素数和，方阵最大乘积

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该博客探讨了如何求解两百万内的素数之和，并研究了一个20x20方阵中，四个相邻数的最大乘积问题。文中提到了两种方法，包括使用一维和二维数组来解决这个问题。

求两百万内的素数之和

public class SumOfPrime {
    public static void main(String[] args) {
        System.out.println(SumPrime(2000000));
    }

    public static long SumPrime(long num) {
        long sum = 2;
        for (int i=3;i <= 2000000;i+=2) {
            if(isPrime(i))
                sum += i;
        }
        return sum;
    }

    //判断是否为素数
    public static boolean isPrime(long x) {
        final int max = (int) Math.sqrt(x);
        for (int i=3;i <= max;i+=2) {
            if (x % i ==0)
                return false;
        }
        return true;
    }
}

方阵最大乘积
在如下的20×20方阵中，有四个呈对角线排列的数被标红了。

在这里插入图片描述

这四个数的乘积是26 × 63 × 78 × 14 = 1788696。

在这个20×20方阵中，四个在同一方向（从下至上、从上至下、从右至左、从左至右或者对角线）上相邻的数的乘积最大是多少？

使用一维数组

public class MaxMatrixProduct {
    public static void main(String[] args) {
        System.out.println(MaxProduct(4));
    }

    public static long MaxProduct(int x) {
        int a[]  = {8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8,
                49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0,
                81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65,
                52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91,
                22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80,
                24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50,
                32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70,
                67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21,
                24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72,
                21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95,
                78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92,
                16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57,
                86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58,
                19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40,
                4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66,
                88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69,
                4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36,
                20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16,
                20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54,
                1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48};
        int sum = 0;
        for (int i = 0;i < 20;i++) {
            for (int j = 0;j < 20;j++) {
                int current = 20 * i + j;
                int right = 1;
                int down = 1;
                int leftUp = 1;
                int rightUp = 1;
                if (current + (x - 1) < 20 * (i + 1)) {
                    for (int k = 0;k < x;k++) {
                        right *= a[current + k];                      //从左到右
                    }
                    if (right > sum)
                        sum = right;
                }

                if (current +(x -1)*20<20*20) {
                    for (int k = 0;k < x;k++) {
                        down *= a[current + k *20];                    //从上到下
                    }
                    if (down > sum)
                        sum = down;
                }

                if (current - (x -1)*20 -(x -1) >= 0) {
                    for (int k=0;k<x;k++) {
                        leftUp *= a[current - k*20 -k];               //右下到左上
                    }
                    if (leftUp > sum)
                        sum = leftUp;
                }

                if (current - (x -1)*20 + (x-1)>= 0) {
                    for (int k=0;k<x;k++) {
                        rightUp *= a[current - k * 20 +k];           //坐下到右上
                    }
                    if (rightUp > sum)
                        sum = rightUp;
                }
            }
        }
        return sum;
    }
}

使用二维数组

public class MaxMatrixProduct {
    public static void main(String[] args) {
        System.out.println(MaxProduct(4));
    }

    public static long MaxProduct(int x) {
        int[][] aa = {{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
                {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0},
                {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
                {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
                {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
                {24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
                {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
                {67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
                {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
                {21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
                {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
                {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
                {86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
                {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
                {4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
                {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
                {4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
                {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
                {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
                {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}};
        int sum = 0;
        for (int i=0;i < 20;i++) {
            for (int j=0;j < 20;j++) {
                int right = 1;
                int down = 1;
                int rightDown = 1;
                int leftDown = 1;
                for (int k = 0;k < x;k++) {
                    right *= aa[j+k][i];            //从上到下
                    if (j > 16)
                        break;
                    if (right > sum)
                        sum = right;
                }

                for (int k =0;k < x;k++) {
                    down *= aa[i][j+k];             //从左到右
                    if (j > 16)
                        break;
                    if (down > sum)
                        sum = down;
                }

                int m = i;
                int n = j;
                for (int k = 0;k < x;k++) {
                    if (m>16 || n>16)
                        break;
                    rightDown *= aa[m+k][n+k];          //左上到右下
                    if (rightDown > sum)
                        sum = rightDown;
                }

                for (int k = 0;k < x;k++) {
                    if (m+n <3 || m>16 || n<3)
                        break;
                    leftDown *= aa[m+k][n-k];            //右上到坐下
                    if (leftDown > sum)
                        sum = leftDown;
                }
            }
        }
        return sum;
    }

}