answer string | choices dict | id string | kind string | lang string | question string | steps list | subject string | text string | topic string |
|---|---|---|---|---|---|---|---|---|---|
Ring substituents take lowest numbers around the benzene. | null | che_0951 | concept | en | How are substituted benzenes numbered? | [
"First group at carbon 1.",
"Lowest set for rest.",
"Or use ortho/meta/para."
] | chemistry | Answer: Lowest numbers on ring.
Steps:
1. First group at carbon 1.
2. Lowest set for rest.
3. Or use ortho/meta/para. | organic_naming |
The name is chlorobenzene: chlorine on a benzene ring. | null | che_0952 | worked_example | en | Name C6H5Cl. | [
"Benzene ring present.",
"Chlorine substituent.",
"Name: chlorobenzene."
] | chemistry | Answer: Chlorobenzene.
Steps:
1. Benzene ring present.
2. Chlorine substituent.
3. Name: chlorobenzene. | organic_naming |
C2H6 je ethan. | null | che_0953 | worked_example | cs | Pojmenuj sloučeninu C2H6. | [
"Dva uhlíky.",
"Jen jednoduché vazby.",
"Název: ethan."
] | chemistry | Answer: Ethan.
Steps:
1. Dva uhlíky.
2. Jen jednoduché vazby.
3. Název: ethan. | organic_naming |
Para means opposite 1,4 positions on a benzene ring. | {
"A": "1,2 positions",
"B": "1,3 positions",
"C": "1,5 positions",
"D": "1,4 positions"
} | che_0954 | multiple_choice | en | What does para- mean on benzene? | [
"Para means opposite.",
"That is 1,4.",
"Select option D."
] | chemistry | Answer: 1,4 positions.
Steps:
1. Para means opposite.
2. That is 1,4.
3. Select option D.
Answer: (D) | organic_naming |
Ortho is 1,2, meta is 1,3, and para is 1,4 on benzene. | null | che_0955 | concept | en | What do ortho, meta, and para mean? | [
"Ortho: adjacent 1,2.",
"Meta: separated 1,3.",
"Para: opposite 1,4."
] | chemistry | Answer: 1,2, 1,3, and 1,4.
Steps:
1. Ortho: adjacent 1,2.
2. Meta: separated 1,3.
3. Para: opposite 1,4. | organic_naming |
Mechanisms break reactions into elementary steps with intermediates. | null | che_0956 | concept | en | What is a reaction mechanism? | [
"Sequence of steps.",
"Intermediates appear.",
"Sum gives overall reaction."
] | chemistry | Answer: Step-by-step pathway.
Steps:
1. Sequence of steps.
2. Intermediates appear.
3. Sum gives overall reaction. | organic_mechanisms |
The slowest step limits the overall reaction rate. | {
"A": "Slowest step",
"B": "Fastest step",
"C": "First step",
"D": "Last step"
} | che_0957 | multiple_choice | en | What is the rate-determining step? | [
"Bottleneck of pathway.",
"Slowest step rules.",
"Select option A."
] | chemistry | Answer: Slowest step.
Steps:
1. Bottleneck of pathway.
2. Slowest step rules.
3. Select option A.
Answer: (A) | organic_mechanisms |
The SN1 rate triples to 3x because rate equals k[RX]. | null | che_0958 | worked_example | en | SN1 rate = k[RX] with tripled [RX]. What is the new rate? | [
"Write: rate = k x 3[RX].",
"Factor: 3 x k[RX].",
"Rate becomes 3x."
] | chemistry | Answer: 3x.
Steps:
1. Write: rate = k x 3[RX].
2. Factor: 3 x k[RX].
3. Rate becomes 3x. | organic_mechanisms |
Elementární reakce je jeden krok mechanismu bez meziproduktů. | null | che_0959 | concept | cs | Co je elementární reakce? | [
"Jeden krok mechanismu.",
"Přímá přeměna.",
"Součet dá celkovou reakci."
] | chemistry | Answer: Jeden krok mechanismu.
Steps:
1. Jeden krok mechanismu.
2. Přímá přeměna.
3. Součet dá celkovou reakci. | organic_mechanisms |
The product is 2-bromobutane, with Br on carbon 2. | null | che_0960 | worked_example | en | What is the HBr addition product of 2-butene? | [
"Symmetric double bond.",
"H and Br add across.",
"Product: 2-bromobutane."
] | chemistry | Answer: 2-bromobutane.
Steps:
1. Symmetric double bond.
2. H and Br add across.
3. Product: 2-bromobutane. | organic_mechanisms |
Electrophilic addition passes through a carbocation intermediate. | {
"A": "Radical",
"B": "Carbocation",
"C": "Carbanion",
"D": "Epoxide"
} | che_0961 | multiple_choice | en | What intermediate forms in electrophilic addition? | [
"Electrophile adds first.",
"Positive carbon remains.",
"Select option B."
] | chemistry | Answer: Carbocation.
Steps:
1. Electrophile adds first.
2. Positive carbon remains.
3. Select option B.
Answer: (B) | organic_mechanisms |
Radical substitution cycles through initiation, propagation, and termination. | null | che_0962 | concept | en | What are the stages of radical substitution? | [
"Initiation makes radicals.",
"Propagation cycles them.",
"Termination pairs them."
] | chemistry | Answer: Initiation to termination.
Steps:
1. Initiation makes radicals.
2. Propagation cycles them.
3. Termination pairs them. | organic_mechanisms |
Bromination gives bromomethane plus HBr via a radical chain. | null | che_0963 | worked_example | en | What are the products of methane bromination (Br2, light)? | [
"Br radical abstracts H.",
"Methyl radical takes Br.",
"Products: CH3Br + HBr."
] | chemistry | Answer: CH3Br + HBr.
