instruction_seed stringlengths 67 28.7k | cot stringlengths 0 81.6k | final_reasoning_trace stringlengths 1.25k 1.15M | response stringlengths 9 1.1M | conversations listlengths 2 2 |
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A boolean circuit in TCS is basically a DAG consisting of And, Or, Not gates, and by what is known is "functional completeness" they can compute all possible functions. eg this is the basic principle in an ALU.
Challenge: create a circuit to determine whether an 8-binary-digit number is divisible by 3 and somehow vis... | Alright, let's tackle this problem. I need to create a boolean circuit that determines if an 8-bit number is divisible by 3. Hmm, functional completeness with AND, OR, NOT gates. Okay, first, I should think about how to compute divisibility by 3 given an 8-bit number.
Divisibility by 3... I remember that for divisibil... | <think> Alright, let's tackle this problem. I need to create a boolean circuit that determines if an 8-bit number is divisible by 3. Hmm, functional completeness with AND, OR, NOT gates. Okay, first, I should think about how to compute divisibility by 3 given an 8-bit number.
Divisibility by 3... I remember that for d... | Creating a boolean circuit to determine if an 8-bit number is divisible by 3 involves a series of state transitions using the modulo properties of binary weights. Here's a structured approach and the resulting circuit visualization:
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### **Algorithm Overview**
The circuit computes \( N \mod 3 \) for an 8-bit binar... | [
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"It's a funny accident that this world happens to have just 1 time dimension, but it doesn't have to(...TRUNCATED) | "Alright, let's try to tackle this 2D Brainfuck puzzle. So the challenge is to create a program with(...TRUNCATED) | "<think> Alright, let's try to tackle this 2D Brainfuck puzzle. So the challenge is to create a prog(...TRUNCATED) | "To solve the given 2D Brainfuck puzzle, we need to design two programs, one for the x dimension and(...TRUNCATED) | [{"from":"human","value":"It's a funny accident that this world happens to have just 1 time dimensio(...TRUNCATED) |
"Today is Mashtali's birthday! He received a Hagh tree from Haj Davood as his birthday present!\n\nA(...TRUNCATED) | "Okay, I need to find the number of unlabeled Hagh trees modulo 998244353 for a given n. Let's start(...TRUNCATED) | "<think> Okay, I need to find the number of unlabeled Hagh trees modulo 998244353 for a given n. Let(...TRUNCATED) | "To solve this problem, we need to count the number of unlabeled Hagh trees for a given \\( n \\), w(...TRUNCATED) | [{"from":"human","value":"Today is Mashtali's birthday! He received a Hagh tree from Haj Davood as h(...TRUNCATED) |
"And while Mishka is enjoying her trip...\n\nChris is a little brown bear. No one knows, where and w(...TRUNCATED) | "Okay, so I've got this problem here about the pedestrian trying to cross the road without getting h(...TRUNCATED) | "<think> Okay, so I've got this problem here about the pedestrian trying to cross the road without g(...TRUNCATED) | "To solve this problem, we need to determine the minimum time required for a pedestrian to cross a r(...TRUNCATED) | [{"from":"human","value":"And while Mishka is enjoying her trip...\n\nChris is a little brown bear. (...TRUNCATED) |
"In FIPS-197 (the Advanced Encryption Standard, known as AES), it is made heavy use of SubBytes, whi(...TRUNCATED) | "Okay, so I need to create a constant-time C function that does exactly what the SubBytes table does(...TRUNCATED) | "<think> Okay, so I need to create a constant-time C function that does exactly what the SubBytes ta(...TRUNCATED) | "Because it's complex to implement the multiplication in a constant-time manner without loops that d(...TRUNCATED) | [{"from":"human","value":"In FIPS-197 (the Advanced Encryption Standard, known as AES), it is made h(...TRUNCATED) |
"ZS the Coder has a large tree. It can be represented as an undirected connected graph of n vertices(...TRUNCATED) | "Okay, so I have this problem where I need to find the number of interesting pairs (u, v) such that (...TRUNCATED) | "<think> Okay, so I have this problem where I need to find the number of interesting pairs (u, v) su(...TRUNCATED) | "To solve this problem, we need to count the number of ordered pairs of vertices (u, v) in a tree su(...TRUNCATED) | [{"from":"human","value":"ZS the Coder has a large tree. It can be represented as an undirected conn(...TRUNCATED) |
"The Little Elephant loves strings very much. \n\nHe has an array a from n strings, consisting of lo(...TRUNCATED) | "Hmm, so I need to solve this problem where for each string in the array, I have to find the number (...TRUNCATED) | "<think> Hmm, so I need to solve this problem where for each string in the array, I have to find the(...TRUNCATED) | "```smol\nConsider the problem where we need to determine, for each string in an array, the number o(...TRUNCATED) | [{"from":"human","value":"The Little Elephant loves strings very much. \n\nHe has an array a from n (...TRUNCATED) |
"GHC command line errors can be horrible, lets make them as bad as possible. To disincentivize very (...TRUNCATED) | "Okay, let's tackle this challenge. The goal is to maximize the score, which is (GHC output bytes) d(...TRUNCATED) | "<think> Okay, let's tackle this challenge. The goal is to maximize the score, which is (GHC output (...TRUNCATED) | "Let me go with the shortest code possible that produces a good error message. Another attempt:\n\n*(...TRUNCATED) | [{"from":"human","value":"GHC command line errors can be horrible, lets make them as bad as possible(...TRUNCATED) |
"Setup\nTake the following 4x4x4 cube along with a 2D view of 3 of its faces, with a common 1x1x1 cu(...TRUNCATED) | "Okay, let's tackle this problem. Hmm, the task is to determine the minimum and maximum number of 1x(...TRUNCATED) | "<think> Okay, let's tackle this problem. Hmm, the task is to determine the minimum and maximum numb(...TRUNCATED) | "To solve this problem, we need to determine the minimum and maximum number of 1x1x1 cubes in a 4x4x(...TRUNCATED) | [{"from":"human","value":"Setup\nTake the following 4x4x4 cube along with a 2D view of 3 of its face(...TRUNCATED) |
"A two dimensional array is called a bracket array if each grid contains one of the two possible bra(...TRUNCATED) | "Okay, let's try to tackle this problem. Hmm, it's about finding the k-th correct bracket array in s(...TRUNCATED) | "<think> Okay, let's try to tackle this problem. Hmm, it's about finding the k-th correct bracket ar(...TRUNCATED) | "To solve this problem, we need to determine the k-th correct two-dimensional bracket array based on(...TRUNCATED) | [{"from":"human","value":"A two dimensional array is called a bracket array if each grid contains on(...TRUNCATED) |
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