NYOJ 309

男娘i 2022-06-16 03:08 145阅读 0赞

## BOBSLEDDING ##

时间限制： 1000 ms  |  内存限制： 65535 KB

难度： 3

描述

Dr.Kong has entered a bobsled competition because he hopes his hefty weight will give his an advantage over the L meter course (2 <= L<= 1000). Dr.Kong will push off the starting line at 1 meter per second, but his speed can change while he rides along the course. Near the middle of every meter Bessie travels, he can change his speed either by using gravity to accelerate by one meter per second or by braking to stay at the same speed or decrease his speed by one meter per second.

Naturally, Dr.Kong must negotiate N (1 <= N <= 500) turns on the way down the hill. Turn i is located T\_i  meters from the course start (1 <= T\_i <= L-1), and  he must be enter the corner meter at  a peed of at most S\_i  meters per second (1 <= S\_i <= 1000).  Dr.Kong can cross the finish line at any speed he likes.

Help Dr.Kong learn the fastest speed he can attain without exceeding the speed limits on the turns.

Consider this course with the meter markers as integers and the  turn speed limits in brackets (e.g., '\[3\]'):

0    1   2   3   4   5   6   7\[3\]   8   9  10  11\[1\]  12   13\[8\]    14

(Start) |------------------------------------------------------------------------|  (Finish)

Below is a chart of  Dr.Kong 's speeds at the beginning of each meter length of the course:

Max:                               \[3\]             \[1\]      \[8\]

Mtrs:   0   1   2   3   4   5   6   7   8   9  10  11  12   13   14

Spd:    1   2   3   4   5   5   4   3   4   3   2   1   2   3    4

His maximum speed was 5 near the beginning of meter 4.

输入

There are multi test cases,your program should be terminated by EOF  
Line 1: Two space-separated integers: L and N  
Lines 2..N+1: Line i+1 describes turn i with two space-separated integers: T\_i and S\_i

输出

Line 1: A single integer, representing the maximum speed which Dr.Kong can attain between the start and the finish line, inclusive.

样例输入

14 3                                            
    7 3
    11 1
    13 8

样例输出

题目的意思是说有一段滑雪路长L,有n个拐点，每个拐点要求速度不超过s\[i\]，且这个人从0开始，只能每秒加速1M或者减速1M求在符合要求的情况下，在这个途中

最大的速度能够达到多少，典型的背包题。

#include<iostream>
    #include<cstdlib>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    #include<cmath>
    using namespace std;
    int main()
    {
        int dp[1005];
        int l,n,a,b;
        while(scanf("%d%d",&l,&n)!=EOF)
        {
            memset(dp,0,sizeof(dp));   //每次循环必须重置啊啊啊啊啊啊啊啊啊啊
            for(int i=0; i<n; i++)
            {
                scanf("%d%d",&a,&b);
                dp[a]=b;             //记录每个拐点的限速
            }
            int s=0;                 //刚开始一定要赋值0，如果此时s=1下面从i=1开始就会漏掉1的时候
            for(int i=0; i<=l; i++)
            {
                if(dp[i]==0)
                    dp[i]=s+1;            //没有拐点就一直加速
                else
                {
                    if(dp[i]>dp[i-1])
                    {
                        dp[i]=dp[i-1]+1;
                    }
                    else
                    {
                        int p=i;              //如果是拐点就往前查找看到哪里能够符合要求通过
                        while(dp[p-1]-dp[p]>1)
                        {
                            dp[p-1]=dp[p]+1;
                            p--;
                        }
                    }
                }
                s=dp[i];
            }
            int max=-3;        //最后求出最大值即可
            for(int i=0; i<=l; i++)
            {
                if(max<dp[i])
                    max=dp[i];
            }
            printf("%d\n",max);
        }
        return 0;
    }