✨ feat：添加欧拉项目第30题和第31题的解决方案

📝 docs：为第31题添加详细的动态规划算法说明文档

solutions/0030.FifthPowers/euler_30.py

@@ -0,0 +1,91 @@
+"""
+Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
+
+    1634 = 1^4 + 6^4 + 3^4 + 4^4
+    8208 = 8^4 + 2^4 + 0^4 + 8^4
+    9474 = 9^4 + 4^4 + 7^4 + 4^4
+
+As 1 = 1^4 is not a sum it is not included.
+
+The sum of these numbers is 19316.
+
+Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
+"""
+
+import time
+from itertools import combinations_with_replacement
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start = time.time()
+        result = func(*args, **kwargs)
+        end = time.time()
+        print(f"{func.__name__} on ({kwargs}) taken: {end - start: .6f} seconds")
+        return result
+
+    return wrapper
+
+
+def fifth_power(n: int, power: int = 5, strict: bool = False) -> tuple[bool, int]:
+    sumx = sum(int(digit) ** power for digit in str(n))
+    if strict:
+        isok = (sumx == n) and (power == len(str(sumx)))
+        return isok, sumx
+    return sumx == n, sumx
+
+
+def top_number(n: int) -> int:
+    beg = (9**n) * n
+    beg_len = len(str(beg))
+    last = n
+    while True:
+        if beg_len >= n:
+            beg = (9**n) * beg_len
+            last = beg_len
+            beg_len = len(str(beg))
+            if beg_len == last:
+                break
+        else:
+            break
+    return int("9" * beg_len)
+
+
+def is_match(num: int, comb: list[str]) -> bool:
+    if num in [1, 0]:
+        return False
+    numstr = str(num).zfill(len(comb))
+    numstr = sorted(numstr)
+    return numstr == sorted(comb)
+
+
+@timer
+def main_just_compute(power: int, strict: bool = False) -> None:
+    res = []
+    top = top_number(power)
+    for i in range(2, top + 1):
+        is_sum, sumx = fifth_power(i, power, strict)
+        if is_sum:
+            print(sumx, end="\t")
+            res.append(sumx)
+    print(f"\nThe sum is {sum(res):,d}")
+
+
+@timer
+def main_combinations(power: int) -> None:
+    top_len = len(str(top_number(power)))
+    res = set()
+    combs = combinations_with_replacement("0123456789", top_len)
+    for comb in combs:
+        tmp = sum(map(lambda x: int(x) ** power, comb))
+        if is_match(tmp, list(comb)):
+            print(tmp, end="\t")
+            res.add(tmp)
+    print(f"\nThe sum is {sum(res):,d}")
+
+
+if __name__ == "__main__":
+    the_power = 5
+    main_just_compute(power=the_power, strict=False)
+    print("=" * 50)
+    main_combinations(power=the_power)