Time: 238 ms (70.14%), Space: 119.6 MB (91.23%) - LeetHub

Author: Gopi-27

2435-paths-in-matrix-whose-sum-is-divisible-by-k/2435-paths-in-matrix-whose-sum-is-divisible-by-k.cpp

@@ -16,17 +16,38 @@ class Solution {
  int numberOfPaths(vector<vector<int>>& grid, int k) {
  int n = grid.size();
  int m = grid[0].size();
- vector<vector<vector<int>>>Dp(n,vector<vector<int>>(m,vector<int>(k)));
- // Tabulation
- for(int s = 0; s < k; s++)if((s + grid[0][0]) % k == 0)Dp[0][0][s] = 1;
- for(int i = 0; i < n; i++){
+ // vector<vector<vector<int>>>Dp(n,vector<vector<int>>(m,vector<int>(k)));
+ // // Tabulation
+ // for(int s = 0; s < k; s++)if((s + grid[0][0]) % k == 0)Dp[0][0][s] = 1;
+ // for(int i = 0; i < n; i++){
+ // for(int j = 0; j < m; j++){
+ // for(int s = 0; s < k; s++){
+ // if(i > 0)Dp[i][j][s] = (Dp[i][j][s] + Dp[i - 1][j][(s + grid[i][j]) % k]) % 1000000007;
+ // if(j > 0)Dp[i][j][s] = (Dp[i][j][s] + Dp[i][j - 1][(s + grid[i][j]) % k]) % 1000000007;
+ // }
+ // }
+ // }
+ // return Dp[n - 1][m - 1][0];
+
+ // Space Optimization
+ vector<vector<int>>prev(m,vector<int>(k));
+ for(int s = 0; s < k; s++)if((s + grid[0][0]) % k == 0)prev[0][s] = 1;
+
+ for(int j = 1; j < m; j++)
+ for(int s = 0; s < k; s++)
+ prev[j][s] += prev[j - 1][(s + grid[0][j]) % k];
+ 
+ for(int i = 1; i < n; i++){
+ vector<vector<int>>curr(m,vector<int>(k));
  for(int j = 0; j < m; j++){
  for(int s = 0; s < k; s++){
- if(i > 0)Dp[i][j][s] = (Dp[i][j][s] + Dp[i - 1][j][(s + grid[i][j]) % k]) % 1000000007;
- if(j > 0)Dp[i][j][s] = (Dp[i][j][s] + Dp[i][j - 1][(s + grid[i][j]) % k]) % 1000000007;
+ if(i > 0)curr[j][s] = (curr[j][s] + prev[j][(s + grid[i][j]) % k]) % 1000000007;
+ if(j > 0)curr[j][s] = (curr[j][s] + curr[j - 1][(s + grid[i][j]) % k]) % 1000000007;
+
  }
  }
+ prev = curr;
  }
- return Dp[n - 1][m - 1][0];
+ return prev[m - 1][0];
  }
 };