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我对 Project Euler的问题 11有一些问题。我设法得到一个答案，但它不是正确的。我得到51267216。这是通过greatestVert方法找到的。我认为问题出在greatestDiaglonal方法上，但我不太确定。有人可以检查我的算法是否正确吗？

任务是找出任何方向（上、下、左、右或对角线）上四个相邻数字的最大乘积在 20x20 网格中。

package euler;

public class Problem11 {

int num1, num2, num3, num4;
int highestNum1, highestNum2, highestNum3, highestNum4;

private int sum = 0;

String[] l = {
"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08",
"49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00",
"81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65",
"52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21",
"24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72",
"21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95",
"78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92",
"16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57",
"86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58",
"19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40",
"04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66",
"88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69",
"04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36",
"20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16",
"20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54",
"01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"
};

int greatestSide() {
    for(int i = 0;i<=19;i++) {
        for(int n = 0;n<=l[i].length()-12;n+=3) {
            num1 = Integer.parseInt(l[i].substring(0+n,3+n).trim());
            num2 = Integer.parseInt(l[i].substring(3+n,6+n).trim());
            num3 = Integer.parseInt(l[i].substring(6+n,9+n).trim());
            num4 = Integer.parseInt(l[i].substring(9+n,12+n).trim());

            if(num1*num2*num3*num4 > sum) {
                sum = num1*num2*num3*num4;
                highestNum1 = num1;
                highestNum2 = num2;
                highestNum3 = num3;
                highestNum4 = num4;
            }   
        }
    }
    return sum;
}

int greatestVert() {
    for(int i = 0; i<=16; i++) {
        for(int n = 0; n<=l[i].length()-3; n+=3) {
            num1 = Integer.parseInt(l[i].substring(0+n,3+n).trim());
            num2 = Integer.parseInt(l[i+1].substring(0+n,3+n).trim());
            num3 = Integer.parseInt(l[i+2].substring(0+n,3+n).trim());
            num4 = Integer.parseInt(l[i+3].substring(0+n,3+n).trim());

            if(num1*num2*num3*num4 > sum) {
                sum = num1*num2*num3*num4;
                highestNum1 = num1;
                highestNum2 = num2;
                highestNum3 = num3;
                highestNum4 = num4;
            }   
        }
    }
    return sum;
}

int greatestDiagonal() {
    for(int i = 19; i>=3; i--) {
        for(int n = 0; n<=l[i].length()-12; n+=3) {
            num4 = Integer.parseInt(l[i].substring(9+n,12+n).trim());
            num3 = Integer.parseInt(l[i-1].substring(6+n,9+n).trim());
            num2 = Integer.parseInt(l[i-2].substring(3+n,6+n).trim());
            num1 = Integer.parseInt(l[i-3].substring(0+n,3+n).trim());

            if(num1*num2*num3*num4 > sum) {
                sum = num1*num2*num3*num4;
                highestNum1 = num1;
                highestNum2 = num2;
                highestNum3 = num3;
                highestNum4 = num4;
            }   
        }
    }

    for(int i = 0; i>=16; i++) {
        for(int n = 0; n<=l[i].length()-12; n+=3) {
            num4 = Integer.parseInt(l[i].substring(9+n,12+n).trim());
            num3 = Integer.parseInt(l[i+1].substring(6+n,9+n).trim());
            num2 = Integer.parseInt(l[i+2].substring(3+n,6+n).trim());
            num1 = Integer.parseInt(l[i+3].substring(0+n,3+n).trim());

            if(num1*num2*num3*num4 > sum) {
                sum = num1*num2*num3*num4;
                highestNum1 = num1;
                highestNum2 = num2;
                highestNum3 = num3;
                highestNum4 = num4;
            }   
        }
    }
    return sum;
}

public static void main(String[] args) {
    Problem11 prog = new Problem11();

    prog.greatestSide();
    prog.greatestVert();
    prog.greatestDiagonal();
    System.out.println(prog.sum);
    System.out.println(prog.highestNum1);
    System.out.println(prog.highestNum2);
    System.out.println(prog.highestNum3);
    System.out.println(prog.highestNum4);
}
}
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2 回答 2

1

您省略了扫描对角线的一个方向：

for(int i = 0; i>=16; i++) {

根本不运行。你的意思是i <= 16那里。

于 2012-11-19T18:35:39.987 回答
0

这是另一个首先将 转换String为二维数组的解决方案：

public class P11 {

    public static void main(String[] args) throws Exception {
        String input = "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48";
        int n = 20;
        int a[][] = getMatrixOfIntegers(input, n);
        System.out.println(maxProduct(a));
    }

    private static long maxProduct(int a[][]) {
        int size = a.length - 4;
        int l = a.length - 1;
        long pMax = 1;
        for ( int i = 0 ; i < size ; i++ ) {
            for ( int j = 0 ; j < size ; j++ ) {
                int prodDiag1 = a[i][j]*a[i+1][j+1]*a[i+2][j+2]*a[i+3][j+3];
                if ( pMax < prodDiag1 ) {
                    pMax = prodDiag1;
                }
                int prodCol = a[i][j]*a[i+1][j]*a[i+2][j]*a[i+3][j];
                if ( pMax < prodCol ) {
                    pMax = prodCol;
                }
                int prodRow = a[i][j]*a[i][j+1]*a[i][j+2]*a[i][j+3];
                if ( pMax < prodRow ) {
                    pMax = prodRow;
                }
                int prodDiag2 = a[i][l-j]*a[i+1][l-j-1]*a[i+2][l-j-2]*a[i+3][l-j-3];
                if ( pMax < prodDiag2 ) {
                    pMax = prodDiag2;
                }               
            }
        }
        return pMax;
    }

    private static int[][] getMatrixOfIntegers(String input, int n) {
        String m[] = input.split(" ");
        int a[][] = new int[n][n];      
        for ( int i = 0 ; i < n*n ; i++ ) {
            a[i/n][i%n] = Integer.parseInt(m[i]);
        }
        return a;
    }

}

时间：maxProduct0.2 毫秒

于 2014-11-13T23:51:56.827 回答