Add solution for the Euler project problem 164.

Author: mindaugl

Diff for: project_euler/problem_164/__init__.py

@@ -0,0 +1,58 @@
+"""
+Project Euler Problem 164: https://projecteuler.net/problem=164
+
+Three Consecutive Digital Sum Limit
+
+How many 20 digit numbers n (without any leading zero) exist such that no three
+consecutive digits of n have a sum greater than 9?
+
+Brute-force recursive solution with caching of intermediate results.
+
+>>> solution(10)
+21838806
+"""
+
+
+def solve(
+    digit: int, prev: int, prev2: int, sum_max: int, first: bool, cache: dict[str, int]
+) -> int:
+    """
+    Solve for remaining 'digit' digits, with previous 'prev' number, and
+    previous-previous 'prev2' number, total sum of 'sum_max'.
+    Pass around 'cache' to store/reuse intermediate results.
+
+    >>> solve(1, 0, 0, 9, True, {})
+    9
+    >>> solve(1, 0, 0, 9, False, {})
+    10
+    """
+    if digit == 0:
+        return 1
+    comb = 0
+    cache_str = f"{digit},{prev},{prev2}"
+    if cache_str in cache:
+        return cache[cache_str]
+    for v in range(sum_max - prev - prev2 + 1):
+        if first and v == 0:
+            continue
+        comb += solve(digit - 1, v, prev, sum_max, False, cache)
+    cache[cache_str] = comb
+    return comb
+
+
+def solution(n_digits: int = 20) -> int:
+    """
+    Solves the problem for n_digits number of digits.
+
+    >>> solution(2)
+    45
+    """
+    sum_max = 9
+    cache: dict[str, int] = {}
+    ans = solve(n_digits, 0, 0, sum_max, True, cache)
+
+    return ans
+
+
+if __name__ == "__main__":
+    print(f"{solution(10) = }")