# 动态规划

2019-08-30 21:50栏目：编程

## poj 3666 Making the Grade (动态规划)

 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4647 Accepted: 2202

Description

A straight dirt road connects two fields on FJ's farm, but it changes elevation more than FJ would like. His cows do not mind climbing up or down a single slope, but they are not fond of an alternating succession of hills and valleys. FJ would like to add and remove dirt from the road so that it becomes one monotonic slope (either sloping up or down).

You are given N integers A1, ... , AN (1 ≤ N ≤ 2,000) describing the elevation (0 ≤ Ai ≤ 1,000,000,000) at each of N equally-spaced positions along the road, starting at the first field and ending at the other. FJ would like to adjust these elevations to a new sequence B1, . ... , BN that is either nonincreasing or nondecreasing. Since it costs the same amount of money to add or remove dirt at any position along the road, the total cost of modifying the road is

|A1六合联盟， - B1| |A2 - B2| ... |AN - BN |

Please compute the minimum cost of grading his road so it becomes a continuous slope. FJ happily informs you that signed 32-bit integers can certainly be used to compute the answer.

Input

* Line 1: A single integer: N
* Lines 2..N 1: Line i 1 contains a single integer elevation: Ai

Output

* Line 1: A single integer that is the minimum cost for FJ to grade his dirt road so it becomes nonincreasing or nondecreasing in elevation.

Sample Input

``````7
1
3
2
4
5
3
9
``````

Sample Output

``````3
``````

a[i]存原始数组，b[j]存排序后递增的数组。

dp[i][j]=min(dp[i-1][0..j]) abs(a[i]-b[j]); （把第i 个数高度改为b[j],此时的最小成本。）

``````#include
#include
#include
#include
#include
#include
#include
using namespace std;
#define ll __int64
#define mem(a,t) memset(a,t,sizeof(a))
#define N 2005
const int M=305;
const int inf=0x7fffffff;
int a[N],b[N];
int dp[N];
void solve(int n)
{
int i,j,tmp;
sort(b,b n);
for(i=0;i
``````

3666 Making the Grade (动态规划) Making the Grade Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4647 Accepted: 2202 Description A straight dirt road connects t...

Description

A straight dirt road connects two fields on FJ's farm, but it changes elevation more than FJ would like. His cows do not mind climbing up or down a single slope, but they are not fond of an alternating succession of hills and valleys. FJ would like to add and remove dirt from the road so that it becomes one monotonic slope (either sloping up or down).

You are given N integers A1, ... , AN (1 ≤ N ≤ 2,000) describing the elevation (0 ≤ Ai ≤ 1,000,000,000) at each of N equally-spaced positions along the road, starting at the first field and ending at the other. FJ would like to adjust these elevations to a new sequence B1, . ... , BN that is either nonincreasing or nondecreasing. Since it costs the same amount of money to add or remove dirt at any position along the road, the total cost of modifying the road is

 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 5797 Accepted: 2714

|A1 - B1| |A2 - B2| ... |AN - BN |
Please compute the minimum cost of grading his road so it becomes a continuous slope. FJ happily informs you that signed 32-bit integers can certainly be used to compute the answer.

Description

Input

A straight dirt road connects two fields on FJ's farm, but it changes elevation more than FJ would like. His cows do not mind climbing up or down a single slope, but they are not fond of an alternating succession of hills and valleys. FJ would like to add and remove dirt from the road so that it becomes one monotonic slope (either sloping up or down).

• Line 1: A single integer: N
• Lines 2..N 1: Line i 1 contains a single integer elevation: Ai

You are given N integers A1, ... , AN (1 ≤ N ≤ 2,000) describing the elevation (0 ≤ Ai ≤ 1,000,000,000) at each of N equally-spaced positions along the road, starting at the first field and ending at the other. FJ would like to adjust these elevations to a new sequence B1, . ... , BN that is either nonincreasing or nondecreasing. Since it costs the same amount of money to add or remove dirt at any position along the road, the total cost of modifying the road is

Output

|A1 - B1| |A2 - B2| ... |AN - BN |

• Line 1: A single integer that is the minimum cost for FJ to grade his dirt road so it becomes nonincreasing or nondecreasing in elevation.

Please compute the minimum cost of grading his road so it becomes a continuous slope. FJ happily informs you that signed 32-bit integers can certainly be used to compute the answer.

Sample Input

Input

7
1
3
2
4
5
3
9
Sample Output

* Line 1: A single integer: N
* Lines 2..N 1: Line i 1 contains a single integer elevation: Ai

3

Output

* Line 1: A single integer that is the minimum cost for FJ to grade his dirt road so it becomes nonincreasing or nondecreasing in elevation.

Sample Input

``````7
1
3
2
4
5
3
9
``````

Sample Output

``````3
``````

Source

USACO 2008 February Gold  ``````/*

f[i,j]表示第i段路升高到是s[j]，abs(h[i]-s[j])为原高度与ans对应高度的差

o(n3)要tle的节奏。

g[i,j]=min(g[i,j-1],f[i,j])。

*/
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#define N 2010
using namespace std;
int s[N],h[N],n,res=2137483648;
int f[N][N],g[N][N];
int cmp(int a,int b){
return a>b;
}
void dp(){
for(int i=1;i<=n;i  ){
for(int j=1;j<=n;j  ){
f[i][j]=g[i-1][j] abs(h[i]-s[j]);
if(j==1) g[i][j]=f[i][j];
else g[i][j]=min(g[i][j-1],f[i][j]);
}
}
for(int i=1;i<=n;i  ){
res=min(res,f[n][i]);
}
}
int main(){
scanf("%d",&n);
for(int i=1;i<=n;i  ){
scanf("%d",h i);s[i]=h[i];
}
sort(s 1,s n 1);dp();
sort(s 1,s n 1,cmp);dp();
printf("%dn",res);
return 0;
}
``````