Problem 11  Largest product in a grid

本文探讨了在20x20数字网格中,寻找四个相邻数(横向、纵向或对角线)的最大乘积的算法实现。通过遍历网格并计算不同方向上的乘积,最终找到最大值。

Problem 11 Largest product in a grid

https://projecteuler.net/problem=11

In the 20×20 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 the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

题意:相同方向(上,下,左,右或对角)的四个相邻数字的最大乘积是多少?

从行、列、左斜、右斜四个方向进行遍历。

c++

#include<iostream>
using namespace std;
#define N 20
int main(){
  int a[20][20]={
    {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 maxx = 0;
  for (int i = 0; i <= 16; i++)
  {
    for (int j = 0; j <= 16; j++)
	{
      int row = a[i][j] * a[i][j+1] * a[i][j+2] * a[i][j+3];  
      int col = a[j][i] * a[j+1][i] * a[j+2][i] * a[j+3][i]; 
      int lef = a[i][N-j-1] * a[i+1][N-j-2] * a[i+2][N-j-3] * a[i+3][N-j-4];
      int rig = a[i][j] * a[i+1][j+1] * a[i+2][j+2] * a[i+3][j+3]; 
       maxx = max(maxx,max(row,max(col,max(lef,rig))));
    }
  }
  printf("%d\n", maxx);
  return 0;
}

 

 

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