https://github.com/analiaburgosdev/java_backtracking_magic-board
The objective of this exercise is to develop an algorithm to place n*n distinct natural numbers, ranging from 1 to a value k (where k > n*n), on an n x n board. The constraint is that the sum of the numbers in each row and each column must be equal to a specific value S.
https://github.com/analiaburgosdev/java_backtracking_magic-board
backtracking-algorithm board java
Last synced: 3 months ago
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The objective of this exercise is to develop an algorithm to place n*n distinct natural numbers, ranging from 1 to a value k (where k > n*n), on an n x n board. The constraint is that the sum of the numbers in each row and each column must be equal to a specific value S.
- Host: GitHub
- URL: https://github.com/analiaburgosdev/java_backtracking_magic-board
- Owner: analiaBurgosDev
- Created: 2025-03-26T21:09:41.000Z (7 months ago)
- Default Branch: main
- Last Pushed: 2025-03-26T21:12:07.000Z (7 months ago)
- Last Synced: 2025-06-11T23:41:36.301Z (4 months ago)
- Topics: backtracking-algorithm, board, java
- Language: Java
- Homepage:
- Size: 3.91 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
## Descripción del Problema
El objetivo de este ejercicio es desarrollar un algoritmo para ubicar n*n números naturales distintos, entre 1 y un valor k (donde k > n*n), en un tablero de tamaño n x n. La restricción es que la suma de los números en cada fila y cada columna debe ser igual a un valor específico S.
## Enfoque
- **Búsqueda Combinatoria**: El algoritmo explora posibles distribuciones de números utilizando técnicas de backtracking y satisfacción de restricciones.
- **Equilibrio en la Matriz**: La solución garantiza que las sumas de filas y columnas se mantengan mientras se ubican los números únicos en la cuadrícula.
## Aplicaciones
Este ejercicio es útil en problemas de asignación de recursos en cuadrículas, diseño de juegos estratégicos y optimización combinatoria en planificación y programación de sistemas.
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## Problem Description
The objective of this exercise is to develop an algorithm to place n*n distinct natural numbers, ranging from 1 to a value k (where k > n*n), on an n x n board. The constraint is that the sum of the numbers in each row and each column must be equal to a specific value S.
## Approach
- **Combinatorial Search**: The algorithm explores possible distributions of numbers using backtracking and constraint satisfaction techniques.
- **Matrix Balancing**: The solution ensures that row and column sums are maintained while placing unique numbers in the grid.
## Applications
This exercise is relevant in problems involving grid-based resource allocation, strategic game design, and combinatorial optimization in scheduling and planning systems.