UESTC 594 我要长高 dp单调队列

//戳这里：594

//补一发之前的单调队列 dp

#include "bits/stdc++.h"
using namespace std;
int N, C;
int h[50010];

int dp[50010][110];
struct Queue
{
    int value;
}q[110], tmp;
int front, rear;

//j > k 时，
//dp[i][j] = min(dp[i - 1][k] + (j - k) * C + (j - h[i]) * (j - h[i]));
//dp[i][j] = min(dp[i - 1][k] - k * C) + j * C + (j - h[i]) * (j - h[i]);

int main()
{
    while(scanf("%d%d", &N, &C) != EOF) {
        //初始化
        memset(dp, 0x3f, sizeof(dp[0]) * (N + 1));
        //输入
        int i;
        for(i = 1; i <= N; ++i) {
            scanf("%d", &h[i]);
        }
        //k 不需要优化的情况
        int j;
        for(j = h[1]; j <= 100; ++j) {
            dp[1][j] = (j - h[1]) * (j - h[1]);
        }
        //从 2 开始dp
        for(i = 2; i <= N; ++i) {
            front = rear = 1;
            for(j = h[i - 1]; j <= 100; ++j) {
                tmp.value = dp[i - 1][j] - j * C;
                for( ; front < rear && tmp.value < q[rear - 1].value; --rear);
                q[rear++] = tmp;
                if(j >= h[i]) {
                    dp[i][j] = q[front].value + j * C + (j - h[i]) * (j - h[i]);
                }
            }
            front = rear = 1;
            for(j = 100; j >= h[i]; --j) {
                tmp.value = dp[i - 1][j] + j * C;
                for( ; front < rear && tmp.value < q[rear - 1].value; --rear);
                q[rear++] = tmp;
                dp[i][j] = min(dp[i][j], q[front].value - j * C + (j - h[i]) * (j - h[i]));
            }
        }
        int res = 0x3f3f3f3f;
        for(i = 1; i <= 100; ++i) {
            res = min(res, dp[N][i]);
        }
        printf("%d
", res);
    }
}