Container With Most Water

[Question]:

Given n non-negative integers a₁, a₂, ..., a_n, where each represents a point at coordinate (i, a_i). n vertical lines are drawn such that the two endpoints of line i is at (i, a_i) and (i, 0). Find two lines, which together with x-axis form a container, such that the container contains the most water.

Note: You may not slant the container.

[Analysis]:

Area(i,j) = Min(Ai, Aj) * (j-i);

The min of (Ai, Aj) decides the area of the container. For k, i<k<j, Area (i, k) < Area(i, j) if Ai < Aj: i.e. all Area(i,k) can be ruled out.

[Solution]:

public class Solution {
    int maxArea(vector<int>& height) {
        int i=0, j=height.size()-1;
        int ret=0;
        while (i<j) {
            ret = max(ret, min(height[i],height[j]) * (j-i));
            if (height[i]<height[j]) i++;
            else j--;
        }
        return ret;
    }
}