init

problems/p53/Cargo.toml

@@ -0,0 +1,7 @@
+[package]
+name = "p53"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+primal = { workspace = true }

problems/p53/src/main.rs

@@ -0,0 +1,54 @@
+use primal::Sieve;
+use std::collections::HashMap;
+
+fn comb_ge_1m(n: u64, r: u64, factor_table: &Vec<Vec<(usize, usize)>>) -> bool {
+    if r == 0 || r > n {
+        return false;
+    }
+
+    let mut all_factors: HashMap<usize, i64> = HashMap::new();
+
+    // Use symmetry: C(n,r) = C(n,n-r), choose smaller r
+    let r = r.min(n - r);
+
+    // 分子：(n-r+1) * (n-r+2) * ... * n
+    for i in (n - r + 1)..=n {
+        let factors = &factor_table[i as usize - 1];
+        for (prime, exp) in factors {
+            *all_factors.entry(*prime).or_insert(0) += *exp as i64;
+        }
+    }
+    // 分母：1 * 2 * ... * r
+    for i in 1..=r {
+        let factors = &factor_table[i as usize - 1];
+        for (prime, exp) in factors {
+            *all_factors.entry(*prime).or_insert(0) -= *exp as i64;
+        }
+    }
+
+    // Check if result >= 1M using logarithms to avoid overflow
+    let mut log_result = 0.0f64;
+    for (prime, exp) in all_factors {
+        if exp != 0 {
+            log_result += (prime as f64).ln() * (exp as f64);
+        }
+    }
+
+    log_result >= 1_000_000.0f64.ln()
+}
+
+fn main() {
+    let mut counter = 0;
+    let sieve = Sieve::new(100);
+    let factor_table: Vec<Vec<(usize, usize)>> =
+        (1..=100).map(|x| sieve.factor(x).unwrap()).collect();
+
+    for n in 1..=100u64 {
+        for r in 1..=n {
+            if comb_ge_1m(n, r, &factor_table) {
+                counter += 1;
+            }
+        }
+    }
+    println!("{counter}");
+}