Steps:
1. Br radical abstracts H.
2. Methyl radical takes Br.
3. Products: CH3Br + HBr. | organic_mechanisms |
Spalováním methanu vzniká CO2 a H2O. | null | che_0964 | worked_example | cs | Jaké produkty dá spalování methanu? | [
"Uhlík oxiduje na CO2.",
"Vodík na H2O.",
"Produkty: CO2 a H2O."
] | chemistry | Answer: CO2 a H2O.
Steps:
1. Uhlík oxiduje na CO2.
2. Vodík na H2O.
3. Produkty: CO2 a H2O. | organic_mechanisms |
Complete combustion of hydrocarbons yields carbon dioxide and water. | {
"A": "CO only",
"B": "C plus H2",
"C": "O2",
"D": "CO2 plus H2O"
} | che_0965 | multiple_choice | en | What are complete combustion products? | [
"C burns to CO2.",
"H burns to H2O.",
"Select option D."
] | chemistry | Answer: CO2 plus H2O.
Steps:
1. C burns to CO2.
2. H burns to H2O.
3. Select option D.
Answer: (D) | organic_mechanisms |
Higher temperature lets more molecules clear the activation barrier. | null | che_0966 | concept | en | Why does heating speed reactions? | [
"Molecules move faster.",
"More exceed barrier.",
"Rate rises sharply."
] | chemistry | Answer: More clear the barrier.
Steps:
1. Molecules move faster.
2. More exceed barrier.
3. Rate rises sharply. | organic_mechanisms |
The Haber process compromises: high pressure, moderate heat, iron catalyst. | null | che_0967 | concept | en | What conditions suit the Haber process? | [
"High pressure favors NH3.",
"Moderate heat balances rate.",
"Iron catalyst speeds up."
] | chemistry | Answer: High P, moderate T, iron.
Steps:
1. High pressure favors NH3.
2. Moderate heat balances rate.
3. Iron catalyst speeds up. | equilibrium |
High pressure with moderate temperature balances yield and rate. | {
"A": "High P, moderate T",
"B": "Low P, high T",
"C": "Low P, low T",
"D": "No catalyst"
} | che_0968 | multiple_choice | en | What conditions optimize Haber NH3 yield? | [
"Pressure favors fewer moles.",
"Too hot kills yield.",
"Select option A."
] | chemistry | Answer: High P, moderate T.
Steps:
1. Pressure favors fewer moles.
2. Too hot kills yield.
3. Select option A.
Answer: (A) | equilibrium |
K is 8.0, from 0.50 divided by 0.25 squared. | null | che_0969 | worked_example | en | For 2NO2 <-> N2O4 with [NO2] = 0.25 M and [N2O4] = 0.50 M, compute K. | [
"Write: K = [N2O4]/[NO2]^2.",
"Substitute: 0.50/0.0625.",
"K = 8.0."
] | chemistry | Answer: 8.0.
Steps:
1. Write: K = [N2O4]/[NO2]^2.
2. Substitute: 0.50/0.0625.
3. K = 8.0. | equilibrium |
Haberova-Boschova syntéza vyrábí amoniak z dusíku a vodíku. | null | che_0970 | concept | cs | Co je Haberova-Boschova syntéza? | [
"N2 + 3H2 na NH3.",
"Vysoký tlak.",
"Železný katalyzátor."
] | chemistry | Answer: Výroba amoniaku.
Steps:
1. N2 + 3H2 na NH3.
2. Vysoký tlak.
3. Železný katalyzátor. | equilibrium |
Iron catalyzes the Haber reaction industrially. | {
"A": "Pt",
"B": "Fe",
"C": "Ni",
"D": "Cu"
} | che_0971 | multiple_choice | en | Which catalyst does the Haber process use? | [
"Iron beds employed.",
"Eliminate Pt, Ni, Cu.",
"Select option B."
] | chemistry | Answer: Fe.
Steps:
1. Iron beds employed.
2. Eliminate Pt, Ni, Cu.
3. Select option B.
Answer: (B) | equilibrium |
The system is at equilibrium with no shift. | null | che_0972 | worked_example | en | Q = 3.0 and K = 3.0. Which way does the system shift? | [
"Compare: Q equals K.",
"No excess either side.",
"No shift."
] | chemistry | Answer: No shift.
Steps:
1. Compare: Q equals K.
2. No excess either side.
3. No shift. | equilibrium |
Le Chatelier's principle predicts shifts opposing concentration, pressure, and heat changes. | null | che_0973 | concept | en | What does Le Chatelier's principle summarize? | [
"Stresses disturb balance.",
"System opposes them.",
"New balance results."
] | chemistry | Answer: Opposition to stresses.
Steps:
1. Stresses disturb balance.
2. System opposes them.
3. New balance results. | equilibrium |
Systems relieve stress by shifting against it. | {
"A": "Same shift",
"B": "Stopping",
"C": "Opposing shift",
"D": "Explosion"
} | che_0974 | multiple_choice | en | How do systems answer stress? | [
"Counteract the change.",
"Shift opposes stress.",
"Select option C."
] | chemistry | Answer: Opposing shift.
Steps:
1. Counteract the change.
2. Shift opposes stress.
3. Select option C.
Answer: (C) | equilibrium |
Odebrání reaktantu posune rovnováhu doleva, k reaktantům. | null | che_0975 | worked_example | cs | Kam se posune rovnováha po odebrání reaktantu? | [
"Reaktantů je málo.",
"Soustava je doplní.",
"Posun doleva."
] | chemistry | Answer: Doleva.
Steps:
1. Reaktantů je málo.
2. Soustava je doplní.
3. Posun doleva. | equilibrium |
Bigger volume lowers pressure, shifting toward two product moles. | null | che_0976 | worked_example | en | Volume rises for PCl5 <-> PCl3 + Cl2. Which way is the shift? | [
"Pressure drops.",
"System favors more moles.",
"Shifts right."
