From 1d81f1e36adb03e3c7593e0a6d4a53e1d3dc3d61 Mon Sep 17 00:00:00 2001
From: tom4649 <tkaaynakiyoshi@gmail.com>
Date: Tue, 11 Aug 2026 20:31:20 +0900
Subject: [PATCH 1/2] step1,2

---
 0528.Random-Pick-with-Weight/memo.md         | 32 ++++++++++++++++
 0528.Random-Pick-with-Weight/step1_bisect.py | 19 ++++++++++
 0528.Random-Pick-with-Weight/step1_naive.py  | 20 ++++++++++
 0528.Random-Pick-with-Weight/step2_alias.py  | 39 ++++++++++++++++++++
 0528.Random-Pick-with-Weight/step2_bisect.py | 17 +++++++++
 5 files changed, 127 insertions(+)
 create mode 100644 0528.Random-Pick-with-Weight/memo.md
 create mode 100644 0528.Random-Pick-with-Weight/step1_bisect.py
 create mode 100644 0528.Random-Pick-with-Weight/step1_naive.py
 create mode 100644 0528.Random-Pick-with-Weight/step2_alias.py
 create mode 100644 0528.Random-Pick-with-Weight/step2_bisect.py

diff --git a/0528.Random-Pick-with-Weight/memo.md b/0528.Random-Pick-with-Weight/memo.md
new file mode 100644
index 0000000..fbbf93d
--- /dev/null
+++ b/0528.Random-Pick-with-Weight/memo.md
@@ -0,0 +1,32 @@
+# 528. Random Pick with Weight
+
+## step1
+9mぐらいでまず naive を書く。計算量 O(N)。
+
+bisectを使って高速化。計算量 O(log N)
+
+## step2
+いい加減な名前で書いてしまったので改善
+
+乱数の書き方を調べる:
+
+- random.randint: uniformと同じ書き方で書ける。もともと整数なのでこちらの方が良さそう
+- random.choices: `return random.choices(list(range(len(self.prefix_sums))), cum_weights=self.prefix_sums)[0]`
+    - 内部で二分探索が走っている
+    - https://github.com/python/cpython/blob/219768ff531fc0686de623139562ee9f9537df98/Lib/random.py#L460
+- np.random.choice: O(N)だがバッチジョブだと高速化
+
+---
+
+Alias method
+
+https://leetcode.com/problems/random-pick-with-weight/solutions/671439/python-smart-o1-solution-with-detailed-e-r0gx/?envType=problem-list-v2&envId=7p55wqm
+
+https://en.wikipedia.org/wiki/Alias_method
+
+O(N)の前計算を行なっておくことでO(1)で生成できる
+
+乱数を考えると非効率な状況もある（e.g. p= 1/2, 1）
+
+## step3
+TODO: alias法を書く
diff --git a/0528.Random-Pick-with-Weight/step1_bisect.py b/0528.Random-Pick-with-Weight/step1_bisect.py
new file mode 100644
index 0000000..6453be1
--- /dev/null
+++ b/0528.Random-Pick-with-Weight/step1_bisect.py
@@ -0,0 +1,19 @@
+import random
+import itertools
+import bisect
+
+class Solution:
+
+    def __init__(self, w: list[int]):
+        self.cumsum = list(itertools.accumulate(w))
+
+
+    def pickIndex(self) -> int:
+        sampled = random.uniform(0, self.cumsum[-1])
+        return bisect.bisect_left(self.cumsum, sampled)
+
+
+
+# Your Solution object will be instantiated and called as such:
+# obj = Solution(w)
+# param_1 = obj.pickIndex()
diff --git a/0528.Random-Pick-with-Weight/step1_naive.py b/0528.Random-Pick-with-Weight/step1_naive.py
new file mode 100644
index 0000000..7477fa1
--- /dev/null
+++ b/0528.Random-Pick-with-Weight/step1_naive.py
@@ -0,0 +1,20 @@
+import random
+import itertools
+
+class Solution:
+
+    def __init__(self, w: list[int]):
+        self.cumsum = list(itertools.accumulate(w))
+
+
+    def pickIndex(self) -> int:
+        sampled = random.uniform(0, self.cumsum[-1])
+        for i in range(len(self.cumsum)):
+            if sampled <= self.cumsum[i]:
+                return i
+
+
+
+# Your Solution object will be instantiated and called as such:
+# obj = Solution(w)
+# param_1 = obj.pickIndex()
diff --git a/0528.Random-Pick-with-Weight/step2_alias.py b/0528.Random-Pick-with-Weight/step2_alias.py
new file mode 100644
index 0000000..7850c94
--- /dev/null
+++ b/0528.Random-Pick-with-Weight/step2_alias.py
@@ -0,0 +1,39 @@
+import random
+
+class Solution:
+
+    def __init__(self, weights: list[int]):
+        n = len(weights)
+        total = sum(weights)
+        scaled_prob = [w * n / total for w in weights]
+
+        self.prob = [0.0] * n
+        self.alias = [0] * n
+        self.n = n
+
+        small, large = [], []
+        for i, p in enumerate(scaled_prob):
+            if p < 1.0:
+                small.append(i)
+            else:
+                large.append(i)
+
+        while small and large:
+            s = small.pop()
+            l = large.pop()
+            self.prob[s] = scaled_prob[s]
+            self.alias[s] = l
+            scaled_prob[l] -= 1.0 - scaled_prob[s]
+            if scaled_prob[l] < 1.0:
+                small.append(l)
+            else:
+                large.append(l)
+
+        while large:
+            self.prob[large.pop()] = 1.0
+        while small:
+            self.prob[small.pop()] = 1.0
+
+    def pickIndex(self) -> int:
+        i = random.randint(0, self.n - 1)
+        return i if random.random() < self.prob[i] else self.alias[i]
diff --git a/0528.Random-Pick-with-Weight/step2_bisect.py b/0528.Random-Pick-with-Weight/step2_bisect.py
new file mode 100644
index 0000000..ce422e6
--- /dev/null
+++ b/0528.Random-Pick-with-Weight/step2_bisect.py
@@ -0,0 +1,17 @@
+import random
+import itertools
+import bisect
+
+class Solution:
+
+    def __init__(self, weights: list[int]):
+        self.prefix_sums = list(itertools.accumulate(weights))
+
+    def pickIndex(self) -> int:
+        target_weight = random.randint(0, self.prefix_sums[-1])
+        return bisect.bisect_left(self.prefix_sums, target_weight)
+
+
+# Your Solution object will be instantiated and called as such:
+# obj = Solution(w)
+# param_1 = obj.pickIndex()

