在以下這個20
20的網格中，四個處於同一對角線上的相鄰數字用紅色標了出來：
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
這四個數字的乘積是：26 63 78 14
= 1788696.
在這個2020網格中，處於任何方向上（上，下，左，右或者對角線）的四個相鄰數字的乘積的最大值是多少？
public class Test {
//從左到右計算最大值
public static long leftToRight(int arr[][]){
int max = 0;
int value = 1;
for(int i = 0; i < 20; i ++){
for(int j = 0 ;j < 17 ; j++){
value = arr[i][j] * arr[i][j+1] * arr[i][j+2] * arr[i][j+3];
if(value > max) max = value;
}
}
return max;
}
//從上到下計算最大值
public static long upToDown(int arr[][]){
int max = 0;
int value = 1;
for(int i = 0; i < 17; i ++){
for(int j = 0 ;j < 20 ; j++){
value = arr[i][j] * arr[i+1][j] * arr[i+2][j] * arr[i+3][j];
if(value > max) max = value;
}
}
return max;
}
//從左上到右下計算最大值
public static long left_uToRight_d(int arr[][]){
int max = 0;
int value = 1;
for(int i = 0; i < 17; i ++){
for(int j = 0;j < 17 ; j++){
value = arr[i][j] * arr[i+1][j+1] * arr[i+2][j+2] * arr[i+3][j+3];
if(value > max) max = value;
}
}
return max;
}
//從右上到左下計算最大值
public static long right_uToLeft_d(int arr[][]){
int max = 0;
int value = 1;
for(int i = 3; i < 20; i ++){
for(int j = 0 ;j < 17 ; j++){
value = arr[i][j] * arr[i-1][j+1] * arr[i-2][j+2] * arr[i-3][j+3];
if(value > max) max = value;
}
}
return max;
}
public static void main(String[] args) {
/* 構建20*20整數數組 */
int arr[][] = {{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},
{67,26,20,68,02,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21},
{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},
};
System.out.println("max :" + max(leftToRight(arr),upToDown(arr),left_uToRight_d(arr),right_uToLeft_d(arr)));
}
private static long max(long a, long b,
long c, long d) {
long max = a;
if(b > max) max = b;
if(c > max) max = c;
if(d > max) max = d;
return max;
}
}