DSA/algorithms/CPlusPlus/Dynamic-Programming/minimum-pathsum.cpp

// (problem Link) - [https://leetcode.com/problems/minimum-path-sum/]

#include <bits/stdc++.h>

using namespace std;

int minSumPathUtil(int i, int j,vector<vector<int>> &matrix,vector<vector<int>> &dp)
{
  if(i==0 && j == 0)
    return matrix[0][0];
  if(i<0 || j<0)
    return 1e9;
  if(dp[i][j]!=-1) return dp[i][j];
    
  int up = matrix[i][j]+minSumPathUtil(i-1,j,matrix,dp);
  int left = matrix[i][j]+minSumPathUtil(i,j-1,matrix,dp);
  
  return dp[i][j] = min(up,left);
  
}

int minSumPath(int n, int m, vector<vector<int> > &matrix){
    vector<vector<int> > dp(n,vector<int>(m,-1));
    return minSumPathUtil(n-1,m-1,matrix,dp);
    
}

int main() {

  vector<vector<int> > matrix{{5,9,6},
                            {11,5,2}};
                            
  int n = matrix.size();
  int m = matrix[0].size();
  
  cout<<minSumPath(n,m,matrix);
}
// Time Complexity: O(N*M)
// Space Complexity: O((M-1)+(N-1)) + O(N*M)
// example : N=2,M=3
// Min pathsum = 5+9+6+2 =21