] | chemistry | Answer: Shifts right.
Steps:
1. Pressure drops.
2. System favors more moles.
3. Shifts right. | equilibrium |
Low pressure favors the side with more gas moles. | {
"A": "High P",
"B": "Low P",
"C": "High T",
"D": "Catalyst"
} | che_0977 | multiple_choice | en | What favors the more-moles side? | [
"More moles need room.",
"Low pressure gives it.",
"Select option B."
] | chemistry | Answer: Low P.
Steps:
1. More moles need room.
2. Low pressure gives it.
3. Select option B.
Answer: (B) | equilibrium |
Heating an exothermic reaction lowers K as reactants gain favor. | null | che_0978 | concept | en | How does temperature change K for exothermic reactions? | [
"Heat acts as product.",
"Warming shifts left.",
"K shrinks."
] | chemistry | Answer: K falls with temperature.
Steps:
1. Heat acts as product.
2. Warming shifts left.
3. K shrinks. | equilibrium |
Teplota je jediná veličina měnící hodnotu K. | null | che_0979 | concept | cs | Jak teplota ovlivňuje rovnovážnou konstantu? | [
"Jediná mění K.",
"Endotermická: K roste.",
"Exotermická: K klesá."
] | chemistry | Answer: Jediná mění hodnotu K.
Steps:
1. Jediná mění K.
2. Endotermická: K roste.
3. Exotermická: K klesá. | equilibrium |
Warming shifts exothermic equilibrium left, shrinking K. | {
"A": "Heating",
"B": "Cooling",
"C": "Pressure",
"D": "Catalyst"
} | che_0980 | multiple_choice | en | What shrinks K of an exothermic reaction? | [
"Heat is a product.",
"Adding it shifts left.",
"Select option A."
] | chemistry | Answer: Heating.
Steps:
1. Heat is a product.
2. Adding it shifts left.
3. Select option A.
Answer: (A) | equilibrium |
The solubility is 1.12 x 10^-4 M, from (5.6 x 10^-12 / 4)^(1/3). | null | che_0981 | worked_example | en | Mg(OH)2 has Ksp = 5.6 x 10^-12. Compute its molar solubility. | [
"Write: Ksp = 4s^3.",
"s^3 = 5.6 x 10^-12 / 4 = 1.4 x 10^-12.",
"s = 1.12 x 10^-4 M."
] | chemistry | Answer: 1.12 x 10^-4 M.
Steps:
1. Write: Ksp = 4s^3.
2. s^3 = 5.6 x 10^-12 / 4 = 1.4 x 10^-12.
3. s = 1.12 x 10^-4 M. | equilibrium |
PbI2 se nevysráží, protože Q = 1,0 x 10^-10 je pod Ksp = 7,1 x 10^-9. | null | che_0982 | worked_example | cs | [Pb2+] = 1e-4 M a [I-] = 1e-3 M. Vysráží se PbI2 (Ksp = 7,1e-9)? | [
"Q = 1e-4 x (1e-3)^2 = 1e-10.",
"Porovnej: 1e-10 < 7,1e-9.",
"Nevysráží se."
] | chemistry | Answer: Ne, Q < Ksp.
Steps:
1. Q = 1e-4 x (1e-3)^2 = 1e-10.
2. Porovnej: 1e-10 < 7,1e-9.
3. Nevysráží se. | equilibrium |
Below Ksp the solution is unsaturated and holds all ions. | {
"A": "Precipitate",
"B": "Saturated",
"C": "Supersaturated",
"D": "Unsaturated"
} | che_0983 | multiple_choice | en | What does Q < Ksp mean? | [
"Ions below limit.",
"More could dissolve.",
"Select option D."
] | chemistry | Answer: Unsaturated.
Steps:
1. Ions below limit.
2. More could dissolve.
3. Select option D.
Answer: (D) | equilibrium |
Electrolysis plates metals, splits water, and refines aluminum. | null | che_0984 | concept | en | What is electrolysis used for? | [
"Plating coats objects.",
"Splitting makes gases.",
"Refining purifies metals."
] | chemistry | Answer: Plating, splitting, refining.
Steps:
1. Plating coats objects.
2. Splitting makes gases.
3. Refining purifies metals. | electrochemistry |
Aluminum is won by electrolyzing molten cryolite ore. | {
"A": "Electrolysis",
"B": "Smelting",
"C": "Distillation",
"D": "Filtration"
} | che_0985 | multiple_choice | en | How is aluminum extracted? | [
"Too reactive for carbon.",
"Electric current frees it.",
"Select option A."
] | chemistry | Answer: Electrolysis.
Steps:
1. Too reactive for carbon.
2. Electric current frees it.
3. Select option A.
Answer: (A) | electrochemistry |
The cell potential is 1.56 V, from 0.80 - (-0.76). | null | che_0986 | worked_example | en | Compute E cell for Zn/Ag with E(Zn) = -0.76 V and E(Ag) = 0.80 V. | [
"Cathode is Ag at 0.80 V.",
"Anode is Zn at -0.76 V.",
"E = 0.80 - (-0.76) = 1.56 V."
] | chemistry | Answer: 1.56 V.
Steps:
1. Cathode is Ag at 0.80 V.
2. Anode is Zn at -0.76 V.
3. E = 0.80 - (-0.76) = 1.56 V. | electrochemistry |
Elektrolyt je látka vedoucí proud pomocí iontů. | null | che_0987 | concept | cs | Co je elektrolyt? | [
"Roztok nebo tavenina.",
"Ionty nesou náboj.",
"Příklad: NaCl ve vodě."
