Solve problem 710

python/e710.py

@@ -0,0 +1,95 @@
+MOD = 10**7
+SPACE = 10**7
+CACHE = [None for _ in range(SPACE * 2)]
+CACHE_TILL = [None for _ in range(SPACE)]
+CACHE_TILL_IS_TWO_EVEN = [None for _ in range(SPACE)]
+CACHE_TILL_IS_TWO_ODD = [None for _ in range(SPACE)]
+CACHE_T_FROM_ACC = [None for _ in range(SPACE * 2)]
+
+
+def t_from_acc(rem: int, is_two: bool) -> int:
+    offset = rem + SPACE * is_two
+    if (value := CACHE_T_FROM_ACC[offset]) is not None:
+        return value
+    if rem < 0:
+        return 0
+    s = t_from(rem, is_two) + t_from_acc(rem - 2, is_two)
+    s %= MOD
+    CACHE_T_FROM_ACC[offset] = s
+    return s
+
+
+def t_from(rem: int, is_two: bool) -> int:
+    offset = rem + SPACE * is_two
+    if (value := CACHE[offset]) is not None:
+        return value
+    s = 0
+    if rem < 0:
+        s = 0
+    elif rem == 1:
+        s = 0
+    elif rem == 0 and is_two:
+        s = 1
+    else:
+        s += t_from(rem - 2, is_two)  # d = 1
+        s %= MOD
+        s += t_from(rem - 4, True)  # d = 2
+        s %= MOD
+        s += t_from_acc(rem - 6, is_two)
+        s %= MOD
+        # Naive (too slow):
+        # for d in range(1, rem // 2 + 1):
+        #     s += t_from(rem - 2 * d, is_two or d == 2)
+        #     s %= MOD
+    CACHE[offset] = s % MOD
+    return s % MOD
+
+
+def t_old(n: int) -> int:
+    # print(f"t({n}) = ", end="")
+    s = 0
+    for i in range(0, n + 1):
+        rem = n - i
+        s += t_from(rem, i == 2)
+    return s % MOD
+
+
+def t(n: int) -> int:
+    s = CACHE_TILL[n - 4]
+    assert s is not None
+    s += t_from(n - 3, False)
+    CACHE_TILL[n - 3] = s % MOD
+    s += t_from(n - 2, True)
+    s %= MOD
+    s += t_from(n - 1, False)
+    s %= MOD
+    s += t_from(n, False)
+    s %= MOD
+    return s
+
+
+def euler_710():
+    for i in range(4):
+        CACHE_TILL[i] = 0
+
+    for n in range(4, 50):
+        t(n)
+    assert t(5) == 1
+    assert t(6) == 4
+    assert t(20) == 824
+    assert t(42) == 1999923
+
+    for n in range(10, SPACE):
+        tn = t(n)
+        if tn % 10**6 == 0:
+            # print(f"t({n}) = {tn} <<<")
+            return n
+        # if tn % 10000 == 0:
+        #     print(f"t({n}) = {tn}")
+    assert False, "Solution not found"
+
+
+if __name__ == "__main__":
+    solution = euler_710()
+    print(f"e710.py: {solution}")
+    assert solution == 1275000