方阵中的最大乘积

来源：互联网发布：手机淘宝如何管理店铺编辑：程序博客网时间：2024/05/01 02:33

在如下的20×20方阵中，有四个呈对角线排列的数被标红了。

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
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？

package EULER11;/** * Created by Administrator on 2016/7/7. * 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？ */public class EULER11 {    public static void main(String[] args) {        int[][] grid = {{8, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 8},                {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, 8, 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, 9, 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, 9, 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, 8, 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, 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, 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}};        long start = System.currentTimeMillis();        int max = 0;        int row = 0;        int column = 0;        for (int x=0;x<20;x++){            for (int y=0;y<20;y++){                int muti = maxMuti(grid,x,y,false);                if (muti>max){                    max = muti;                    row = x;                    column = y;                }            }        }        maxMuti(grid,row,column,true);        long end = System.currentTimeMillis();        System.out.print("总用时:"+(end-start)+"毫秒");    }    public static int maxMuti(int[][] grid,int x,int y,boolean show){        int max = 0;        int type = 0;        if (x<17){            int muti = grid[x][y]*grid[x+1][y]*grid[x+2][y]*grid[x+3][y];            if (muti>max){                max = muti;                type = 1;            }        }        if (y<17){            int muti = grid[x][y]*grid[x][y+1]*grid[x][y+2]*grid[x][y+3];            if (muti>max){                max = muti;                type = 2;            }        }        if (y>2&&x<17){            int muti = grid[x][y]*grid[x+1][y-1]*grid[x+2][y-2]*grid[x+3][y-3];            if (muti>max){                max = muti;                type = 3;            }        }        if (y<17&&x<17){            int muti = grid[x][y]*grid[x+1][y+1]*grid[x+2][y+2]*grid[x+3][y+3];            if (muti>max){                max = muti;                type = 4;            }        }        if (show){            switch (type){                case 1:System.out.print("从第"+(x+1)+"行，第"+(y+1)+"列开始，从上到下，乘积为"+max);break;                case 2:System.out.print("从第"+(x+1)+"行，第"+(y+1)+"列开始，从左到右，乘积为"+max);break;                case 3:System.out.print("从第"+(x+1)+"行，第"+(y+1)+"列开始，从右上到左下，乘积为"+max);break;                case 4:System.out.print("从第"+(x+1)+"行，第"+(y+1)+"列开始，从左上到右下，乘积为"+max);break;            }        }        return max;    }}

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