From 31be8230f3e2b899a1cd959796c5b4644294d97f Mon Sep 17 00:00:00 2001
From: myoshizumi <myoshizumi@alumni.berklee.edu>
Date: Sat, 28 Jun 2025 12:15:09 +0900
Subject: [PATCH] =?UTF-8?q?=E7=B9=B0=E3=82=8A=E8=BF=94=E3=81=97=E4=BA=8C?=
 =?UTF-8?q?=E4=B9=97=E6=B3=95=EF=BC=88Exponentiation=20by=20Squaring?=
 =?UTF-8?q?=EF=BC=89?=
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---
 .../ExponentiationBySquaring.js               | 22 ++++++
 .../ExponentiationBySquaring.py               | 13 ++++
 .../Exponentiation by Squaring/README.md      | 78 +++++++++++++++++++
 3 files changed, 113 insertions(+)
 create mode 100644 Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.js
 create mode 100644 Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.py
 create mode 100644 Mathematics/Exponentiation by Squaring/README.md

diff --git a/Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.js b/Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.js
new file mode 100644
index 00000000..cd435a59
--- /dev/null
+++ b/Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.js	
@@ -0,0 +1,22 @@
+const fs = require('fs');
+
+// 入力読み取り
+const input = fs.readFileSync('/dev/stdin', 'utf8').trim();
+const [A, B, M] = input.split(' ').map(Number);
+
+// 繰り返し二乗法
+function modPow(a, b, m) {
+    let result = 1;
+    a = a % m;
+    while (b > 0) {
+        if (b & 1) {
+            result = (result * a) % m;
+        }
+        a = (a * a) % m;
+        b >>= 1;
+    }
+    return result;
+}
+
+// 出力
+console.log(modPow(A, B, M));
diff --git a/Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.py b/Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.py
new file mode 100644
index 00000000..8a1d7580
--- /dev/null
+++ b/Mathematics/Exponentiation by Squaring/ExponentiationBySquaring.py	
@@ -0,0 +1,13 @@
+def modpow(a: int, b: int, m: int) -> int:
+    ans = 1
+    while 0 < b:
+        if b & 1 == 1:
+            ans = (ans * a) % m
+        a = (a * a) % m
+        b >>= 1
+    return ans
+a: int
+b: int
+m: int
+a, b, m = map(int, input().split())
+print(modpow(a, b, m))
\ No newline at end of file
diff --git a/Mathematics/Exponentiation by Squaring/README.md b/Mathematics/Exponentiation by Squaring/README.md
new file mode 100644
index 00000000..1e5b708b
--- /dev/null
+++ b/Mathematics/Exponentiation by Squaring/README.md	
@@ -0,0 +1,78 @@
+繰り返し二乗法（Exponentiation by Squaring）を用いて `A^B mod M` を高速に計算する JavaScript のコードです。標準入力に対応しています（`fs` モジュールを使用）。
+
+---
+
+### ✅ JavaScript 解答コード（繰り返し二乗法 + 標準入力対応）
+
+```javascript
+const fs = require('fs');
+
+// 入力読み取り
+const input = fs.readFileSync('/dev/stdin', 'utf8').trim();
+const [A, B, M] = input.split(' ').map(Number);
+
+// 繰り返し二乗法
+function modPow(a, b, m) {
+  let result = 1;
+  a = a % m;
+  while (b > 0) {
+    if (b & 1) {
+      result = (result * a) % m;
+    }
+    a = (a * a) % m;
+    b >>= 1;
+  }
+  return result;
+}
+
+// 出力
+console.log(modPow(A, B, M));
+```
+
+---
+
+### 🔍 処理の流れ（`2^13 mod M` の例をもとに）
+
+```
+初期状態:
+a = 2, b = 13 → b(2進数) = 1101, m = 7, result = 1
+
+1回目: b & 1 = 1 → result = result * a = 1 * 2 = 2
+        a = a * a = 4, b = 6 (110)
+
+2回目: b & 1 = 0 → result unchanged
+        a = 16, b = 3 (11)
+
+3回目: b & 1 = 1 → result = 2 * 16 = 32
+        a = 256, b = 1
+
+4回目: b & 1 = 1 → result = 32 * 256
+        a = 65536, b = 0
+
+最後に result % 7 = 4 を返す
+```
+
+---
+
+### ✅ 実行例
+
+#### 入力:
+
+```
+2 5 7
+```
+
+#### 出力:
+
+```
+4
+```
+
+---
+
+### ⏱ 計算量
+
+* 時間計算量: `O(log B)` （Bの2進数のビット長に比例）
+* 空間計算量: `O(1)`
+
+---