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2024年第十五届蓝桥杯C&C++大学A组--成绩统计

题目：

动态规划，

对于该题，考虑动态规划解法，先取前k个人的成绩计算其方差，并将成绩记录在数组中，记录当前均值，设小蓝已检查前i-1个人的成绩，若方差依然大于T，找出离均值最远的一个成绩，若第i个人的成绩距离当前均值更近，则剔除离均值较远的成绩，使得方差变小，若遍历完整个数组均找不到更小的方差，返回-1。

代码：

#include<bits/stdc++.h>
using namespace std;
int n, k, T;
vector<int> nums;
vector<int> team;bool is0()
{double mean,val;double sum = 0;for (auto num : team){sum += num;}mean = sum / k;val = 0;for (auto num : team){val += (num - mean) * (num - mean);}val /= k;if (val < T) return true;else return false;
}int main()
{cin >> n >> k >> T;int N = n;while (N--){double temp;cin >> temp;nums.push_back(temp);}if (n < k){cout << -1;return 0;}double sum = 0;for (int i = 0;i < k; i++){team.push_back(nums[i]);sum += nums[i];}double mean = sum / k;if (is0()){cout << k;return 0;}for (int i = k; i < nums.size(); ++i){double sub = 0;int x = -1;for (int j = 0; j < team.size(); ++j){if (abs(team[j] - mean) > sub)//找出距离平均值最远的值和下标{sub = abs(team[j] - mean);x = j;}}if (x != -1 && sub > abs(nums[i] - mean))team[x] = nums[i];if (is0()){cout << i + 1;return 0;}return -1;}return 0;
}