] | chemistry | Answer: Vodič proudu ionty.
Steps:
1. Roztok nebo tavenina.
2. Ionty nesou náboj.
3. Příklad: NaCl ve vodě. | electrochemistry |
Ions migrating through the electrolyte carry the current. | {
"A": "Electrons",
"B": "Ions",
"C": "Photons",
"D": "Neutrons"
} | che_0988 | multiple_choice | en | How does an electrolyte conduct? | [
"Ions move to electrodes.",
"Charge flows with them.",
"Select option B."
] | chemistry | Answer: Ions.
Steps:
1. Ions move to electrodes.
2. Charge flows with them.
3. Select option B.
Answer: (B) | electrochemistry |
ΔG is -151 kJ, from -1 x 96485 x 1.56 J. | null | che_0989 | worked_example | en | Compute ΔG for n = 1 and E = 1.56 V (F = 96485 C/mol). | [
"Write: ΔG = -1 x 96485 x 1.56.",
"Multiply: -150,517 J.",
"ΔG = -151 kJ."
] | chemistry | Answer: -151 kJ.
Steps:
1. Write: ΔG = -1 x 96485 x 1.56.
2. Multiply: -150,517 J.
3. ΔG = -151 kJ. | electrochemistry |
The potential is 1.53 V, from 1.56 - 0.0296 x log(10). | null | che_0990 | worked_example | en | E° = 1.56 V, n = 2, Q = 10 at 25 C. Compute E. | [
"Write: E = 1.56 - 0.0296 x 1.",
"Subtract: 1.56 - 0.0296.",
"E = 1.53 V."
] | chemistry | Answer: 1.53 V.
Steps:
1. Write: E = 1.56 - 0.0296 x 1.
2. Subtract: 1.56 - 0.0296.
3. E = 1.53 V. | electrochemistry |
More electrons divide the Nernst slope, shrinking the correction. | {
"A": "Bigger",
"B": "Zero",
"C": "Smaller",
"D": "Negative"
} | che_0991 | multiple_choice | en | How does bigger n change the Nernst correction? | [
"Slope is 0.0592/n.",
"Larger n divides more.",
"Select option C."
] | chemistry | Answer: Smaller.
Steps:
1. Slope is 0.0592/n.
2. Larger n divides more.
3. Select option C.
Answer: (C) | electrochemistry |
Electroplating coats objects with metal for protection and shine. | null | che_0992 | concept | en | Why is electroplating done? | [
"Metal layer deposits.",
"Resists corrosion.",
"Looks attractive."
] | chemistry | Answer: Protection and shine.
Steps:
1. Metal layer deposits.
2. Resists corrosion.
3. Looks attractive. | electrochemistry |
Vyloučí se 107,87 g stříbra, protože 1 mol elektronů dá 1 mol Ag. | null | che_0993 | worked_example | cs | Kolik stříbra vyloučí 1 mol elektronů (M = 107,87 g/mol)? | [
"1 e- dá 1 Ag.",
"Moly Ag = 1.",
"Hmotnost = 107,87 g."
] | chemistry | Answer: 107,87 g.
Steps:
1. 1 e- dá 1 Ag.
2. Moly Ag = 1.
3. Hmotnost = 107,87 g. | electrochemistry |
One mole of electrons plates one mole of silver at 107.87 g. | {
"A": "53.94 g",
"B": "215.74 g",
"C": "96.49 g",
"D": "107.87 g"
} | che_0994 | multiple_choice | en | What mass of Ag does 1 mol of electrons plate? | [
"1 e- gives 1 Ag.",
"Mass is 107.87 g.",
"Select option D."
] | chemistry | Answer: 107.87 g.
Steps:
1. 1 e- gives 1 Ag.
2. Mass is 107.87 g.
3. Select option D.
Answer: (D) | electrochemistry |
The time is 13.4 h, from 48,243 C divided by 1.00 A. | null | che_0995 | worked_example | en | How long at 1.00 A to pass 0.500 mol of electrons? | [
"Q = 0.500 x 96485 = 48,243 C.",
"t = 48,243/1.00 = 48,243 s.",
"t = 13.4 h."
] | chemistry | Answer: 13.4 h.
Steps:
1. Q = 0.500 x 96485 = 48,243 C.
2. t = 48,243/1.00 = 48,243 s.
3. t = 13.4 h. | electrochemistry |
One ampere is one coulomb per second. | {
"A": "C/s",
"B": "J/C",
"C": "J/s",
"D": "V/m"
} | che_0996 | multiple_choice | en | What is an ampere? | [
"Current is charge flow.",
"Unit is C/s.",
"Select option A."
] | chemistry | Answer: C/s.
Steps:
1. Current is charge flow.
2. Unit is C/s.
3. Select option A.
Answer: (A) | electrochemistry |
One volt is one joule per coulomb. | {
"A": "C/s",
"B": "J/C",
"C": "Ohm",
"D": "Mol"
} | che_0997 | multiple_choice | en | What is a volt? | [
"Potential is energy per charge.",
"Unit is J/C.",
"Select option B."
] | chemistry | Answer: J/C.
Steps:
1. Potential is energy per charge.
2. Unit is J/C.
3. Select option B.
Answer: (B) | electrochemistry |
Galvanizace je pokovení předmětu zinkem proti korozi. | null | che_0998 | concept | cs | Co je galvanizace? | [
"Zinkový povlak.",
"Chrání ocel.",
"Obětovaná ochrana."
] | chemistry | Answer: Pozinkování proti korozi.
Steps:
1. Zinkový povlak.
2. Chrání ocel.
3. Obětovaná ochrana. | electrochemistry |
Galvanizing coats steel with a protective zinc layer. | {
"A": "Zn",
"B": "Cu",
"C": "Au",
"D": "Fe"
} | che_0999 | multiple_choice | en | Which metal is used for galvanizing? | [
"Zinc sacrifices itself.",
"Coats the steel.",
"Select option A."
