Number of increasing paths in a grid

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

57.4% acceptance

Feb 25, 2026

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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 10^9 + 7.

Solution

Rust

Time O(n * m)

Space O(n * m)

LeetCode

solution.rs

impl Solution {
  pub fn count_paths(grid: Vec<Vec<i32>>) -> i32 {
    const MOD: i64 = 1_000_000_007;
    let m = grid.len();
    let n = grid[0].len();
    let mut dp = vec![vec![0i64; n]; m];

    let mut cells: Vec<(i32, usize, usize)> = Vec::with_capacity(m * n);
    for i in 0..m {
      for j in 0..n {
        cells.push((grid[i][j], i, j));
      }
    }
    cells.sort_unstable();

    let dirs: [(i32, i32); 4] = [(0, 1), (0, -1), (1, 0), (-1, 0)];
    let mut ans: i64 = 0;

    for (val, i, j) in cells {
      dp[i][j] = 1;
      for (di, dj) in dirs {
        let ni = i as i32 + di;
        let nj = j as i32 + dj;
        if ni >= 0 && ni < m as i32 && nj >= 0 && nj < n as i32 {
          let (ni, nj) = (ni as usize, nj as usize);
          if grid[ni][nj] < val {
            dp[i][j] = (dp[i][j] + dp[ni][nj]) % MOD;
          }
        }
      }
      ans = (ans + dp[i][j]) % MOD;
    }
    ans as i32
  }
}