300.longest increasing subsequence

300/memo.md

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+# 300. Longest Increasing Subsequence
+- sol1: 愚直な解法。素直に解くことができた
+    - O(n**2)
+- O(nlogn)の解法を思いつくことはできない
+- https://github.com/mamo3gr/arai60/blob/300_longest-increasing-subsequence/300_longest-increasing-subsequence/memo.md
+    - この方針だけ読んで考えてたが無理
+    - コードを読んでやっと理解
+
+bisectの使い方
+
+https://docs.python.org/3/library/bisect.html
+
+```python
+from bisect import bisect_left, bisect_right
+
+a = [1, 3, 5]
+print(bisect_left(a, 2))  # 1
+print(bisect_left(a, 3))  # 1
+print(bisect_right(a, 3))  # 2
+```
+
+https://docs.google.com/document/d/11HV35ADPo9QxJOpJQ24FcZvtvioli770WWdZZDaLOfg/edit?tab=t.0
+> 日本語で長々と書くと、「lengths[i] とは、仮に nums[i] がシーケンスの最後であると仮定した場合に可能な、最も長いシーケンスの長さ」ですよね。
+- 自分のsol1もlength_of_isなのでこの指摘が当てはまる
+
+https://discord.com/channels/1084280443945353267/1200089668901937312/1209563502407065602
+
+https://github.com/mamo3gr/arai60/blob/300_longest-increasing-subsequence/300_longest-increasing-subsequence/memo.md
+
+- セグ木を使った解法、Binary Indexed Treeを使った解法
+
+https://github.com/mamo3gr/arai60/blob/300_longest-increasing-subsequence/300_longest-increasing-subsequence/memo.md
+- 色々まとめてくれている
+
+- セグメントツリー
+    - https://github.com/naoto-iwase/leetcode/pull/36
+- ほとんど写経で書いてみる
+- 1-indexedにすることで、k%2==1: 右の子、k%2==0:左の子となる
+- 座標圧縮を行う
+- 自分より小さい数字であることを（座標圧縮した）indexで処理し、自分より前の数字であることをnumsの順番のループで処理
+- 自力ではかけない
+
+- BITを使った解法: LLMに書かせたが自分では読んでいない。(sol4)
+    - https://algo-logic.info/binary-indexed-tree/
+    - 和の区間を最初からに限定することで、メモリと計算効率を上昇
+    - bit演算で親や子への移動が可能
+    - index & -index = lowbit[index]
+    - これを足すことで親に移る
+    - 自分では書けない

300/sol1.py

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+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        # Length of increasing subsequence
+        len_is = [1] * len(nums)
+        for i, num in enumerate(nums):
+            for j in range(i):
+                if num > nums[j]:
+                    len_is[i] = max(
+                        len_is[i],
+                        len_is[j] + 1,
+                    )
+
+        return max(len_is)

300/sol2.py

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+from bisect import bisect_left
+
+
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        # tails[i] is the smallest ending element of all increasing subsequences of length (i + 1)
+        tails = []
+        for n in nums:
+            pos_insert_n = bisect_left(tails, n)
+            if pos_insert_n >= len(tails):
+                tails.append(n)
+                continue
+            tails[pos_insert_n] = n
+
+        return len(tails)

300/sol3.py

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+from bisect import bisect_left
+
+
+class SegTree:
+    def __init__(self, size):
+        n = 1
+        while n < size:
+            n *= 2
+        self.offset = n
+        self.data = [0] * 2 * n
+
+    def _to_leaf_index(self, index):
+        return index + self.offset - 1
+
+    def update(self, index, value):
+        k = self._to_leaf_index(index)
+        self.data[k] = max(self.data[k], value)
+        k //= 2
+        while k >= 1:
+            self.data[k] = max(self.data[2 * k], self.data[2 * k + 1])
+            k //= 2
+
+    def query(self, first_index, last_index):
+        if first_index > last_index:
+            return 0
+        l, r = self._to_leaf_index(first_index), self._to_leaf_index(last_index)
+        result = 0
+        while l <= r:
+            if l % 2 == 1:
+                result = max(result, self.data[l])
+                l += 1
+            if r % 2 == 0:
+                result = max(result, self.data[r])
+                r -= 1
+            l //= 2
+            r //= 2
+        return result
+
+
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        nums_sorted = sorted(set(nums))
+
+        def num_to_rank(n):
+            return bisect_left(nums_sorted, n) + 1
+
+        seg_tree = SegTree(len(nums))
+
+        max_len = 0
+        for n in nums:
+            rank = num_to_rank(n)
+            max_len_with_smaller = seg_tree.query(1, rank - 1)
+            seg_tree.update(rank, max_len_with_smaller + 1)
+            max_len = max(max_len, max_len_with_smaller + 1)
+
+        return max_len

300/sol4.py

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+# Generated by LLM
+from bisect import bisect_left
+from typing import List
+
+
+class BITMax:
+    def __init__(self, size: int):
+        self.n = size
+        self.bit = [0] * (size + 1)
+
+    def update(self, index: int, value: int) -> None:
+        while index <= self.n:
+            if value > self.bit[index]:
+                self.bit[index] = value
+            index += index & -index
+
+    def query(self, index: int) -> int:
+        result = 0
+        while index > 0:
+            if self.bit[index] > result:
+                result = self.bit[index]
+            index -= index & -index
+        return result
+
+
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        if not nums:
+            return 0
+
+        coords = sorted(set(nums))
+
+        def to_rank(x: int) -> int:
+            return bisect_left(coords, x) + 1
+
+        bit = BITMax(len(coords))
+        ans = 0
+        for x in nums:
+            r = to_rank(x)
+            best_prev = bit.query(r - 1)
+            cur = best_prev + 1
+            bit.update(r, cur)
+            if cur > ans:
+                ans = cur
+        return ans

bisect_test.py

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+from bisect import bisect_left, bisect_right
+
+a = [1, 3, 5]
+print(bisect_left(a, 2))  # 1
+print(bisect_left(a, 3))  # 1
+print(bisect_right(a, 3))  # 2