Saturday, November 15, 2014

[LeetCode] Container With Most Water

Given n non-negative integers a1a2, ..., an, where each represents a point at coordinate (iai). n vertical lines are drawn such that the two endpoints of line i is at (iai) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water.
Note: You may not slant the container.


思路:

由于ai和aj (i<j) 组成的container的面积:S(i,j) = min(ai, aj) * (j-i)

所以对于任何S(i'>=i, j'<=j) >= S(i,j),由于j'-i' <= j-i,必然要有min(ai',aj')>=min(ai,aj)才行。同样可以采用头尾双指针向中间移动:

当a(left) < a(right)时,对任何j<right来说

(1) min(a(left),aj) <= a(left) = min(a(left), a(right))
(2) j-left < right-left

所以S(left, right) > S(left, j<right)。排除了所有以left为左边界的组合,因此需要右移left。同理,当a(left) > a(right)时,需要左移right。而当a(left) = a(right)时,需要同时移动left和right。

思路整理:
left = 0, right = n-1
(1) a[left] < a[right], left++
(2) a[left] > a[right], right--
(3) a[left] = a[right], left++, right--
终止条件:left>-right



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

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