11 Container With Most Water

Given n non-negative integers a1, a2, ..., an, 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 forms a container, such that the container contains the most water.

Solution

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

Notes
TODO: 严格证明解法的正确性！