MathLib.gcd/lcm/divisors

NASU41 · NASU41 · commit cadb741fca3a · 2021-02-06T23:28:07.000+09:00
diff --git a/Math/MathLib.java b/Math/MathLib.java
@@ -22,6 +22,17 @@ private static long[] inv_gcd(long a, long b){
         return new long[]{s,m0};
     }
 
+    public static long gcd(long a, long b){
+        a = java.lang.Math.abs(a);
+        b = java.lang.Math.abs(b);
+        return inv_gcd(a, b)[0];       
+    }
+    public static long lcm(long a, long b){
+        a = java.lang.Math.abs(a);
+        b = java.lang.Math.abs(b);
+        return a / gcd(a,b) * b;
+    }
+
     public static long pow_mod(long x, long n, int m){
         assert n >= 0;
         assert m >= 1;
@@ -86,4 +97,18 @@ public static long floor_sum(long n, long m, long a, long b){
         ans += floor_sum(y_max, a, m, (a-x_max%a)%a);
         return ans;
     }
+
+    public static java.util.ArrayList<Long> divisors(long n){
+        java.util.ArrayList<Long> divisors = new ArrayList<>();
+        java.util.ArrayList<Long> large = new ArrayList<>();
+
+        for(long i=1; i*i<=n; i++) if(n%i==0){
+            divisors.add(i);
+            if(i*i<n) large.add(n/i);
+        }
+        for(int p=large.size()-1; p>=0; p--){
+            divisors.add(large.get(p));
+        }
+        return divisors;
+    }
 }
diff --git a/Math/README.md b/Math/README.md
@@ -21,4 +21,18 @@ $$ x \equiv r[i] \mod m[i] $$ を解きます.
 public static long floor_sum(long n, long m, long a, long b)
 ```
 
-$ \sigma_{i=0}^{n-1} floor(\frac{a*i+b}{m}) $を返します.
+$ \sigma_{i=0}^{n-1} floor(\frac{a*i+b}{m}) $を返します.
+
+## gcd, lcm
+
+```java
+public static long gcd(long a, long b)
+public static long lcm(long a, long b)
+```
+二整数 a, b の最大公約数/最小公倍数を返します. 返り値は必ず非負整数になります.
+
+```java
+public static java.util.ArrayList<Long> divisors(int n)
+```
+整数nの約数を昇順に含んだリストを返します.
+計算量: O(√n)
