Return optional<int> from segment tree binary search methods

[Copilot]

The find_first and find_last methods returned the same value (n and -1 respectively) both when no position satisfied the condition and when boundary conditions were met, creating ambiguity for callers.

Changes

• Modified return type from int to optional<int> for find_first and find_last in:
  • structure/segment-tree/segment-tree.hpp
  • structure/segment-tree/lazy-segment-tree.hpp
• Return nullopt when condition is never satisfied or parameters are out of bounds
• Return integer value when a valid position is found

Usage

auto seg = SegmentTree(monoid, v);

// Before: ambiguous - both return n
auto pos1 = seg.find_first(0, check);  // condition satisfied at n
auto pos2 = seg.find_first(0, check);  // condition never satisfied

// After: unambiguous
auto pos = seg.find_first(0, check);
if (pos.has_value()) {
  // found at pos.value()
} else {
  // not found
}

Original prompt

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This section details on the original issue you should resolve

<issue_title>セグ木の二分探索</issue_title>
<issue_description>find_first
右端が n で条件を満たした場合は n を返す
ところで、条件を満たさなかった場合も n を返しており、n+1 か -1 を返した方がいいかも</issue_description>

Comments on the Issue (you are @copilot in this section)

@ei1333 一周回って optional を返すか

• Fixes セグ木の二分探索 #147

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