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Problema del Cambio de Monedas\n\n## Descripción del Problema\nDado un conjunto **C** de **N** tipos de monedas con un número ilimitado de cada una, el objetivo es determinar el mínimo número de monedas necesarias para formar una cantidad **M**.\n\nPor ejemplo, si un cajero automático tiene billetes de valores: **100$, 25$, 10$, 5$ y 1$**, y se necesita pagar **289$**, la mejor solución consiste en dar **10 billetes**: \n- **2 de 100$**\n- **3 de 25$**\n- **1 de 10$**\n- **4 de 1$**\n\n## Enfoque\n- **Algoritmo voraz (Greedy)**: Si las denominaciones lo permiten, se usa un enfoque voraz para seleccionar la moneda más grande posible primero.\n- **Programación dinámica**: Si el enfoque voraz no es óptimo, se implementa programación dinámica para garantizar el número mínimo de monedas.\n- **Casos límite**: Se consideran situaciones en las que no es posible formar la cantidad **M** exacta.\n\n## Aplicaciones\nEste problema es útil en diversas áreas:\n- **Sistemas financieros y de pago**: Cajeros automáticos, máquinas expendedoras y transacciones en línea.\n- **Algoritmos de optimización**: Asignación eficiente de recursos y problemas de minimización.\n- **Teoría de la computación**: Análisis de eficiencia de algoritmos y complejidad computacional.\n\n- -------------------------------------------------------------------------------------\n\n# Coin Change Problem\n\n## Problem Description\nGiven a set **C** of **N** coin types, with an unlimited supply of each, the goal is to determine the minimum number of coins needed to obtain a total amount **M**. \n\nFor example, if a cash machine has bills of values: **100$, 25$, 10$, 5$, and 1$**, and we need to pay **289$**, the optimal solution is to give **10 bills**: \n- **2 of 100$**\n- **3 of 25$**\n- **1 of 10$**\n- **4 of 1$**\n\n## Approach\n- **Greedy Algorithm**: If the coin denominations allow it, use a greedy approach to take the largest possible coin first.\n- **Dynamic Programming**: If the greedy approach is not optimal, use dynamic programming to ensure the minimal number of coins is selected.\n- **Edge Cases**: Consider cases where it's impossible to make the exact amount **M**.\n\n## Applications\nThis problem is widely used in:\n- **Finance \u0026 Payment Systems**: ATM cash withdrawals, vending machines, and online transactions.\n- **Optimization Algorithms**: Resource allocation and minimization problems.\n- **Theoretical Computer Science**: Algorithm efficiency and computational complexity analysis.\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fanaliaburgosdev%2Fjava_greedy_coin-change","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fanaliaburgosdev%2Fjava_greedy_coin-change","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fanaliaburgosdev%2Fjava_greedy_coin-change/lists"}