#2328 - Number of Increasing Paths in a Grid

Hard • View on LeetCode • View on GitHub

Array Dynamic Programming Depth-First Search Matrix Breadth-First Search Graph Memoization Topological Sort

Problem Description

You are given an m x n integer matrix grid, where you can move from a cell to any adjacent cell in all 4 directions.

Return the 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 109 + 7.

Two paths are considered different if they do not have exactly the same sequence of visited cells.

Solution

/**
 * @param {number[][]} grid
 * @return {number}
 */
var countPaths = function(grid) {
  const MOD = 1e9 + 7;
  const rows = grid.length;
  const cols = grid[0].length;
  const cache = new Array(rows).fill().map(() => new Array(cols).fill(0));
  const directions = [[0, 1], [1, 0], [0, -1], [-1, 0]];

  function explore(row, col) {
    if (cache[row][col]) return cache[row][col];

    let paths = 1;
    for (const [dr, dc] of directions) {
      const newRow = row + dr;
      const newCol = col + dc;
      if (
        newRow >= 0 && newRow < rows && newCol >= 0
        && newCol < cols && grid[newRow][newCol] > grid[row][col]
      ) {
        paths = (paths + explore(newRow, newCol)) % MOD;
      }
    }

    return cache[row][col] = paths;
  }

  let total = 0;
  for (let i = 0; i < rows; i++) {
    for (let j = 0; j < cols; j++) {
      total = (total + explore(i, j)) % MOD;
    }
  }

  return total;
};