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#12 ModInt の四則演算メソッドを強化 #21

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Merged
suisen-cp merged 3 commits into from
Sep 9, 2020
Merged

#12 ModInt の四則演算メソッドを強化 #21

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fdfb41d
ModInt に即値の四則演算を追加
suisen-cp Sep 9, 2020
2536ad1
ModInt: fix Readme
suisen-cp Sep 9, 2020
5a5807c
ModInt: fix Readme
suisen-cp Sep 9, 2020
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102 changes: 102 additions & 0 deletions ModInt/ModInt.java
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -39,15 +39,55 @@ public int value() {
public ModInt add(ModInt mi) {
return new ModInt(ma.add(value, mi.value));
}
public ModInt add(ModInt mi1, ModInt mi2) {
return new ModInt(ma.add(value, mi1.value)).addAsg(mi2);
}
public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3) {
return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3);
}
public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3).addAsg(mi4);
}
public ModInt add(ModInt mi1, ModInt... mis) {
ModInt mi = add(mi1);
for (ModInt m : mis) mi.addAsg(m);
return mi;
}
public ModInt add(long mi) {
return new ModInt(ma.add(value, ma.remainder(mi)));
}
public ModInt sub(ModInt mi) {
return new ModInt(ma.sub(value, mi.value));
}
public ModInt sub(long mi) {
return new ModInt(ma.sub(value, ma.remainder(mi)));
}
public ModInt mul(ModInt mi) {
return new ModInt(ma.mul(value, mi.value));
}
public ModInt mul(ModInt mi1, ModInt mi2) {
return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2);
}
public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3) {
return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3);
}
public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4);
}
public ModInt mul(ModInt mi1, ModInt... mis) {
ModInt mi = mul(mi1);
for (ModInt m : mis) mi.mulAsg(m);
return mi;
}
public ModInt mul(long mi) {
return new ModInt(ma.mul(value, ma.remainder(mi)));
}
public ModInt div(ModInt mi) {
return new ModInt(ma.div(value, mi.value));
}
public ModInt div(long mi) {
return new ModInt(ma.div(value, ma.remainder(mi)));
}
public ModInt inv() {
return new ModInt(ma.inv(value));
}
Expand All @@ -58,18 +98,60 @@ public ModInt addAsg(ModInt mi) {
this.value = ma.add(value, mi.value);
return this;
}
public ModInt addAsg(ModInt mi1, ModInt mi2) {
return addAsg(mi1).addAsg(mi2);
}
public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3) {
return addAsg(mi1).addAsg(mi2).addAsg(mi3);
}
public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return addAsg(mi1).addAsg(mi2).addAsg(mi3).addAsg(mi4);
}
public ModInt addAsg(ModInt... mis) {
for (ModInt m : mis) addAsg(m);
return this;
}
public ModInt addAsg(long mi) {
this.value = ma.add(value, ma.remainder(mi));
return this;
}
public ModInt subAsg(ModInt mi) {
this.value = ma.sub(value, mi.value);
return this;
}
public ModInt subAsg(long mi) {
this.value = ma.sub(value, ma.remainder(mi));
return this;
}
public ModInt mulAsg(ModInt mi) {
this.value = ma.mul(value, mi.value);
return this;
}
public ModInt mulAsg(ModInt mi1, ModInt mi2) {
return mulAsg(mi1).mulAsg(mi2);
}
public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3) {
return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3);
}
public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4);
}
public ModInt mulAsg(ModInt... mis) {
for (ModInt m : mis) mulAsg(m);
return this;
}
public ModInt mulAsg(long mi) {
this.value = ma.mul(value, ma.remainder(mi));
return this;
}
public ModInt divAsg(ModInt mi) {
this.value = ma.div(value, mi.value);
return this;
}
public ModInt divAsg(long mi) {
this.value = ma.div(value, ma.remainder(mi));
return this;
}
@Override
public String toString() {
return String.valueOf(value());
Expand All @@ -90,6 +172,7 @@ public int hashCode() {

private interface ModArithmetic {
public int mod();
public int remainder(long value);
public int add(int a, int b);
public int sub(int a, int b);
public int mul(int a, int b);
Expand Down Expand Up @@ -119,6 +202,7 @@ public static ModArithmetic of(int mod) {