From d98d45bac15d30e2e3169d217d0cf1bed07e0076 Mon Sep 17 00:00:00 2001
From: tom4649 <tkaaynakiyoshi@gmail.com>
Date: Fri, 14 Aug 2026 19:47:27 +0900
Subject: [PATCH 2/2] step3

---
 0528.Random-Pick-with-Weight/memo.md        |  4 +-
 0528.Random-Pick-with-Weight/step3_alias.py | 42 +++++++++++++++++++++
 2 files changed, 45 insertions(+), 1 deletion(-)
 create mode 100644 0528.Random-Pick-with-Weight/step3_alias.py

diff --git a/0528.Random-Pick-with-Weight/memo.md b/0528.Random-Pick-with-Weight/memo.md
index fbbf93d..04a3710 100644
--- a/0528.Random-Pick-with-Weight/memo.md
+++ b/0528.Random-Pick-with-Weight/memo.md
@@ -29,4 +29,6 @@ O(N)の前計算を行なっておくことでO(1)で生成できる
 乱数を考えると非効率な状況もある（e.g. p= 1/2, 1）
 
 ## step3
-TODO: alias法を書く
+詰まった点：
+- scaled_weights で n 倍するのを忘れる
+- 最後の while 処理を忘れる
diff --git a/0528.Random-Pick-with-Weight/step3_alias.py b/0528.Random-Pick-with-Weight/step3_alias.py
new file mode 100644
index 0000000..c5a4b14
--- /dev/null
+++ b/0528.Random-Pick-with-Weight/step3_alias.py
@@ -0,0 +1,42 @@
+import random
+
+class Solution:
+
+    def __init__(self, weights: list[int]):
+        self.n = len(weights)
+        total = sum(weights)
+        scaled_weights = [w / total * self.n for w in weights]
+
+        self.prob = [0.0] * self.n
+        self.alias = [0] * self.n
+
+        small = []
+        large = []
+        for i, p in enumerate(scaled_weights):
+            if p < 1.0:
+                small.append(i)
+            else:
+                large.append(i)
+
+        while small and large:
+            i_small = small.pop()
+            i_large =large.pop()
+            self.alias[i_small] = i_large
+            self.prob[i_small] =  scaled_weights[i_small]
+            scaled_weights[i_large] -= 1.0 - scaled_weights[i_small]
+            if scaled_weights[i_large] < 1.0:
+                small.append(i_large)
+            else:
+                large.append(i_large)
+
+        while large:
+            i = large.pop()
+            self.prob[i] = 1.0
+        while small:
+            i = small.pop()
+            self.prob[i] = 1.0
+
+
+    def pickIndex(self) -> int:
+        i = random.randint(0, self.n - 1)
+        return i if random.random() < self.prob[i] else self.alias[i]