Hi :)
These are some LCA (lowest common ancestor) problems. I hope you enjoy them.
I tried to sort them by difficulty. If you know more problems, add it to comments.

208E - Blood Cousins
191C - Fools and Roads
519E - A and B and Lecture Rooms
587C - Duff in the Army
609E - Minimum spanning tree for each edge
178B3 - Greedy Merchants
176E - Archaeology
466E - Information Graph

Hi :)
Some problem about powerful data structure and algorithm SQRT decomposition.
If you want to learn this algorithm click here.
And a big thank to mr_agha_seyed for helping.



220B - Little Elephant and Array
86D - Powerful array
13E - Holes
455D - Serega and Fun
375D - Tree and Queries
446C - DZY Loves Fibonacci Numbers
487D - Conveyor Belts
506D - Mr. Kitayuta's Colorful Graph
348C - Subset Sums
617E - XOR and Favorite Number
444C - DZY Loves Colors
398D - Instant Messanger
342E - Xenia and Tree

Maybe some of them can solve by other data structures like segment tree.

Hi :)
These are some segment tree problems on codeforces. Ofcourse it is not complete and I hope we will complete it with your help. And great thank to NikaraBika for helping me.

UPD : more Segment Tree

Classic :
339D - Xenia and Bit Operations
356A - Knight Tournament
459D - Pashmak and Parmida's problem
61E - Enemy is weak
380C - Sereja and Brackets
474F - Ant colony
292E - Copying Data
501D - Misha and Permutations Summation
220E - Little Elephant and Inversions
338E - Optimize!
19D - Points
351D - Jeff and Removing Periods
515E - Drazil and Park
540E - Infinite Inversions
609F - Frogs and mosquitoes
594D - REQ
455E - Function

Lazy Propagating:
52C - Circular RMQ
145E - Lucky Queries
558E - A Simple Task
240F - TorCoder
446C - DZY Loves Fibonacci Numbers
115E - Linear Kingdom Races
438D - The Child and Sequence
121E - Lucky Array
610E - Alphabet Permutations
580E - Kefa and Watch

Segment tree with Vector:
369E - Valera and Queries
610D - Vika and Segments

Offline Query:
301D - Yaroslav and Divisors
500E - New Year Domino

Segment Tree & Dp:
474E - Pillars
597C - Subsequences
56E - Domino Principle

Segment Tree & Bits:
482B - Interesting Array
242E - XOR on Segment

Segment Tree & Tree:
383C - Propagating tree
343D - Water Tree
173E - Camping Groups
276E - Little Girl and Problem on Trees
396C - On Changing Tree
516D - Drazil and Morning Exercise
375D - Tree and Queries

titles are not tag :))

I need help to solve this problem :))

186E - Clever Fat Rat