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// 2328. Number of Increasing Paths in a Grid
#include <stdio.h>
#include <stdlib.h>
/*
* given an 'm x n' integer matrix 'grid' where you can move from a cell to any
* adjacent cell in all 4 directions. return th number of strictly increasing
* paths in the grid such that you can start from any cell and end at any cell.
* since the answer may be very large, return it modulo 10^9+7. two paths are
* considered different if they do not have exactly the same sequence of visited
* cells.
*/
const int MOD = 1e9 + 7;
int dfs(int **grid, int grid_size, int *grid_col_size, int row, int col,
int prev, int *ans, int **seen) {
if (row < 0 || row >= grid_size || col < 0 || col >= *grid_col_size ||
grid[row][col] <= prev)
return 0;
if (seen[row][col])
return seen[row][col];
int tmp = 1;
tmp += dfs(grid, grid_size, grid_col_size, row + 1, col, grid[row][col], ans,
seen);
tmp += dfs(grid, grid_size, grid_col_size, row - 1, col, grid[row][col], ans,
seen);
tmp += dfs(grid, grid_size, grid_col_size, row, col + 1, grid[row][col], ans,
seen);
tmp += dfs(grid, grid_size, grid_col_size, row, col - 1, grid[row][col], ans,
seen);
tmp %= MOD;
seen[row][col] = tmp;
return seen[row][col];
}
int countPaths(int **grid, int grid_size, int *grid_col_size) {
int **seen = (int **)malloc(sizeof(int *) * grid_size), ans = 0;
for (int i = 0; i < grid_size; i++)
seen[i] = calloc(*grid_col_size, sizeof(int));
for (int i = 0; i < grid_size; i++)
for (int j = 0; j < *grid_col_size; j++) {
if (seen[i][j] == 0)
seen[i][j] = dfs(grid, grid_size, grid_col_size, i, j, -1, &ans, seen);
ans = (ans + seen[i][j]) % MOD;
}
return ans;
}
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