【机器学习】机器学习引领数学难题攻克：迈向未知数学领域的新突破

import java.util.ArrayList;
import java.util.List;

public class FourColorTheorem {
    private int numVertices;
    private int[][] adjacencyMatrix;
    private int[] colors;
    private static final int NUM_COLORS = 4;

    public FourColorTheorem(int numVertices) {
        this.numVertices = numVertices;
        adjacencyMatrix = new int[numVertices][numVertices];
        colors = new int[numVertices];
    }

    public void addEdge(int u, int v) {
        adjacencyMatrix[u][v] = 1;
        adjacencyMatrix[v][u] = 1;
    }

    private boolean isSafe(int vertex, int color) {
        for (int i = 0; i < numVertices; i++) {
            if (adjacencyMatrix[vertex][i] == 1 && colors[i] == color) {
                return false;
            }
        }
        return true;
    }

    private boolean graphColoring(int vertex) {
        if (vertex == numVertices) {
            return true;
        }
        for (int color = 1; color <= NUM_COLORS; color++) {
            if (isSafe(vertex, color)) {
                colors[vertex] = color;
                if (graphColoring(vertex + 1)) {
                    return true;
                }
                colors[vertex] = 0;
            }
        }
        return false;
    }

    public void solve() {
        if (graphColoring(0)) {
            System.out.println("The graph can be colored with 4 colors:");
            for (int i = 0; i < numVertices; i++) {
                System.out.println("Vertex " + i + " has color " + colors[i]);
            }
        } else {
            System.out.println("The graph cannot be colored with 4 colors.");
        }
    }

    public static void main(String[] args) {
        FourColorTheorem graph = new FourColorTheorem(5);
        graph.addEdge(0, 1);
        graph.addEdge(0, 2);
        graph.addEdge(1, 2);
        graph.addEdge(1, 3);
        graph.addEdge(2, 3);
        graph.addEdge(3, 4);
        graph.solve();
    }
}

import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;

public class RiemannZetaFunction {
    private static final MathContext MC = new MathContext(100, RoundingMode.HALF_UP);

    public static BigDecimal zetaFunction(double real, double imag) {
        BigDecimal sum = BigDecimal.ZERO;
        for (int n = 1; n <= 10000; n++) {
            BigDecimal base = BigDecimal.valueOf(n);
            BigDecimal exponent = BigDecimal.valueOf(real + imag * 1i);
            BigDecimal term = base.pow(-1).multiply(exponent.exp());
            sum = sum.add(term);
        }
        return sum;
    }

    public static void main(String[] args) {
        double real = 0.5;
        double imag = 14.134725141734693790457251983562470270784257115699348847267;
        BigDecimal result = zetaFunction(real, imag);
        System.out.println("Zeta(" + real + " + " + imag + "i) = " + result);
    }
}