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LeetCode -- Sliding Window Maximum

news 来源：原创 2024/4/27 17:47:14

题目描述：

Given an array nums, there is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position.

For example,
Given nums = [1,3,-1,-3,5,3,6,7], and k = 3.

Window position Max
--------------- -----
[1 3 -1] -3 5 3 6 7 3
1 [3 -1 -3] 5 3 6 7 3
1 3 [-1 -3 5] 3 6 7 5
1 3 -1 [-3 5 3] 6 7 5
1 3 -1 -3 [5 3 6] 7 6
1 3 -1 -3 5 [3 6 7] 7
Therefore, return the max sliding window as [3,3,5,5,6,7].

Note:
You may assume k is always valid, ie: 1 ≤ k ≤ input array's size for non-empty array.

就是在一个数组中，存在一个长度为k的窗口，每次把这个窗口向后移动1个单元，把最大值取出放入list，直到窗口右端到达数组末尾为止，把最大值的数组list返回。

思路：
1.本题主要是需要使用1个list来表达窗口，在首位移除，末端添加。
2.为了优化性能，可以维护1个maxIndex变量来减小最大值的计算次数。当窗口发生移动时，假设index表示窗口的末尾位置，则：
a.如果首位移除的是maxIndex，则重新计算最大值并更新maxIndex
b.如果首位移除的不是maxIndex，则只需比较nums[maxIndex]与nums[index]即可，更新maxIndex

实现代码：

public class Solution {
    public int[] MaxSlidingWindow(int[] nums, int k) {
        if(nums.Length == 0){
    		return new int[0];
    	}
    	if(k > nums.Length - 1){
    		return new int[]{nums.Max()};
    	}
    	 
    	 var result = new List<int>();
    	 var window = new List<int>();
    	 var maxIndex = 0;
    	 for(var i = 0;i < k; i++){
    	 	window.Add(nums[i]);
    		if(nums[maxIndex] < nums[i]){
    			maxIndex = i;
    		}
    	 }
    	 result.Add(nums[maxIndex]);
    	 
    	 var right = k;
    	 while(right < nums.Length){
    	 	window.RemoveAt(0);
    		window.Add(nums[right]);
    		
    		if(right - k == maxIndex){
    			maxIndex = CalcMaxIndex(right-k+1, k, nums);
    		}else{
    			if(nums[right] > nums[maxIndex]){
    				maxIndex = right;
    			}
    		}
    		result.Add(nums[maxIndex]);
    		right ++;
    	 }
    	 
    	 return result.ToArray();
}


private int CalcMaxIndex(int left, int k, int[] nums){
	var maxIndex = left ;
	for(var j = left ;j < left + k; j++){
		if(nums[j] > nums[maxIndex]){
			maxIndex = j;
		}
	}
	return maxIndex;
}
    
}