//644

Given an array consisting of n integers, find the contiguous subarray whose length is greater than or equal to k that has the maximum average value. And you need to output the maximum average value.

Example 1:
Input: [1,12,-5,-6,50,3], k = 4
Output: 12.75
Explanation:
when length is 5, maximum average value is 10.8,
when length is 6, maximum average value is 9.16667.
Thus return 12.75.
Note:
1 <= k <= n <= 10,000.
Elements of the given array will be in range [-10,000, 10,000].
The answer with the calculation error less than 10-5 will be accepted.

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

class Solution {
private:
    bool check(vector<int>& nums,double mid,int k){
        //nums[i]-mid+nums[i+1]-mid +...nums[j]-mid>=0
        //update max_val=mid,while <=0,need check all possible
        //change into sums[j]-sums[i]>=0,j-i>=k+1;min sums[i],
        //max(sums[j]-sums[i])? 0 ,prev note min sums[i]
        //sum[i]--[0...k],prev--[0...i-k],min_sum--[0...j](j<=i-k)
        double sum=0,prev=0,min_sum=0;
        for(int i=0;i<k;i++){
            sum+=nums[i]-mid;
        }
        if(sum>=0){
            return true;
        }

        for(int i=k;i<nums.size();i++){
            sum+=nums[i]-mid;
            prev+=nums[i-k]-mid;
            min_sum=min(prev,min_sum);
            if(sum>=min_sum){
                return true;
            }
        }
        return false;
    }
public:
    double findMaxAverage(vector<int>& nums, int k) {
        double max_val=nums[0];
        double min_val=nums[0];
        for(int i=1;i<nums.size();i++){
            max_val=max(max_val,(double)nums[i]);
            min_val=min(min_val,(double)nums[i]);
        }
        double prev_mid=max_val,error=INT32_MAX;
        while(error>0.00001){
            double mid=(max_val+min_val)*0.5;
            if(check(nums,mid,k)){
                min_val=mid;
            } else{
                max_val=mid;
            }
            error=fabs(prev_mid-mid);
            prev_mid=mid;
        }
        return min_val;
    }
};

int main(){
    int k=1;
    int arr[]={1,12,-5,-6,50,3};
    vector<int> vec(arr,arr+sizeof(arr)/sizeof(int));

    cout<<Solution().findMaxAverage(vec,k)<<endl;
    return 0;
}