/ DSA with C++ / Phase 22 Phase 22 Days 123-128
Advanced Data Structures Range-query power tools: Fenwick, segment trees (+ lazy), sparse tables, Mo's
Phase Goal Add the structures that answer range queries and updates in log time, plus when to use each.
Day 123: Sparse table & prefix structures
Prefix / difference recap
Practice, delayed recall, and independent transfer Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique label Spend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisites Use a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timer Before a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassess Record help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adapt Reserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisites Prove progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only
Day 124: Fenwick tree (BIT)
Practice, delayed recall, and independent transfer Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique label Spend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisites Use a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timer Before a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassess Record help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adapt Reserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisites Prove progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only
Day 125: Segment tree — basics
Point update, range query
Practice, delayed recall, and independent transfer Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique label Spend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisites Use a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timer Before a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassess Record help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adapt Reserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisites Prove progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only
Day 126: Segment tree — lazy propagation
Advanced segment trees (intro)
Practice, delayed recall, and independent transfer Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique label Spend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisites Use a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timer Before a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassess Record help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adapt Reserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisites Prove progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only
Day 127: Segment tree applications & Mo's
Practice, delayed recall, and independent transfer Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique label Spend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisites Use a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timer Before a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassess Record help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adapt Reserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisites Prove progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only
Day 128: Advanced DS recap
Practice, delayed recall, and independent transfer Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique label Spend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisites Use a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timer Before a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassess Record help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adapt Reserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisites Prove progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only
After this phase, you'll be able to:
Sparse table & prefix structures Fenwick tree (BIT) Segment tree — basics Segment tree — lazy propagation Segment tree applications & Mo's Advanced DS recap After Phase 22, explain a core invariant, reconstruct a solution after a delay, diagnose a bug, and solve one unlabelled variation. Repair a failed prerequisite before advancing; record help separately from independent work.