Problem 11 of What is the greatest product of four adjacent numbers-优快云博客

本文链接：https://blog.youkuaiyun.com/comkingfly/article/details/7348587

本文探讨了一个20x20数字网格中四个相邻数的最大乘积问题，这些数可以沿任何方向（水平、垂直或对角线）排列。通过编程方法解决了这一挑战，并给出了最大乘积的具体数值。

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In the 2020 grid below, four numbers along a diagonal line have been marked in red.

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

The product of these numbers is 26 63 78 14 = 1788696.

What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 2020 grid?

public class GridProduct {
	public static void main(String args[]){
		int [][] a={
				{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},
		};
		int mul1=1,mul2=1,mul3=1,mul4=1;
		//down
		for(int i=0;i<20;i++){
			for(int j=0;j<17;j++){
				int pro1=a[i][j]*a[i][j+1]*a[i][j+2]*a[i][j+3];
				if(mul1<pro1){
					mul1=pro1;
				}
			}
		}
		//left
		for(int i=0;i<17;i++){
			for(int j=0;j<20;j++){
				int pro2=a[i][j]*a[i+1][j]*a[i+2][j]*a[i+3][j];
				if(mul2<pro2){
					mul2=pro2;
				}
			}
		}
		//diagonally right
		for(int i=0;i<17;i++){
			for(int j=0;j<17;j++){
				int pro3=a[i][j]*a[i+1][j+1]*a[i+2][j+2]*a[i+3][j+3];
				if(mul3<pro3){
					mul3=pro3;
				}
			}
		}
		//diagonally left
		for(int i=19;i>=3;i--){
			for(int j=0;j<17;j++){
				int pro4=a[i][j]*a[i-1][j+1]*a[i-2][j+2]*a[i-3][j+3];
				if(mul4<pro4){
					mul4=pro4;
				}
			}
		}
		
		System.out.println("mul1="+mul1+",mul2="+mul2+",mul3="+mul3+",mul4="+mul4);
	}
}

Answer:

70600674

import java.util.HashMap;

public class Recss {

	static HashMap<Integer, String> horHashmap=new HashMap<Integer, String>();
	public static int horizental(int [][] array){
		int result=0;
		for(int m=0;m<20;m++){
			for(int n=0;n<17;n++){
				
					int temp=array[m][n]*array[m][n+1]*array[m][n+2]*array[m][n+3];
					if(temp>result){
						horHashmap.put(temp,String.valueOf(array[m][n])+","+String.valueOf(array[m][n+1])+","+String.valueOf(array[m][n+2])+","+String.valueOf(array[m][n+3]));
						result=temp;
					
				}
			}
		}
		return result;
	}
	
	static HashMap<Integer, String> verHashmap=new HashMap<Integer, String>();
	public static int vertal(int [][] array){
		int result=0;
		for(int m=0;m<17;m++){
			for(int n=0;n<20;n++){
					int temp=array[m][n]*array[m+1][n]*array[m+2][n]*array[m+3][n];
					if(temp>result){
						verHashmap.put(temp,String.valueOf(array[m][n])+","+String.valueOf(array[m+1][n])+","+String.valueOf(array[m+2][n])+","+String.valueOf(array[m+3][n]));
						result=temp;
					
				}
			}
		}
		return result;
	}
	static HashMap<Integer, String> xieHashmap=new HashMap<Integer, String>();
	public static int xie(int [][] array){
		int result=0;
		for(int m=0;m<17;m++){
			for(int n=0;n<17;n++){
					int temp=array[m][n]*array[m+1][n+1]*array[m+2][n+2]*array[m+3][n+3];
					if(temp>result){
						xieHashmap.put(temp,String.valueOf(array[m][n])+","+String.valueOf(array[m+1][n+2])+","+String.valueOf(array[m+2][n+3])+","+String.valueOf(array[m+3][n+4]));
						result=temp;
					
				}
			}
		}
		return result;
	}
	static HashMap<Integer, String> fanxiangHashmap=new HashMap<Integer, String>();
	public static int fanxiang(int [][] array){
		int result=0;
		for(int m=19;m>2;m--){
			for(int n=0;n<17;n++){
					int temp=array[m][n]*array[m-1][n+1]*array[m-2][n+2]*array[m-3][n+3];
					if(temp>result){
						fanxiangHashmap.put(temp,String.valueOf(array[m][n])+","+String.valueOf(array[m-1][n+1])+","+String.valueOf(array[m-2][n+2])+","+String.valueOf(array[m-3][n+3]));
						result=temp;
					
				}
			}
		}
		return result;
	}
	public static void main(String[] args) {
		int [][] array={{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}};
		Recss rec=new Recss();
		System.out.println(horizental(array));
		System.out.println(horHashmap.get(horizental(array)));
		System.out.println(vertal(array));
		System.out.println(verHashmap.get(vertal(array)));
		System.out.println(xie(array));
		System.out.println(xieHashmap.get(xie(array)));
		System.out.println(fanxiang(array));
		System.out.println(fanxiangHashmap.get(fanxiang(array)));
	}
	
}