Add Algorithm to Compute Sum of Squares for Binary Sequence Without Three Consecutive Ones #12059
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| # Initialize population | ||
| self.population = self.initialize_population() | ||
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| def initialize_population(self) -> list[np.ndarray]: |
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As there is no test file in this pull request nor any test function or class in the file genetic_algorithm/genetic_algorithm_optimization.py, please provide doctest for the function initialize_population
| for _ in range(self.population_size) | ||
| ] | ||
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| def fitness(self, individual: np.ndarray) -> float: |
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As there is no test file in this pull request nor any test function or class in the file genetic_algorithm/genetic_algorithm_optimization.py, please provide doctest for the function fitness
| value = float(self.function(*individual)) # Ensure fitness is a float | ||
| return value if self.maximize else -value # If minimizing, invert the fitness | ||
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| def select_parents( |
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As there is no test file in this pull request nor any test function or class in the file genetic_algorithm/genetic_algorithm_optimization.py, please provide doctest for the function select_parents
| ) | ||
| ) | ||
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| def evolve(self, verbose=True) -> np.ndarray: |
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As there is no test file in this pull request nor any test function or class in the file genetic_algorithm/genetic_algorithm_optimization.py, please provide doctest for the function evolve
Please provide type hint for the parameter: verbose
| MOD = 10**9 + 7 | ||
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| def matrix_mult(a, b, mod=MOD): |
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As there is no test file in this pull request nor any test function or class in the file project_euler/problem_912/sol1.py, please provide doctest for the function matrix_mult
Please provide return type hint for the function: matrix_mult. If the function does not return a value, please provide the type hint as: def function() -> None:
Please provide descriptive name for the parameter: a
Please provide type hint for the parameter: a
Please provide descriptive name for the parameter: b
Please provide type hint for the parameter: b
Please provide type hint for the parameter: mod
| ] | ||
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| def matrix_pow(mat, exp, mod=MOD): |
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As there is no test file in this pull request nor any test function or class in the file project_euler/problem_912/sol1.py, please provide doctest for the function matrix_pow
Please provide return type hint for the function: matrix_pow. If the function does not return a value, please provide the type hint as: def function() -> None:
Please provide type hint for the parameter: mat
Please provide type hint for the parameter: exp
Please provide type hint for the parameter: mod
| return res | ||
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| def fib_like_sequence(n, mod=MOD): |
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As there is no test file in this pull request nor any test function or class in the file project_euler/problem_912/sol1.py, please provide doctest for the function fib_like_sequence
Please provide return type hint for the function: fib_like_sequence. If the function does not return a value, please provide the type hint as: def function() -> None:
Please provide descriptive name for the parameter: n
Please provide type hint for the parameter: n
Please provide type hint for the parameter: mod
| return result[0][0] # This gives the n-th Fibonacci-like term | ||
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| def calculate_sum_of_squares(limit): |
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As there is no test file in this pull request nor any test function or class in the file project_euler/problem_912/sol1.py, please provide doctest for the function calculate_sum_of_squares
Please provide return type hint for the function: calculate_sum_of_squares. If the function does not return a value, please provide the type hint as: def function() -> None:
Please provide type hint for the parameter: limit
| return total_sum | ||
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| def solution(limit=10**16): |
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As there is no test file in this pull request nor any test function or class in the file project_euler/problem_912/sol1.py, please provide doctest for the function solution
Please provide return type hint for the function: solution. If the function does not return a value, please provide the type hint as: def function() -> None:
Please provide type hint for the parameter: limit
Describe your change:
This PR introduces a new algorithm that calculates the sum of squares for indices where the corresponding integer (in the sequence of positive integers without three consecutive ones in their binary representation) is odd. The algorithm uses dynamic programming with matrix exponentiation for efficient computation, particularly for large inputs like ( N = 10^{16} ), and includes modular arithmetic to return the result modulo ( 10^9 + 7 ).
Checklist: