Contest Reality Ladder

What This Ladder Trains: Real contest conditions where you don't know the topic in advance. These 20 problems mix DP, graphs, data structures, strings, math, and greedy -- sorted purely by difficulty. The topic tag is hidden so you must identify the technique yourself. This is the bridge between structured practice and actual competition performance.

Use this as a capstone, not a fourth practice option. It is not a parallel ladder to the topic ladders — it's the test you take after them. Three good moments to come back here:

• After finishing a rating-band ladder, before declaring it "done."
• After plateauing in topic ladders, to confirm the gap is recognition rather than algorithm.
• As the warm-up for a virtual contest block, to re-engage the "I don't know what topic this is" reflex.

Quick Revisit

• SKILL FOCUS: technique identification -- mixed topics with hidden tags, simulating real contests
• DIFFICULTY: 1200--1900
• PROBLEMS: 20
• PREREQUISITE: topic-specific ladders (04--07) or the 1400-1700 ladder
• HEADLINE METRIC: technique identification accuracy before hint or editorial (track this; solves are secondary)

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Contents

• Warm-Up (1200-1400)
• Core (1400-1600)
• Advanced (1600-1900)
• How to Use This Ladder

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Warm-Up (1200-1400)

6 problems across mixed topics. Identify the technique before coding.

#	Problem	Rating	Topic	Hint
1	Cut Ribbon	1300	Topic DP	Hint Coin-change variant: dp[len] = max pieces using the three ribbon sizes.
2	Ice Skating	1200	Topic Graphs / DSU	Hint Points sharing x or y coordinate are connected. Answer = connected components - 1.
3	Delete Two Elements	1200	Topic Data Structures / Map	Hint Compute required pair sum from total. Count matching pairs with a frequency map.
4	Substring Removal	1200	Topic Strings / Combinatorics	Hint Count valid results: prefix of one char + suffix of one char. Handle same-character overlap.
5	Little Girl and Maximum Sum	1500	Topic Greedy / Difference Array	Hint Difference array for query frequency per position, then sort and pair largest values with most-queried positions.
6	Ball in Berland	1400	Topic Combinatorics / Sets	Hint Count total pairs minus conflicting pairs. Two pairs conflict if they share a boy or a girl.

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Core (1400-1600)

8 problems. The difficulty jump is real -- budget 45 minutes each.

#	Problem	Rating	Topic	Hint
7	Vacations	1400	Topic DP	Hint dp[i][last] with last in {rest, gym, contest}. Minimize rest days respecting availability and no-repeat constraint.
8	Kefa and Park	1500	Topic Graphs / DFS	Hint DFS from root tracking consecutive cats. A leaf restaurant is reachable if cat-count never exceeds m.
9	Sleeping Schedule	1500	Topic DP	Hint dp[i][time mod h] = max good wake-ups. Two choices per day: sleep a[i] or a[i]-1 hours.
10	Fox and Two Dots	1500	Topic Graphs / DFS	Hint For each color, check if the subgraph has a cycle using DFS. A cycle exists if you find a visited non-parent neighbor.
11	Good Substrings	1500	Topic Strings / Trie	Hint Insert substrings into a trie, counting bad characters. A node represents a good substring if bad <= k and it's a new node.
12	Two Arrays	1600	Topic DP / Combinatorics	Hint Non-decreasing a[] and non-increasing b[] with a[m] <= b[1]. Equivalent to choosing 2m values with stars-and-bars.
13	Chocolate Bunny	1600	Topic Interactive / Math	Hint Query (i,j) and (j,i). The mod results reveal which position has the smaller value -- place it and continue.
14	Ayoub and Lost Array	1500	Topic DP	Hint dp[i][r] = ways to fill positions 1..i so running sum === r (mod 3). Transition: try each valid value in position i's range.

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Advanced (1600-1900)

6 problems. These require confident technique identification and clean implementation.

#	Problem	Rating	Topic	Hint
15	Graph Without Long Directed Paths	1700	Topic Graphs / Bipartite	Hint Orient edges so no path has length >= 2. Only possible if bipartite -- 2-color and orient each edge from one color to the other.
16	Consecutive Subsequence	1700	Topic DP	Hint LIS variant where consecutive values differ by exactly 1. Use a map: dp[v] = length of longest ending at value v.
17	Kefa and Dishes	1800	Topic DP / Bitmask	Hint Bitmask DP: dp[mask][last] = max satisfaction eating the set of dishes in mask, ending with last.
18	Multiset	1900	Topic Data Structures / BIT	Hint BIT on values. Delete k-th smallest by binary searching the prefix sum. Process all deletions, output the survivor.
19	Password	1700	Topic Strings / Z-function	Hint Z-function gives all prefix matches. Find the longest prefix that is both a suffix (z[i]+i = n) and appears as a middle substring.
20	Dijkstra?	1900	Topic Graphs / Shortest Path	Hint Standard Dijkstra from node 1 to n with path reconstruction. Use long long and handle the n=1 / unreachable cases.

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How to Use This Ladder

1. Don't peek at the topic tags. The whole point is to identify the technique yourself. Only reveal the tag after you've committed to an approach or given up.
2. Simulate contest conditions. Set a timer. Work problems in order within each tier. No editorial access until after the timer.
3. Time-box per tier:

• Warm-Up: 20 min per problem (2 hours total)
• Core: 30 min per problem (4 hours total)
• Advanced: 45 min per problem (4.5 hours total)

4. After each session, review: "How quickly did I identify the technique? What signal told me?" Build your personal pattern-trigger list.
5. Track your identification accuracy. If you consistently mis-identify DP problems as greedy (or vice versa), that's a specific skill to train -- revisit the Problem Pattern Recognition guide.

Scoring Guide

The primary metric is identification accuracy — for each problem, did you name the right technique before peeking at the topic tag or hint? Solve count is secondary; a problem where you correctly identified the technique but ran out of implementation time still counts as a recognition win.

Identification accuracy	Meaning	Next Step
≥ 80% (e.g. 16/20)	Recognition is contest-ready at this range	Verify with solves: if also ≥ 16/20 solved, climb to the 1700→2100 ladder
60-79%	Recognition mostly works but has blind spots	Identify which topic categories you mis-tag and revisit the matching topic ladder (04-07)
40-59%	Pattern triggers are not yet wired	Re-read Problem Pattern Recognition, then redo this ladder
< 40%	Topic ladders haven't yet generalized	Return to topic-specific ladders (04-07) and re-attempt after each

After identification accuracy is solid, look at solve count as the secondary check — it tells you whether implementation under time pressure is keeping up with recognition.

Progression Check

• [ ] Warm-Up: solved >= 5/6, identified technique correctly for all
• [ ] Core: solved >= 6/8, identified technique correctly for >= 5
• [ ] Advanced: attempted all 6, solved >= 3
• [ ] Technique identification accuracy >= 80% (correct guess before coding)
• [ ] Average solve time is within the time-box for each tier

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See also: Problem Pattern Recognition | Rating ladders | Topic ladders