] | chemistry | Answer: Zn.
Steps:
1. Zinc sacrifices itself.
2. Coats the steel.
3. Select option A.
Answer: (A) | electrochemistry |
Rust is hydrated iron(III) oxide with formula Fe2O3.xH2O. | {
"A": "FeO",
"B": "Fe3O4",
"C": "Fe2O3.xH2O",
"D": "FeCl3"
} | che_1000 | multiple_choice | en | What is the formula of rust? | [
"Iron(III) oxide base.",
"Water bound in.",
"Select option C."
] | chemistry | Answer: Fe2O3.xH2O.
Steps:
1. Iron(III) oxide base.
2. Water bound in.
3. Select option C.
Answer: (C) | electrochemistry |
Binary search halves a sorted array each step, reaching O(log n) time. | null | cs_0001 | concept | en | How does binary search work? | [
"Require a sorted array.",
"Compare middle to target.",
"Recurse into the matching half."
] | computer_science | Answer: Halve sorted array each step.
Steps:
1. Require a sorted array.
2. Compare middle to target.
3. Recurse into the matching half. | algorithms |
Binary search runs in O(log n) time on sorted data. | {
"A": "O(n)",
"B": "O(log n)",
"C": "O(n log n)",
"D": "O(1)"
} | cs_0002 | multiple_choice | en | What is the time complexity of binary search? | [
"Halving each step.",
"Log steps total.",
"Select option B."
] | computer_science | Answer: O(log n).
Steps:
1. Halving each step.
2. Log steps total.
3. Select option B.
Answer: (B) | algorithms |
Finding 7 takes 4 comparisons: mids 8, 4, 6, then 7. | null | cs_0003 | worked_example | en | Binary search for 7 in [1..15]. How many comparisons? | [
"Mid of 1-15 is 8: go left.",
"Mid of 1-7 is 4: go right.",
"Mid of 5-7 is 6: go right; mid of 7-7 is 7: found in 4."
] | computer_science | Answer: 4 comparisons.
Steps:
1. Mid of 1-15 is 8: go left.
2. Mid of 1-7 is 4: go right.
3. Mid of 5-7 is 6: go right; mid of 7-7 is 7: found in 4. | algorithms |
Binární vyhledávání půlí seřazené pole a běží v čase O(log n). | null | cs_0004 | concept | cs | Co je binární vyhledávání? | [
"Vyžaduje seřazené pole.",
"Porovná střed s cílem.",
"Pokračuje v polovině."
] | computer_science | Answer: Půlení seřazeného pole.
Steps:
1. Vyžaduje seřazené pole.
2. Porovná střed s cílem.
3. Pokračuje v polovině. | algorithms |
Quicksort averages O(n log n) via partitioning around pivots. | {
"A": "O(n)",
"B": "O(log n)",
"C": "O(n log n)",
"D": "O(n^2) average"
} | cs_0005 | multiple_choice | en | What is quicksort's average complexity? | [
"Partition around pivot.",
"Recurse both sides.",
"Select option C."
] | computer_science | Answer: O(n log n).
Steps:
1. Partition around pivot.
2. Recurse both sides.
3. Select option C.
Answer: (C) | algorithms |
Bubble sort needs 2 swaps: [3,1,2] -> [1,3,2] -> [1,2,3]. | null | cs_0006 | worked_example | en | How many swaps bubble-sort [3,1,2]? | [
"Compare 3,1: swap to [1,3,2].",
"Compare 3,2: swap to [1,2,3].",
"Total swaps = 2."
] | computer_science | Answer: 2 swaps.
Steps:
1. Compare 3,1: swap to [1,3,2].
2. Compare 3,2: swap to [1,2,3].
3. Total swaps = 2. | algorithms |
Merge sort splits the array, sorts halves, and merges them in O(n log n). | null | cs_0007 | concept | en | How does merge sort work? | [
"Divide array in half.",
"Sort each half.",
"Merge sorted halves."
] | computer_science | Answer: Divide, sort, merge.
Steps:
1. Divide array in half.
2. Sort each half.
3. Merge sorted halves. | algorithms |
Lineárním vyhledáváním najdeme 5 na 3. porovnání. | null | cs_0008 | worked_example | cs | Kolik porovnání najde 5 v [2,4,5,7] lineárně? | [
"Porovnej 2: ne.",
"Porovnej 4: ne.",
"Porovnej 5: ano, celkem 3."
] | computer_science | Answer: 3 porovnání.
Steps:
1. Porovnej 2: ne.
2. Porovnej 4: ne.
3. Porovnej 5: ano, celkem 3. | algorithms |
Merge sort is stable: equal elements keep their order. | {
"A": "Merge sort",
"B": "Quicksort",
"C": "Heap sort",
"D": "Selection sort"
} | cs_0009 | multiple_choice | en | Which sort is stable? | [
"Stable keeps equal order.",
"Merge sort qualifies.",
"Select option A."
] | computer_science | Answer: Merge sort.
Steps:
1. Stable keeps equal order.
2. Merge sort qualifies.
3. Select option A.
Answer: (A) | algorithms |
Every recursion needs a base case that stops the calls. | null | cs_0010 | concept | en | What is a base case in recursion? | [
"Recursive calls shrink input.",
"Base case returns directly.",
"Without it, stack overflows."
] | computer_science | Answer: Stopping condition.
Steps:
1. Recursive calls shrink input.
2. Base case returns directly.
3. Without it, stack overflows. | algorithms |
factorial(5) = 120, from 5 x 4 x 3 x 2 x 1. | null | cs_0011 | worked_example | en | Compute factorial(5) recursively. | [
"5 x factorial(4).",
"Unwind: 5x4x3x2x1.",
"Result = 120."
