Solve problem 113.

python/e113.py

@@ -0,0 +1,52 @@
+def is_non_bouncy(n: int):
+    digits = list(map(int, list(str(n))))
+    decreasing = True
+    increasing = True
+    for i in range(len(digits) - 1):
+        increasing = increasing and digits[i] <= digits[i + 1]
+        decreasing = decreasing and digits[i] >= digits[i + 1]
+    return increasing or decreasing
+
+
+def non_bouncy_below_naiv(digits: int):
+    threshold = 10 ** digits
+    non_bouncy = sum([1 for i in range(1, threshold) if is_non_bouncy(i)])
+    return non_bouncy
+
+
+def non_bouncy_below(digits: int):
+    # increasing
+    s = [1 for _ in range(1, 10)]
+    result = sum(s)
+    for _ in range(digits - 1):
+        s = [sum(s[i:]) for i in range(9)]
+        result += sum(s) - 9
+    # The -9 is to avoid double counting 11, 22, 33 for increasing and
+    # decreasing.
+
+    # decreasing
+    decreasing_count = 0
+    s = [i + 1 for i in range(1, 10)]
+    for _ in range(digits - 1):
+        # print(s)
+        decreasing_count += sum(s)
+        s = [sum(s[:i]) + 1 for i in range(1, 10)]
+    result += decreasing_count
+    return result
+
+
+def euler_113():
+    assert non_bouncy_below_naiv(6) == 12951
+    assert non_bouncy_below(6) == 12951
+    assert non_bouncy_below(10) == 277032
+    assert is_non_bouncy(134468)
+    assert is_non_bouncy(66420)
+    assert (not is_non_bouncy(155349))
+    return non_bouncy_below(100)
+
+
+if __name__ == "__main__":
+    solution = euler_113()
+    print("e113.py: " + str(solution))
+    assert(solution == 51161058134250)
+