Symbol(clack:cancel)

solutions/0000_0029/0004.palindrome/eular_4.py

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+"""
+A palindromic number reads the same both ways.
+The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
+Find the largest palindrome made from the product of two 3-digit numbers.
+"""
+
+
+def is_palindrome(n: int) -> bool:
+    return str(n) == str(n)[::-1]
+
+
+def initial_idea() -> None:
+    a = 999
+    b = 999
+    y = (0, 0)
+    max_palindrome = 0
+    for i in range(a, 99, -1):
+        for j in range(b, 99, -1):
+            product = i * j
+            if is_palindrome(product) and product > max_palindrome:
+                max_palindrome = product
+                y = (i, j)
+    print(f"{max_palindrome} = {y[0]} × {y[1]}")
+
+
+def largest_palindrome_product():
+    max_palindrome = 0
+    max_factors = (0, 0)
+
+    # 外层循环从大到小，且只遍历11的倍数
+    for i in range(990, 100, -11):  # 从990开始（最大的11的倍数）
+        # 内层循环从i开始（避免重复，利用乘法交换律）
+        for j in range(999, i - 1, -1):
+            product = i * j
+
+            # 提前终止：如果乘积已小于当前最大值
+            if product <= max_palindrome:
+                break
+
+            # 检查是否为回文数
+            if str(product) == str(product)[::-1]:
+                max_palindrome = product
+                max_factors = (i, j)
+                break  # 找到即可跳出内层循环
+
+    return max_palindrome, max_factors
+
+
+if __name__ == "__main__":
+    initial_idea()
+    x, y = largest_palindrome_product()
+    print(f"{x} = {y[0]} × {y[1]}")