poj_1836 动态规划

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<string.h>
int dp_inc_beg[1005];	//dp_inc_beg[i]表示从i到到队尾的最长上升序列长度
int dp_inc_end[1005];	//dp_inc_end[i]表示从队头到i的最长上升序列长度
int dp_dec_beg[1005];
int dp_dec_end[1005];

double height[1005];
int main(){
	int n;
	scanf("%d", &n);

	for (int i = 1; i <= n; i++){
		scanf("%lf", &height[i]);
	}
	memset(dp_inc_beg, 0, sizeof(dp_inc_beg));
	memset(dp_inc_end, 0, sizeof(dp_inc_end));
	memset(dp_dec_beg, 0, sizeof(dp_dec_beg));
	memset(dp_dec_end, 0, sizeof(dp_dec_end));


	for (int i = 1; i <= n; i++){
		int max_inc = 0, max_dec = 0;
		for (int j = 1; j < i; j++){
			if (height[i] > height[j])
				max_inc = max_inc > dp_inc_end[j] ? max_inc : dp_inc_end[j];
			if (height[i] < height[j])
				max_dec = max_dec > dp_dec_end[j] ? max_dec : dp_dec_end[j];
		}
		dp_inc_end[i] = max_inc + 1;
		dp_dec_end[i] = max_dec + 1;
	}
	for (int i = n; i >= 1; i--){
		int max_inc = 0, max_dec = 0;
		for (int j = i + 1; j <= n; j++){
			if (height[i] < height[j])
				max_inc = max_inc > dp_inc_beg[j] ? max_inc : dp_inc_beg[j];
			if (height[i] > height[j])
				max_dec = max_dec > dp_dec_beg[j] ? max_dec : dp_dec_beg[j];
		}
		dp_inc_beg[i] = max_inc + 1;
		dp_dec_beg[i] = max_dec + 1;
	}
	int max = 0;
	for (int i = 1; i <= n; i++){
		//最大上升序列长度
		if (dp_inc_beg[i] + dp_inc_end[i] - 1 > max){
			max = dp_inc_beg[i] + dp_inc_end[i] - 1;
		}
		//最大下降序列长度
		if (dp_dec_beg[i] + dp_dec_end[i] - 1 > max){
			max = dp_dec_beg[i] + dp_dec_end[i] - 1;
		}
		//如果以i为中心，向两边均呈下降序列
		if (dp_inc_end[i] + dp_dec_beg[i] - 1 > max){
			max = dp_inc_end[i] + dp_dec_beg[i] - 1;
		}
		//左边一个上升序列[1...i] 右边一个下降序列[j...n]， 其中 i < j
		for (int j = i + 1; j <= n; j++){
			if (dp_inc_end[i] + dp_dec_beg[j] > max)
				max = dp_dec_beg[j] + dp_inc_end[i];
		}
	}
	printf("%d\n", n - max);
	return 0;
}