【LeetCode】11. Container With Most Water 解題報告

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11. Container With Most Water / Medium

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 the line i is at (i, ai) and (i, 0). Find two lines, which, together with the x-axis forms a container, such that the container contains the most water.

Notice that you may not slant the container.

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: 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.

Example 2:

Input: height = [1,1]
Output: 1

Example 3:

Input: height = [4,3,2,1,4]
Output: 16

Example 4:

Input: height = [1,2,1]
Output: 2

Constraints:

n == height.length
2 <= n <= 10^5
0 <= height[i] <= 10^4

Solution: Two Pointer Approach

思路

因為雙迴圈暴力列舉一定會超時，所以得用類似 Greedy 的解法，左右兩個指標，計算目前圍起來的面積，計算完之後，紀錄是否比目前最大面積還大。接著，比較短的那一邊指標向中心縮，直到兩個指標交會。

效能

Complexity

  • Time Complexity: O(N)
  • Space Complexity: O(1)

LeetCode Result

Code

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class Solution {
public:
    int maxArea(vector<int>& height) {
        int n = height.size();
        if(n == 2) return min(height[0], height[1]);
        int maxArea = 0;
        int left = 0, right = n-1;
        while(left < right) {
            maxArea = max(min(height[left], height[right]) * (right-left), maxArea);
            if(height[left] < height[right]) {
                ++left;
            } else {
                --right;
            }
        }

        return maxArea;
    }
};