 75 03 34
+88 02 77 73 07 63 67
+99 65 04 28 06 16 70 92
+41 41 26 56 83 40 80 70 33
+41 48 72 33 47 32 37 16 94 29
+53 71 44 65 25 43 91 52 97 51 14
+70 11 33 28 77 73 17 78 39 68 17 57
+91 71 52 38 17 14 91 43 58 50 27 29 48
+63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
+
+NOTE: As there are only 16384 routes, it is possible to solve this problem
+by trying every route. However, Problem 67, is the same challenge with a t
+riangle containing one-hundred rows; it cannot be solved by brute force, and
+requires a clever method! ;o)
+"""
+import copy
+data = """\
+75
+95 64
+17 47 82
+18 35 87 10
+20 04 82 47 65
+19 01 23 75 03 34
+88 02 77 73 07 63 67
+99 65 04 28 06 16 70 92
+41 41 26 56 83 40 80 70 33
+41 48 72 33 47 32 37 16 94 29
+53 71 44 65 25 43 91 52 97 51 14
+70 11 33 28 77 73 17 78 39 68 17 57
+91 71 52 38 17 14 91 43 58 50 27 29 48
+63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
+"""
+def traditional():
+    # Initialization of data
+    global data
+    data = data.splitlines()
+    data = [x.split() for x in data]
+
+    # Converting string to int
+    for i in range(len(data)):
+        data[i] = map(int, data[i])
+
+    # Creating a answer matrix
+    ans = copy.deepcopy(data)
+
+    for i in range(len(data)-1):
+        # Updating current matrix with answer matrix
+        data = copy.deepcopy(ans)
+        for j in range(len(data[i])):
+            # Computing the left child
+            temp = data[i][j] + data[i+1][j]
+            ans[i+1][j] = max(ans[i+1][j], temp)
+
+            # Computing the right child
+            temp = data[i][j] + data[i+1][j+1]
+            ans[i+1][j+1] = max(ans[i+1][j+1], temp)
+
+    return max(ans[-1])
+
+print "Answer:", traditional()