Worst case time complexity for recursion

Question

int memo[101][101];  
int findMinPath(vector<vector<int> >& V, int r, int c) {  
  int R = V.size();  
  int C = V[0].size();  
  if (r >= R || c >= C) return 100000000; // Infinity  
  if (r == R - 1 && c == C - 1) return 0;  
  if (memo[r][c] != -1) return memo[r][c];  
  memo[r][c] =  V[r][c] + min(findMinPath(V, r + 1, c), findMinPath(V, r, c + 1));  
  return memo[r][c];  
}  

Callsite :   
memset(memo, -1, sizeof(memo));  
findMinPath(V, 0, 0);

In the above code, what will be the worst case time complexity?.I understand that every function will call other functions atmost one time, but I am not clear with the calculation of the time complexity.

Answer 1

The memoisation is the key here. Normally this would have exponential growth, but because you never perform additional recursive steps if the result is previously computed in memo , then it is reduced to the number of elements in memo as a worst case. ie O( 101 x 101 )