] | computer_science | Answer: 120.
Steps:
1. 5 x factorial(4).
2. Unwind: 5x4x3x2x1.
3. Result = 120. | algorithms |
DFS uses a stack to explore deep before wide. | {
"A": "Queue",
"B": "Heap",
"C": "Tree",
"D": "Stack"
} | cs_0012 | multiple_choice | en | Which structure does DFS use? | [
"DFS goes deep first.",
"Stack gives LIFO.",
"Select option D."
] | computer_science | Answer: Stack.
Steps:
1. DFS goes deep first.
2. Stack gives LIFO.
3. Select option D.
Answer: (D) | algorithms |
Rekurze je volání funkce sebe sama s ukončovací podmínkou. | null | cs_0013 | concept | cs | Co je rekurze? | [
"Funkce volá sebe.",
"Vstup se zmenšuje.",
"Báze zastaví volání."
] | computer_science | Answer: Sebevolání s bází.
Steps:
1. Funkce volá sebe.
2. Vstup se zmenšuje.
3. Báze zastaví volání. | algorithms |
BFS expands level by level, so first visit is shortest in unweighted graphs. | {
"A": "Longest path",
"B": "Shortest path",
"C": "Random path",
"D": "No path"
} | cs_0014 | multiple_choice | en | What does BFS find in unweighted graphs? | [
"Levels expand evenly.",
"First hit is nearest.",
"Select option B."
] | computer_science | Answer: Shortest path.
Steps:
1. Levels expand evenly.
2. First hit is nearest.
3. Select option B.
Answer: (B) | algorithms |
Insertion sort gives [2,4,5]: insert 2 first, then 4. | null | cs_0015 | worked_example | en | Insertion-sort [5,2,4]. What are the steps? | [
"Insert 2 before 5: [2,5,4].",
"Insert 4 between: [2,4,5].",
"Sorted in 2 insertions."
] | computer_science | Answer: [2,4,5].
Steps:
1. Insert 2 before 5: [2,5,4].
2. Insert 4 between: [2,4,5].
3. Sorted in 2 insertions. | algorithms |
Big-O bounds growth rate, ignoring constants and small inputs. | null | cs_0016 | concept | en | What is Big-O notation? | [
"Measures growth with n.",
"Keeps dominant term.",
"Example: O(n^2)."
] | computer_science | Answer: Growth-rate bound.
Steps:
1. Measures growth with n.
2. Keeps dominant term.
3. Example: O(n^2). | complexity |
Nested loops over n each give O(n^2) time. | {
"A": "O(n)",
"B": "O(log n)",
"C": "O(n^2)",
"D": "O(1)"
} | cs_0017 | multiple_choice | en | Two nested loops over n give what complexity? | [
"Inner runs n per outer.",
"Total n x n.",
"Select option C."
] | computer_science | Answer: O(n^2).
Steps:
1. Inner runs n per outer.
2. Total n x n.
3. Select option C.
Answer: (C) | complexity |
A double loop with n = 100 runs 10,000 iterations. | null | cs_0018 | worked_example | en | How many iterations for nested loops with n = 100? | [
"Outer runs 100 times.",
"Inner runs 100 each.",
"Total = 100 x 100 = 10,000."
] | computer_science | Answer: 10,000.
Steps:
1. Outer runs 100 times.
2. Inner runs 100 each.
3. Total = 100 x 100 = 10,000. | complexity |
Časová složitost měří růst doby běhu s velikostí vstupu. | null | cs_0019 | concept | cs | Co je časová složitost? | [
"Závislost na n.",
"Zápis O(...).",
"Příklad: O(n log n)."
] | computer_science | Answer: Růst doby s n.
Steps:
1. Závislost na n.
2. Zápis O(...).
3. Příklad: O(n log n). | complexity |
Linear search best case finds the target first: O(1). | {
"A": "O(n)",
"B": "O(log n)",
"C": "O(n^2)",
"D": "O(1)"
} | cs_0020 | multiple_choice | en | What is linear search's best case? | [
"Target at index 0.",
"One comparison.",
"Select option D."
] | computer_science | Answer: O(1).
Steps:
1. Target at index 0.
2. One comparison.
3. Select option D.
Answer: (D) | complexity |
Worst case bounds the slowest input; average case weights typical inputs. | null | cs_0021 | concept | en | How do worst and average case differ? | [
"Worst: slowest input.",
"Average: typical input.",
"Quicksort: O(n^2) vs O(n log n)."
] | computer_science | Answer: Slowest versus typical.
Steps:
1. Worst: slowest input.
2. Average: typical input.
3. Quicksort: O(n^2) vs O(n log n). | complexity |
Binary search on 1024 items needs at most 10 steps, since log2(1024) = 10. | null | cs_0022 | worked_example | en | How many binary search steps for n = 1024? | [
"Steps = log2(n).",
"log2(1024) = 10.",
"At most 10 steps."
] | computer_science | Answer: 10 steps.
Steps:
1. Steps = log2(n).
2. log2(1024) = 10.
3. At most 10 steps. | complexity |
Dvě vnořené smyčky po 50 dají 2500 operací. | null | cs_0023 | worked_example | cs | Kolik operací mají vnořené smyčky n = 50? | [
"Vnější běží 50krát.",
"Vnitřní pokaždé 50krát.",
"Celkem 50 x 50 = 2500."
] | computer_science | Answer: 2500.
Steps:
1. Vnější běží 50krát.
2. Vnitřní pokaždé 50krát.
3. Celkem 50 x 50 = 2500. | complexity |
O(1) means constant time regardless of input size. | {
"A": "Linear time",
"B": "Constant time",
"C": "Log time",
"D": "Quadratic time"
} | cs_0024 | multiple_choice | en | What does O(1) mean? | [
"No growth with n.",
"Fixed cost.",
"Select option B."