static final class ModArithmetic1 implements ModArithmetic {
public int mod() {return 1;}
public int remainder(long value) {return 0;}
public int add(int a, int b) {return 0;}
public int sub(int a, int b) {return 0;}
public int mul(int a, int b) {return 0;}
Expand All @@ -127,6 +211,7 @@ static final class ModArithmetic1 implements ModArithmetic {
}
static final class ModArithmetic2 implements ModArithmetic {
public int mod() {return 2;}
public int remainder(long value) {return (int) (value & 1);}
public int add(int a, int b) {return a ^ b;}
public int sub(int a, int b) {return a ^ b;}
public int mul(int a, int b) {return a & b;}
Expand All @@ -144,6 +229,9 @@ static final class ModArithmetic998244353 implements ModArithmetic {
public int mod() {
return mod;
}
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
public int add(int a, int b) {
int res = a + b;
return res >= mod ? res - mod : res;
Expand Down Expand Up @@ -192,6 +280,9 @@ static final class ModArithmetic1000000007 implements ModArithmetic {
public int mod() {
return mod;
}
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
public int add(int a, int b) {
int res = a + b;
return res >= mod ? res - mod : res;
Expand Down Expand Up @@ -267,6 +358,10 @@ private int reduce(long x) {
return (int) (x < mod ? x : x - mod);
}
@Override
public int remainder(long value) {
return generate((value %= mod) < 0 ? value + mod : value);
}
@Override
public int mul(int a, int b) {
return reduce((long) a * b);
}
Expand Down Expand Up @@ -306,6 +401,10 @@ private int reduce(long x) {
return (int) (x < mod ? x : x - mod);
}
@Override
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
@Override
public int mul(int a, int b) {
return reduce((long) a * b);
}
Expand All @@ -318,6 +417,9 @@ public ModArithmeticDynamic(int mod) {
public int mod() {
return mod;
}
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
public int add(int a, int b) {
int sum = a + b;
return sum >= mod ? sum - mod : sum;
Expand Down
118 changes: 105 additions & 13 deletions ModInt/README.md
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -79,47 +79,93 @@ public int mod()
public int value()
```

保持している値を返します．__注意: `ModInt` のフィールド `int value` に直接アクセスはしないで下さい. 正しい値が取得できない可能性があります.__
保持している値を返します．__注意: `ModInt` のフィールド `int value` に直接アクセスしないで下さい. 正しい値が取得できない可能性があります.__

計算量: $O(1)$

#### add

```java
// (1)
public ModInt add(ModInt mi)
// (2)
public ModInt add(ModInt mi1, ModInt mi2)
// (3)
public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3)
// (4)
public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4)
// (5)
public ModInt add(ModInt mi1, ModInt... mis)
// (6)
public ModInt add(long mi)
```

値 `(a + b) % mod` を持つ `ModInt` を新たに生成します (`a` および `b` の値は書き換わりません).
1. 値 `(a + b) % mod` を持つ `ModInt` を新たに生成します.
2. 値 `(a + b + c) % mod` を持つ `ModInt` を新たに生成します.
3. 値 `(a + b + c + d) % mod` を持つ `ModInt` を新たに生成します.
4. 値 `(a + b + c + d + e) % mod` を持つ `ModInt` を新たに生成します.
5. 値 `(a + b + c + d + e + f + ...) % mod` を持つ `ModInt` を新たに生成します.
6. 値 `(a + b) % mod` を持つ `ModInt` を新たに生成します. 定数の加算でこれを用いると便利です.

計算量: $O(1)$
計算量:

- (1)~(4), (6): $O(1)$
- (5): $n$ を可変長引数の長さとして，$O(n)$

#### sub

```java
// (1)
public ModInt sub(ModInt mi)
// (2)
public ModInt sub(long mi)
```

値 `(a - b) % mod` を持つ `ModInt` を新たに生成します (`a` および `b` の値は書き換わりません).
1. 値 `(a - b) % mod` を持つ `ModInt` を新たに生成します.
2. 値 `(a - b) % mod` を持つ `ModInt` を新たに生成します. 定数の減算でこれを用いると便利です.

計算量: $O(1)$

#### mul

```java
// (1)
public ModInt mul(ModInt mi)
// (2)
public ModInt mul(ModInt mi1, ModInt mi2)
// (3)
public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3)
// (4)
public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4)
// (5)
public ModInt mul(ModInt mi1, ModInt... mis)
// (6)
public ModInt mul(long mi)
```

値 `(a * b) % mod` を持つ `ModInt` を新たに生成します (`a` および `b` の値は書き換わりません).
1. 値 `(a * b) % mod` を持つ `ModInt` を新たに生成します.
2. 値 `(a * b * c) % mod` を持つ `ModInt` を新たに生成します.
3. 値 `(a * b * c * d) % mod` を持つ `ModInt` を新たに生成します.
4. 値 `(a * b * c * d * e) % mod` を持つ `ModInt` を新たに生成します.
5. 値 `(a * b * c * d * e * f * ...) % mod` を持つ `ModInt` を新たに生成します.
6. 値 `(a * b) % mod` を持つ `ModInt` を新たに生成します. 定数の乗算でこれを用いると便利です.

計算量: $O(1)$
計算量:

- (1)~(4), (6): $O(1)$
- (5): $n$ を可変長引数の長さとして，$O(n)$

#### div

