Given n non-negative integers where each represents a point at coordinate . ‘ n ‘ vertical lines are drawn such that the two endpoints of line i is at and .
Find two lines, which together with x-axis forms a container, such that the container contains the most water.
The program should return an integer which corresponds to the maximum area of water that can be contained ( maximum area instead of maximum volume sounds weird but this is 2D plane we are working with for simplicity ).
Note : You may not slant the container.
Input : [1, 5, 4, 3] Output : 6 Explanation : 5 and 3 are distance 2 apart. So the size of the base = 2. Height of container = min(5, 3) = 3. So total area = 3 * 2 = 6 Input : [3, 1, 2, 4, 5] Output : 12 Explanation : 5 and 3 are distance 4 apart. So the size of the base = 4. Height of container = min(5, 3) = 3. So total area = 4 * 3 = 12
Note 1 : When you consider a1 and aN, then the area is (N-1) * min(a1, aN). Note 2 : The base (N-1) is the maximum possible.
- This implies that if there was a better solution possible, it will definitely have the Height greater than min(a1, aN).
- We know that, Base min(a1, aN)
This means that we can discard min(a1, aN) from our set and look to solve this problem again from the start.
- If a1 < aN, then the problem reduces to solving the same thing for a2, aN.
- Else, it reduces to solving the same thing for a1, aN-1
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Improved By : Mithun Kumar