Solve problem 149.

python/e149.py

@@ -0,0 +1,105 @@
+def gen_numbers():
+    numbers = []
+    for k in range(1, 56):
+        n = (100_003 - 200_003*k + 300_007*k**3) % 1_000_000 - 500_000
+        numbers.append(n)
+    for k in range(56, 2000 * 2000 + 1):
+        n = (numbers[k-24-1] + numbers[k-55-1] + 1_000_000) % 1_000_000 - 500_000
+        numbers.append(n)
+    return numbers
+
+
+def split(xs, n):
+    return [xs[i:i + n] for i in range(0, len(xs), n)]
+
+
+def diags(rows):
+    n = len(rows)
+    diags = []
+    for col_i in range(-n + 1, n):
+        d = []
+        for row_i in range(n):
+            if col_i >= 0 and col_i < n:
+                d.append(rows[row_i][col_i])
+            col_i += 1
+        diags.append(d)
+    return diags
+
+
+def anti_diags(rows):
+    n = len(rows)
+    diags = []
+    for col_i in range(-n + 1, n):
+        d = []
+        for row_i in range(n - 1, -1, -1):
+            if col_i >= 0 and col_i < n:
+                d.append(rows[row_i][col_i])
+            col_i += 1
+        diags.append(d)
+    return diags
+
+
+def shorten(xs):
+    r = []
+    i = 0
+    while i < len(xs):
+        r.append(0)
+        if xs[i] < 0:
+            while i < len(xs) and xs[i] < 0:
+                r[-1] += xs[i]
+                i += 1
+        else:
+            while i < len(xs) and xs[i] >= 0:
+                r[-1] += xs[i]
+                i += 1
+    if r[0] <= 0:
+        r = r[1:]
+    if r and r[-1] <= 0:
+        r = r[:-1]
+    return r
+
+
+def max_subarray(numbers):
+    """Find the largest sum of any contiguous subarray.
+
+    https://en.wikipedia.org/wiki/Maximum_subarray_problem
+
+    Emberassing that I didn't come up with that myself...
+    """
+    best_sum = -10**12
+    current_sum = 0
+    for x in numbers:
+        current_sum = max(x, current_sum + x)
+        best_sum = max(best_sum, current_sum)
+    return best_sum
+
+
+def max_subarray_naiv(xs):
+    """ Naiv implementation in O(n^3) or something. """
+    r = 0
+    xs = shorten(xs)
+    for width in range(1, len(xs) + 1, 2):
+        for i in range(len(xs)):
+            r = max(r, sum(xs[i:i+width]))
+    return r
+
+
+def euler_149():
+    ns = gen_numbers()
+    assert ns[10-1] == -393027
+    assert ns[100-1] == 86613
+
+    rows = split(ns, 2000)
+    cols = list(map(list, zip(*rows)))
+
+    r = 0
+    for elems in [rows, cols, diags(rows), anti_diags(rows)]:
+        for xs in elems:
+            r = max(max_subarray(xs), r)
+    return r
+
+
+if __name__ == "__main__":
+    solution = euler_149()
+    print("e149.py: " + str(solution))
+    assert solution == 52852124