2022 USP Try-outs

13 problems from 2022 USP Try-outs (contest 103934), difficulty -. 13/13 solutions verified against sample I/O.

13 items

2022 USP Try-outs

Special | 13 problems | 13/13 verified | Difficulty - | 13m 36s

#	Problem	Rating	Tags	Accepted	Time	✓
A	The army of Thutmose III				55s	✓
B	Tuk-Tuk Express				1m 3s	✓
C	Book of the Dead's spells				3m 27s	✓
D	Inflation				1m 1s	✓
E	Fig trees of Hatshepsut				1m	✓
F	Indiana Jiang and the sphinx riddle				43s	✓
G	Mmoohhaammeedd				42s	✓
H	Tomb of Tutankhamun				52s	✓
I	Offering to god Ra				40s	✓
J	Apep, the Lord of Chaos				50s	✓
K	Railways				48s	✓
L	Cris's vacations in Cairo				49s	✓
M	Egyptian municipal elections				46s	✓

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CF 103934M - Egyptian municipal elections

We are given a graph of post offices connected by bidirectional routes. A message starts at some office, travels along a simple path to another office, and at every intermediate office the message’s “mark” is flipped.

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CF 103934L - Cris's vacations in Cairo

We are given a sequence of n days. On each day i there are two exchange rates: one for dollars and one for Brazilian reals, both measured in Egyptian pounds.

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CF 103934K - Railways

We are given a straight railway line where every point can be treated as an integer coordinate on a number line. Each resident has a home position and a work position on this line, and they start walking toward work at time zero with speed 1 unit per second.

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CF 103934J - Apep, the Lord of Chaos

We are given an undirected weighted graph representing cities connected by roads. Initially, the graph is connected. Each road has a strength value. A road is considered “critical” if removing it disconnects the graph. In graph terms, this is exactly a bridge.

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CF 103934I - Offering to god Ra

We are building a number of grams of food that Thiago will offer. Each valid offering must be composed of baskets of fixed size A, so the total amount must be a multiple of A.

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CF 103934H - Tomb of Tutankhamun

We are given two sets of entities: historians and paintings. Each historian can be assigned to at most one painting, and each painting can be assigned to at most one historian, so any valid solution is a matching in a bipartite graph.

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CF 103934C - Book of the Dead's spells

We are given a collection of words, each paired with a positive value. A valid “spell” is a sequence of words where every next word must extend the previous one by exactly one or more characters, meaning the previous word is a proper prefix of the next.

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CF 103934G - Mmoohhaammeedd

We are given several independent strings, each representing a name made of lowercase English letters. The transformation rule defines how a new version of the string is constructed: every character is inspected together with its immediate neighbors, and the character is…

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CF 103934F - Indiana Jiang and the sphinx riddle

We start with a row of spheres labeled from 1 to N in increasing order. Two agents repeatedly shrink this row by removing every second remaining element, but they sweep in opposite directions.

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CF 103934D - Inflation

We are given a collection of $n$ distinct primes $a1, a2, dots, an$. From these primes we form a single huge product $P = prod ai$. Each item in the store is defined in an unusual way: the price of item $i$ is the product of all primes except $ai$.

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CF 103934E - Fig trees of Hatshepsut

We are maintaining a sequence of numbers arranged in a line, where each position represents a fig tree and the value at that position is the number of figs on that tree.

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CF 103934B - Tuk-Tuk Express

There are three independent taxi services, each running an infinite sequence of shared tuk-tuks between a city center and a hotel. Each service has its own travel time and capacity.

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CF 103934A - The army of Thutmose III

We are given a collection of time intervals, each representing the construction period of a building. A chosen day corresponds to sending the army to inspect all buildings that are under construction on that day.