hard 2

exercises/hard/solutiont2/src/prime_factor.rs

@@ -1,15 +1,15 @@
+use std::time::Instant;
+
 pub fn find_max_prime_factor(number: u128) -> u128 {
     let mut n = number;
 
     let mut max_factor = 0;
 
-    // Remove all factors of 2
     while n % 2 == 0 {
         max_factor = 2;
         n /= 2;
     }
 
-    // Check for odd factors from 3 to sqrt(n)
     let mut factor = 3;
     while factor * factor <= n {
         while n % factor == 0 {
@@ -39,12 +39,64 @@ fn is_prime(n: u128) -> bool {
     if n % 2 == 0 || n % 3 == 0 {
         return false;
     }
-    let mut i = 5;
-    while i * i <= n {
-        if n % i == 0 || n % (i + 2) == 0 {
-            return false;
+
+    let bases = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37];
+    let (s, d) = {
+        let mut d = n - 1;
+        let mut s = 0;
+        while d % 2 == 0 {
+            d /= 2;
+            s += 1;
+        }
+        (s, d)
+    };
+
+    'outer: for &a in bases.iter() {
+        if a >= n {
+            continue;
+        }
+        let mut x = mod_pow(a, d, n);
+        if x == 1 || x == n - 1 {
+            continue;
         }
-        i += 6;
+        for _ in 0..s - 1 {
+            x = mod_pow(x, 2, n);
+            if x == n - 1 {
+                continue 'outer;
+            }
+        }
+        return false;
     }
     true
 }
+
+// 分步模乘法防溢出
+fn mod_pow(base: u128, exp: u128, modulus: u128) -> u128 {
+    let mut result = 1;
+    let mut base = base % modulus;
+    let mut exp = exp;
+
+    while exp > 0 {
+        if exp % 2 == 1 {
+            result = mod_mul(result, base, modulus);
+        }
+        exp >>= 1;
+        base = mod_mul(base, base, modulus);
+    }
+    result
+}
+
+// 核心：将乘法分解为加法避免溢出 <button class="citation-flag" data-index="7">
+fn mod_mul(mut a: u128, mut b: u128, modulus: u128) -> u128 {
+    let mut result = 0;
+    a %= modulus;
+    b %= modulus;
+    while b > 0 {
+        if b % 2 == 1 {
+            result = (result + a) % modulus;
+        }
+        a = (a << 1) % modulus;
+        b >>= 1;
+    }
+    result
+}

exercises/hard/solutiont2/src/tests.rs

@@ -33,7 +33,7 @@ mod tests {
             if duration <= Duration::new(3, 0) && result == *expected {
                 total_score += 10.0;
             } else {
-                println!("Test failed for input: {}, expected: {}, got: {}, use time: {}", input, expected, result, duration.as_millis());
+                println!("Test failed for input: {}, expected: {}, got: {}, use time: {} ms", input, expected, result, duration.as_millis());
             }
         }
         println!("Total score: {:.2}", total_score);