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Leetcode 贪心 container with most water

2024-07-20 07:40:05   209人阅读

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Container With Most Water

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Given n non-negative integers a1, a2, ..., an, where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of line i is at (i, ai) 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.



题意：二维坐标系里有 n 个点 (i, ai)， ai >= 0，从 (i, ai)到(i, 0)划竖线，共有 n 条竖线。
找出两条竖线，使得它们构成的矩形的面积最大，矩形的高取决于最短的竖线。
思路：贪心
从首尾两个下标head 和trail 处开始扫描，用一个变量 maxArea 保持当前最大的矩形面积。
如果head 指向的竖线短于 trail 的，则右移 head
否则左移 trail
计算面积，更新 maxArea
复杂度：时间O(n)，空间O(1)

int maxArea(vector<int> &height){
	if(height.size() < 2) return 0;
	int maxArea = min(height.front(), height.back()) * ( height.size() - 1);
	for(int head = 0, trail = height.size() - 1; head < trail; ){
		if(height[head] < height[trail]) head++;
		else trail--;
		int newArea = min(height[head], height[trail]) * (trail - head);
		maxArea = max(maxArea, newArea);
	}
	return maxArea;
}


Leetcode 贪心 container with most water


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