Project Euler Problem 11

Problem 11

22 February 2002

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?

Answer: 70600674

 

 

* Human eye

 

87*97*94*89

 

* C#

 

static void problem11() {
 var n = new[,]{
    {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}};
 var size = n.GetLength(0);
 var max = 0;

 // array guard
 Func<int, int, int> get = (y, x) => {
  if (x >= 0 && x < size && y >= 0 && y < size)
   return n[y, x];
  else
   return 0;
 };

 for (var y = 0; y < size; y++) {
  for (var x = 0; x < size; x++) {
   // direction -
   max = Math.Max(max, get(y, x) * get(y, x + 1) * get(y, x + 2) * get(y, x + 3));
   // direction |
   max = Math.Max(max, get(y, x) * get(y + 1, x) * get(y + 2, x) * get(y + 3, x));
   // direction /
   max = Math.Max(max, get(y, x) * get(y - 1, x + 1) * get(y - 2, x + 2) * get(y - 3, x + 3));
   // direction \
   max = Math.Max(max, get(y, x) * get(y + 1, x + 1) * get(y + 2, x + 2) * get(y + 3, x + 3));
  }
 }
 Console.WriteLine(max);
}

 

 

* C

 

#include <stdio.h>

// array guard
int get(int n[][20], int y, int x) {
  const int size = 20;
  if (x >= 0 && x < size && y >= 0 && y < size)
    return n[y][x];
  else
    return 0;
}

int max(int a, int b) {
  return a > b ? a : b;
}

void problem11() {
  int n[][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, 9,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95},
    {78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92},
    {16,39, 5,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57},
    {86,56,00,48,35,71,89, 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 size = sizeof(n);
  int maxP = 0;
 
  int y, x;
  for (y = 0; y < size; y++) {
    for (x = 0; x < size; x++) {
      // direction -
      maxP = max(maxP, get(n, y, x) * get(n, y, x + 1) * get(n, y, x + 2) * get(n, y, x + 3));
      // direction |
      maxP = max(maxP, get(n, y, x) * get(n, y + 1, x) * get(n, y + 2, x) * get(n, y + 3, x));
      // direction /
      maxP = max(maxP, get(n, y, x) * get(n, y - 1, x + 1) * get(n, y - 2, x + 2) * get(n, y - 3, x + 3));
      // direction \
      maxP = max(maxP, get(n, y, x) * get(n, y + 1, x + 1) * get(n, y + 2, x + 2) * get(n, y + 3, x + 3));
    }
  }
  printf("%d\n", maxP);
}

int main() {
  problem11();
}