1. Container With Most Water
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 and n is at least 2.
The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.
解析:这个问题可以看成在底和高之间不断取舍的问题。先取最长底,算出一个容积。然后去不断尝试用底的损失去换取一个可以带来更大容积的高。不断放弃无法带来更大容积的高,最终确定最优解。
/**
* @param {number[]} height
* @return {number}
*/
var maxArea = function(height) {
if (!height || height.length <= 1) return 0;
// 双指针来进行优化
// 时间复杂度是O(n)
let leftPos = 0;
let rightPos = height.length - 1;
let max = 0;
while(leftPos < rightPos) {
const currentArea = Math.abs(leftPos - rightPos) * Math.min(height[leftPos] , height[rightPos]);
if (currentArea > max) {
max = currentArea;
}
// 更新小的
if (height[leftPos] < height[rightPos]) {
leftPos++;
} else { // 如果相等就随便了
rightPos--;
}
}
return max;
};