Problem 11: Largest product in a grid
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?
#include<iostream>
#include<fstream>
using namespace std;
const int ROWS = 20;
const int COLS = 20;
void display2DArray(int arr[][COLS], int rows, int cols) {
for (int i = 0; i < ROWS; i++) {
for (int j = 0; j < COLS; j++) {
cout << arr[i][j] << " ";
}
cout << endl;
}
}
int maxHP(int arr[][COLS], int rows, int cols) {
int max = 0;
int imax, jmax, num;
for (int i = 0; i < ROWS; i++) {
for (int j = 0; j <= COLS - 4; j++) {
// cout << "Checking product at i = " << i << ", j = " << j << "." << endl;
num = arr[i][j] * arr[i][j+1] * arr[i][j+2] * arr[i][j+3];
// cout << arr[i][j] << " * " << arr[i][j+1] << " * " << arr[i][j+2]
// << " * " << arr[i][j+3] << " = " << num << endl;
if (num > max) {
max = num;
imax = i;
jmax = j;
// cout << "NEW MAX OF " << max << " AT " << imax << ", " << jmax << endl;
}
}
}
// cout << "maxHP: arr[" << imax << "][" << jmax << "] = " << max << endl;
return max;
}
int maxVP(int arr[][COLS], int rows, int cols) {
int max = 0;
int imax, jmax, num;
for (int i = 0; i <= ROWS - 4; i++) {
for (int j = 0; j < COLS; j++) {
num = arr[i][j] * arr[i+1][j] * arr[i+2][j] * arr[i+3][j];
if (num > max) {
max = num;
imax = i;
jmax = j;
// cout << "NEW MAX OF " << max << " AT " << imax << ", " << jmax << endl;
}
}
}
// cout << "maxVP: arr[" << imax << "][" << jmax << "] = " << max << endl;;
return max;
}
int maxDP(int arr[][COLS], int rows, int cols) {
int max = 0;
int imax, jmax, num;
for (int i = 0; i <= ROWS - 4; i++) {
for (int j = 0; j <= COLS - 4; j++) {
num = arr[i][j] * arr[i+1][j+1] * arr[i+2][j+2] * arr[i+3][j+3];
if (num > max) {
max = num;
imax = i;
jmax = j;
// cout << "NEW MAX OF " << max << " AT " << imax << ", " << jmax << endl;
}
}
}
// cout << "maxDP: arr[" << imax << "][" << jmax << "] = " << max << endl;
return max;
}
int maxDP2(int arr[][COLS], int rows, int cols) {
int max = 0;
int imax, jmax, num;
for (int i = 0; i <= ROWS - 4; i++) {
for (int j = 3; j < COLS; j++) {
num = arr[i][j] * arr[i+1][j-1] * arr[i+2][j-2] * arr[i+3][j-3];
if (num > max) {
max = num;
imax = i;
jmax = j;
// cout << "NEW MAX OF " << max << " AT " << imax << ", " << jmax << endl;
}
}
}
// cout << "maxDP2: arr[" << imax << "][" << jmax << "] = " << max << endl;
return max;
}
int main() {
int grid[ROWS][COLS] = {};
ifstream fin("grid.txt");
for (int i = 0; i < ROWS; i++) {
for (int j = 0; j < COLS; j++) {
fin >> grid[i][j];
}
}
cout << max(max(maxHP(grid, ROWS, COLS), maxVP(grid, ROWS, COLS)),
max(maxDP(grid, ROWS, COLS), maxDP2(grid, ROWS, COLS))) << endl;
}
Answer: 70600674