] | computer_science | Answer: Constant time.
Steps:
1. No growth with n.
2. Fixed cost.
3. Select option B.
Answer: (B) | complexity |
Space complexity measures extra memory growth with input size. | null | cs_0025 | concept | en | What is space complexity? | [
"Count extra memory.",
"Express in n.",
"Example: merge sort O(n)."
] | computer_science | Answer: Memory growth with n.
Steps:
1. Count extra memory.
2. Express in n.
3. Example: merge sort O(n). | complexity |
Iterative binary search uses O(1) extra space with two indices. | null | cs_0026 | worked_example | en | What extra space does iterative binary search use? | [
"Only lo/hi indices stored.",
"No recursion stack.",
"Extra space = O(1)."
] | computer_science | Answer: O(1).
Steps:
1. Only lo/hi indices stored.
2. No recursion stack.
3. Extra space = O(1). | complexity |
Bad pivots degrade quicksort to O(n^2) worst case. | {
"A": "O(n)",
"B": "O(log n)",
"C": "O(n^2)",
"D": "O(1)"
} | cs_0027 | multiple_choice | en | What is quicksort's worst case? | [
"Pivot splits 1 vs n-1.",
"Depth becomes n.",
"Select option C."
] | computer_science | Answer: O(n^2).
Steps:
1. Pivot splits 1 vs n-1.
2. Depth becomes n.
3. Select option C.
Answer: (C) | complexity |
Amortizovaná složitost průměruje cenu operací v sekvenci. | null | cs_0028 | concept | cs | Co je amortizovaná složitost? | [
"Drahé operace vzácné.",
"Průměr přes sekvenci.",
"Příklad: append O(1)."
] | computer_science | Answer: Průměrná cena v sekvenci.
Steps:
1. Drahé operace vzácné.
2. Průměr přes sekvenci.
3. Příklad: append O(1). | complexity |
The sum 1..100 is 5050, from 100 x 101 / 2. | null | cs_0029 | worked_example | en | Compute the sum 1 + 2 + ... + 100. | [
"Formula: n(n+1)/2.",
"Substitute: 100 x 101/2.",
"Sum = 5050."
] | computer_science | Answer: 5050.
Steps:
1. Formula: n(n+1)/2.
2. Substitute: 100 x 101/2.
3. Sum = 5050. | complexity |
NP problems verify in polynomial time; P also solves in polynomial time. | {
"A": "Verifiable fast",
"B": "Solvable fast",
"C": "Unsolvable",
"D": "Trivial"
} | cs_0030 | multiple_choice | en | What defines class NP? | [
"Solutions check quickly.",
"Finding may be slow.",
"Select option A."
] | computer_science | Answer: Verifiable fast.
Steps:
1. Solutions check quickly.
2. Finding may be slow.
3. Select option A.
Answer: (A) | complexity |
Arrays index in O(1) but insert slowly; linked lists insert fast but index in O(n). | null | cs_0031 | concept | en | How do arrays and linked lists differ? | [
"Array: contiguous, O(1) index.",
"List: nodes, O(n) index.",
"List inserts in O(1) given node."
] | computer_science | Answer: Index speed versus insert speed.
Steps:
1. Array: contiguous, O(1) index.
2. List: nodes, O(n) index.
3. List inserts in O(1) given node. | data_structures |
Array indexing is O(1) via address arithmetic. | {
"A": "O(n)",
"B": "O(1)",
"C": "O(log n)",
"D": "O(n^2)"
} | cs_0032 | multiple_choice | en | What is array index access time? | [
"Base plus offset.",
"Single step.",
"Select option B."
] | computer_science | Answer: O(1).
Steps:
1. Base plus offset.
2. Single step.
3. Select option B.
Answer: (B) | data_structures |
After pushing 1, 2, 3, pop returns 3 (LIFO). | null | cs_0033 | worked_example | en | Push 1, 2, 3 onto a stack. What does pop return? | [
"Stack top is 3.",
"Pop removes top.",
"Returns 3."
] | computer_science | Answer: 3.
Steps:
1. Stack top is 3.
2. Pop removes top.
3. Returns 3. | data_structures |
Zásobník je LIFO struktura s operacemi push a pop. | null | cs_0034 | concept | cs | Co je zásobník (stack)? | [
"Poslední dovnitř, první ven.",
"Operace push a pop.",
"Příklad: zásobník volání."
] | computer_science | Answer: LIFO struktura.
Steps:
1. Poslední dovnitř, první ven.
2. Operace push a pop.
3. Příklad: zásobník volání. | data_structures |
A queue is FIFO: first in, first out. | {
"A": "FIFO",
"B": "LIFO",
"C": "LILO",
"D": "FILO"
} | cs_0035 | multiple_choice | en | What order does a queue use? | [
"Enqueue at back.",
"Dequeue from front.",
"Select option A."
] | computer_science | Answer: FIFO.
Steps:
1. Enqueue at back.
2. Dequeue from front.
3. Select option A.
Answer: (A) | data_structures |
After enqueueing 1, 2, dequeue returns 1 (FIFO). | null | cs_0036 | worked_example | en | Enqueue 1, 2 into a queue. What does dequeue return? | [
"Front holds 1.",
"Dequeue removes front.",
"Returns 1."
] | computer_science | Answer: 1.
Steps:
1. Front holds 1.
2. Dequeue removes front.
3. Returns 1. | data_structures |
Collisions occur when two keys hash to one slot, fixed by chaining or probing. | null | cs_0037 | concept | en | What is a hash collision? | [
"Two keys, one slot.",
"Chain them in a list.",
"Or probe next slots."