```java
// (1)
public ModInt div(ModInt mi)
// (2)
public ModInt div(long mi)
```

値 `(a * b^(-1)) % mod` を持つ `ModInt` を新たに生成します (`a` および `b` の値は書き換わりません). ただし，`b^(-1)` は `(b * x) % mod = 1` を満たす `x` です.
1. 値 `(a * b^(-1)) % mod` を持つ `ModInt` を新たに生成します. ただし，`b^(-1)` は `(b * x) % mod = 1` を満たす `x` です.
2. 値 `(a * b^(-1)) % mod` を持つ `ModInt` を新たに生成します. 定数の除算でこれを用いると便利です.

計算量: $O(\log \mod)$

Expand Down Expand Up @@ -154,40 +200,86 @@ public ModInt pow(long n)
#### addAsg

```java
// (1)
public ModInt addAsg(ModInt mi)
// (2)
public ModInt addAsg(ModInt mi1, ModInt mi2)
// (3)
public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3)
// (4)
public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4)
// (5)
public ModInt addAsg(ModInt... mis)
// (6)
public ModInt addAsg(long mi)
```

`a += b` を行います. `a` の値は書き換えられます.
1. `a += b` を行います. `a` の値は書き換えられます.
2. `a += b + c` を行います. `a` の値は書き換えられます.
3. `a += b + c + d` を行います. `a` の値は書き換えられます.
4. `a += b + c + d + e` を行います. `a` の値は書き換えられます.
5. `a += b + c + d + e + f + ...` を行います. `a` の値は書き換えられます.
6. `a += b` を行います. `a` の値は書き換えられます. 定数の加算でこれを用いると便利です.

計算量: $O(1)$
計算量:

- (1)~(4), (6): $O(1)$
- (5): $n$ を可変長引数の長さとして，$O(n)$

#### subAsg

```java
// (1)
public ModInt subAsg(ModInt mi)
// (2)
public ModInt subAsg(long mi)
```

`a -= b` を行います. `a` の値は書き換えられます.
1. `a -= b` を行います. `a` の値は書き換えられます.
2. `a -= b` を行います. `a` の値は書き換えられます. 定数の減算でこれを用いると便利です.

計算量: $O(1)$

#### mulAsg

```java
// (1)
public ModInt mulAsg(ModInt mi)
// (2)
public ModInt mulAsg(ModInt mi1, ModInt mi2)
// (3)
public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3)
// (4)
public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4)
// (5)
public ModInt mulAsg(ModInt... mis)
// (6)
public ModInt mulAsg(long mi)
```

`a *= b` を行います. `a` の値は書き換えられます.
1. `a *= b` を行います. `a` の値は書き換えられます.
2. `a *= b * c` を行います. `a` の値は書き換えられます.
3. `a *= b * c * d` を行います. `a` の値は書き換えられます.
4. `a *= b * c * d * e` を行います. `a` の値は書き換えられます.
5. `a *= b * c * d * e * f * ...` を行います. `a` の値は書き換えられます.
6. `a *= b` を行います. `a` の値は書き換えられます. 定数の乗算でこれを用いると便利です.

計算量: $O(1)$
計算量:

- (1)~(4), (6): $O(1)$
- (5): $n$ を可変長引数の長さとして，$O(n)$

#### divAsg

```java
// (1)
public ModInt divAsg(ModInt mi)
// (2)
public ModInt divAsg(long mi)
```

`a *= b^(-1)` を行います (`a /= b`). `a` の値は書き換えられます. ただし，`b^(-1)` は `(b * x) % mod = 1` を満たす `x` です.
1. `a *= b^(-1)` を行います. `a` の値は書き換えられます. ただし，`b^(-1)` は `(b * x) % mod = 1` を満たす `x` です.
2. `a *= b^(-1)` を行います. `a` の値は書き換えられます. 定数の除算でこれを用いると便利です.

計算量: $O(\log \mod)$

Expand Down