技術標籤：Codeforces

題目
參考
題意：給定n個數，要求改動一個數（可以改成任意數），使得改動後這n個數的hill數和valley數的和最小。
hill:如果 a i > a i − 1 & & a i > a i + 1 a_i>a_{i-1}\&\&a_i>a_{i+1} ai​>ai−1​&&ai​>ai+1​，則 a i a_i ai​為hill
valley:如果 a i < a i − 1 & & a i < a i + 1 a_i<a_{i-1}\&\&a_i<a_{i+1}

#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int maxn = 300010;


int n;
int a[maxn];

int check(int i) {
	if (i == 0 || i == n - 1) return 0;
	if
 
 (a[i] > a[i-1] && a[i] > a[i+1])
		return 1;
	if (a[i] < a[i-1] && a[i] < a[i+1])
		return 1;
	return 0;
}

int cal(int i) {
	return check(i-1) + check(i) + check(i+1);
}

int main() {
	int t;
	scanf("%d", &t);
	while (t--) {
		scanf("%d", &n);
 

		for (int i = 0; i < n; ++i) {
			scanf("%d", &a[i]);
		}
		int num = 0;
		for (int i = 1; i < n - 1; ++i) {
			num += check(i);
		}
		
		int mx = 0;
		for (int i = 1; i < n - 1; ++i) {
			int tmp = a[i];
			
			int res = cal(i);
			a[i] = a[i-1];
			int mn = cal(i);
			a[i] = a[i+1];
			mn = min(mn, cal(i));
			
			mx = max(mx, res - mn);
			
			a[i] = tmp;
			
		}
//		printf("num:%d mx:%d\n", num, mx);
		printf("%d\n", num - mx);
		
	}
}