Water collected between towers

Question

I recently came across an interview question asked by Amazon and I am not able to find an optimized algorithm to solve this question:

You are given an input array wh

Answer 1

Once the water's done falling, each position will fill to a level equal to the smaller of the highest tower to the left and the highest tower to the right.

Find, by a rightward scan, the highest tower to the left of each position. Then find, by a leftward scan, the highest tower to the right of each position. Then take the minimum at each position and add them all up.

Something like this ought to work:

int tow[N]; // nonnegative tower heights
int hl[N] = {0}, hr[N] = {0}; // highest-left and highest-right
for (int i = 0; i < n; i++) hl[i] = max(tow[i], (i!=0)?hl[i-1]:0);
for (int i = n-1; i >= 0; i--) hr[i] = max(tow[i],i<(n-1) ? hr[i+1]:0);
int ans = 0;
for (int i = 0; i < n; i++) ans += min(hl[i], hr[i]) - tow[i];