Trapping Rain Water Algorithm
A storm drain, storm sewer (unite Kingdom, America and Canada), surface water drain / sewer (unite Kingdom), or stormwater drain (Australia and New Zealand)Many storm drainage systems are gravity sewers that drain untreated storm water into rivers or streams — so it is unacceptable to pour hazardous substances into the drains. Other examples of early civilizations with components of stormwater drain systems include early people of Mainland Orkney such as Gurness and the Brough of Birsay in Scotland. For example, in Minoan Crete around 2000 BC, city such as Phaistos were designed to have storm drains and channels to collect precipitation runoff. At Cretan Knossos, storm drains include stone-lined structures large enough for a person to crawl through.
// O(n) time, O(n) space
class Solution {
public:
int trap(int A[], int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
int max_from_left[n];
int max_from_right[n];
max_from_left[0] = A[0];
for (int i = 1; i < n; i++)
max_from_left[i] = max(max_from_left[i-1], A[i]);
max_from_right[n-1] = A[n-1];
for (int i = n - 2; i >= 0; i--)
max_from_right[i] = max(max_from_right[i+1], A[i]);
int water = 0;
for (int i = 1; i < n - 1; i++) {
int min_height = min(max_from_left[i-1], max_from_right[i+1]);
if (min_height > A[i])
water += min_height - A[i];
}
return water;
}
};
// O(n) time, O(1) space
class Solution {
public:
int trap(int A[], int n) {
int maxh = 0;
int water = 0;
int temp = 0;
for (int i = 0; i < n; i++) {
if (A[i] <= maxh) {
temp += maxh - A[i];
} else {
maxh = A[i];
water += temp;
temp = 0;
}
}
maxh = 0;
temp = 0;
for (int i = n - 1; i >= 0; i--) {
if (A[i] < maxh) {
temp += maxh - A[i];
} else {
maxh = A[i];
water += temp;
temp = 0;
}
}
return water;
}
};
