拥抱创新：深入探讨 Java 中贪心算法的本质

2023-10-24 11:15:35

贪心算法的魅力在于它的简单和高效，它通过对问题进行分解，将其转化为一系列局部最优解的子问题，然后通过合并这些局部最优解，得到全局最优解。贪心算法的思想核心是，在每个局部最优解的选取上，都尽可能使当前的解决方案整体最优。

贪心算法拥有几个重要的性质，包括：

它总是局部最优的。
它总是渐进逼近的。
它对某些问题是有效的。

贪心算法在许多场景中有着广泛的应用，以下是一些典型的例子：

活动选择问题：在给定的时间范围内，选择最多不相交的活动。
最小生成树：在一个连通的、带权重的无向图中，寻找一个权重最小的生成树。
迪杰斯特拉算法：在给定的加权图中，从一个顶点到其他所有顶点的最短路径。
Prim算法：在给定的加权图中，构造一个最小生成树。

为了进一步巩固您的理解，我们将在 Java 中实现一个经典的贪心算法——活动选择问题。

import java.util.Arrays;
import java.util.Comparator;

public class ActivitySelection {

    // Function to find the maximum number of activities that can be performed
    public static int maxActivities(int[] starts, int[] finishes) {
        // Sort the activities according to their finishing times
        Activity[] activities = new Activity[starts.length];
        for (int i = 0; i < starts.length; i++) {
            activities[i] = new Activity(starts[i], finishes[i]);
        }
        Arrays.sort(activities, Comparator.comparingInt(Activity::getFinish));

        // Initialize the count of activities that can be performed
        int count = 1;

        // Initialize the last activity that was performed
        int lastActivity = activities[0].getFinish();

        // Iterate over the remaining activities
        for (int i = 1; i < activities.length; i++) {
            // If the current activity starts after the last activity finished,
            // then it can be performed
            if (activities[i].getStart() >= lastActivity) {
                count++;
                lastActivity = activities[i].getFinish();
            }
        }

        // Return the count of activities that can be performed
        return count;
    }

    // Activity class to store the start and finish times of an activity
    private static class Activity {
        private int start;
        private int finish;

        public Activity(int start, int finish) {
            this.start = start;
            this.finish = finish;
        }

        public int getStart() {
            return start;
        }

        public int getFinish() {
            return finish;
        }
    }

    public static void main(String[] args) {
        // Sample input data
        int[] starts = {1, 3, 0, 5, 8, 5};
        int[] finishes = {2, 4, 6, 7, 9, 9};

        // Find the maximum number of activities that can be performed
        int maxActivities = maxActivities(starts, finishes);

        // Print the result
        System.out.println("The maximum number of activities that can be performed is: " + maxActivities);
    }
}