] | computer_science | Answer: Two keys, one slot.
Steps:
1. Two keys, one slot.
2. Chain them in a list.
3. Or probe next slots. | data_structures |
Klíč 7 v tabulce velikosti 5 patří na index 2. | null | cs_0038 | worked_example | cs | Kam patří klíč 7 v hash tabulce velikosti 5? | [
"Spočti 7 mod 5.",
"Zbytek je 2.",
"Index = 2."
] | computer_science | Answer: 2.
Steps:
1. Spočti 7 mod 5.
2. Zbytek je 2.
3. Index = 2. | data_structures |
Balanced BST search averages O(log n). | {
"A": "O(n)",
"B": "O(1)",
"C": "O(log n)",
"D": "O(n^2)"
} | cs_0039 | multiple_choice | en | What is average BST search time? | [
"Halve tree each step.",
"Depth is log n.",
"Select option C."
] | computer_science | Answer: O(log n).
Steps:
1. Halve tree each step.
2. Depth is log n.
3. Select option C.
Answer: (C) | data_structures |
Inorder visits left-root-right; preorder root-first; postorder root-last. | null | cs_0040 | concept | en | What are the tree traversal orders? | [
"Inorder: left, root, right.",
"Preorder: root first.",
"Postorder: root last."
] | computer_science | Answer: Inorder, preorder, postorder.
Steps:
1. Inorder: left, root, right.
2. Preorder: root first.
3. Postorder: root last. | data_structures |
Inorder of root 2 with children 1, 3 gives 1, 2, 3. | null | cs_0041 | worked_example | en | Inorder-traverse root 2, left 1, right 3. What order? | [
"Visit left: 1.",
"Visit root: 2.",
"Visit right: 3."
] | computer_science | Answer: 1, 2, 3.
Steps:
1. Visit left: 1.
2. Visit root: 2.
3. Visit right: 3. | data_structures |
A min-heap root always holds the smallest element. | {
"A": "Largest",
"B": "Median",
"C": "Random",
"D": "Smallest"
} | cs_0042 | multiple_choice | en | What does a min-heap root hold? | [
"Heap orders by extremum.",
"Min-heap keeps min top.",
"Select option D."
] | computer_science | Answer: Smallest.
Steps:
1. Heap orders by extremum.
2. Min-heap keeps min top.
3. Select option D.
Answer: (D) | data_structures |
Fronta je datová struktura FIFO s operacemi enqueue a dequeue. | null | cs_0043 | concept | cs | Co je fronta (queue)? | [
"První dovnitř, první ven.",
"Přidávání na konec.",
"Odebírání ze začátku."
] | computer_science | Answer: FIFO struktura.
Steps:
1. První dovnitř, první ven.
2. Přidávání na konec.
3. Odebírání ze začátku. | data_structures |
Head insertion only rewires one pointer: O(1). | {
"A": "O(1)",
"B": "O(n)",
"C": "O(log n)",
"D": "O(n^2)"
} | cs_0044 | multiple_choice | en | What is linked-list head insertion time? | [
"Point new node at head.",
"Update head.",
"Select option A."
] | computer_science | Answer: O(1).
Steps:
1. Point new node at head.
2. Update head.
3. Select option A.
Answer: (A) | data_structures |
The list 3 -> 5 -> 7 -> None has 3 nodes. | null | cs_0045 | worked_example | en | How many nodes in 3 -> 5 -> 7 -> None? | [
"Count 3.",
"Count 5.",
"Count 7: total 3."
] | computer_science | Answer: 3.
Steps:
1. Count 3.
2. Count 5.
3. Count 7: total 3. | data_structures |
Lists are mutable while tuples are immutable in Python. | null | cs_0046 | concept | en | How do Python lists and tuples differ? | [
"Lists allow item changes.",
"Tuples forbid them.",
"Both support indexing."
] | computer_science | Answer: Mutable versus immutable.
Steps:
1. Lists allow item changes.
2. Tuples forbid them.
3. Both support indexing. | python |
Tuples are immutable; lists, dicts, and sets are mutable. | {
"A": "list",
"B": "tuple",
"C": "dict",
"D": "set"
} | cs_0047 | multiple_choice | en | Which Python type is immutable? | [
"Lists mutate.",
"Dicts and sets mutate.",
"Select option B."
] | computer_science | Answer: tuple.
Steps:
1. Lists mutate.
2. Dicts and sets mutate.
3. Select option B.
Answer: (B) | python |
The comprehension yields [0, 2, 4] by doubling 0, 1, 2. | null | cs_0048 | worked_example | en | What does [x*2 for x in range(3)] produce? | [
"range(3) gives 0, 1, 2.",
"Double each: 0, 2, 4.",
"Result [0, 2, 4]."
] | computer_science | Answer: [0, 2, 4].
Steps:
1. range(3) gives 0, 1, 2.
2. Double each: 0, 2, 4.
3. Result [0, 2, 4]. | python |
Seznam je měnitelná posloupnost prvků v hranatých závorkách. | null | cs_0049 | concept | cs | Co je seznam (list) v Pythonu? | [
"Hranaté závorky.",
"Prvky lze měnit.",
"Indexování od 0."
] | computer_science | Answer: Měnitelná posloupnost.
Steps:
1. Hranaté závorky.
2. Prvky lze měnit.
3. Indexování od 0. | python |
len('hello') counts 5 characters. | {
"A": "4",
"B": "6",
"C": "5",
"D": "0"
} | cs_0050 | multiple_choice | en | What is len('hello')? | [
"Count h,e,l,l,o.",
"Total 5.",
"Select option C."
] | computer_science | Answer: 5.
Steps:
1. Count h,e,l,l,o.
2. Total 5.
3. Select option C.
Answer: (C) | python |
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