5 seconds
256 megabytes
standard input
standard output
Sonya was unable to think of a story for this problem, so here comes the formal description.
You are given the array containing n positive integers. At one turn you can pick any element and increase or decrease it by 1. The goal is the make the array strictly increasing by making the minimum possible number of operations. You are allowed to change elements in any way, they can become negative or equal to 0.
The first line of the input contains a single integer n (1 ≤ n ≤ 3000) — the length of the array.
Next line contains n integer ai (1 ≤ ai ≤ 109).
Print the minimum number of operation required to make the array strictly increasing.
7
2 1 5 11 5 9 11
9
5
5 4 3 2 1
12
In the first sample, the array is going to look as follows:
2 3 5 6 7 9 11
|2 - 2| + |1 - 3| + |5 - 5| + |11 - 6| + |5 - 7| + |9 - 9| + |11 - 11| = 9
And for the second sample:
1 2 3 4 5
|5 - 1| + |4 - 2| + |3 - 3| + |2 - 4| + |1 - 5| = 12
题意：求一个序列变为严格递增序列的最小花费。
思路：这题和POJ3666本质相似，POJ3666求的是非严格递增，在这题的条件下，我们只要将a[i]-i预处理，再按照相同的做法就可以保证严格递增了。QD某校赛比赛时候看到这题就觉得好像，结果一直没有想出来怎么改，POJ那题还是最近做过的呐。/.\另外这题还可以用优先队列做...
/** @Date : 2016-11-26-17.16
* @Author : Lweleth (SoungEarlf@gmail.com)
* @Link : https://github.com/
* @Version :
*/ #include<bits/stdc++.h>
#define LL long long
#define MMF(x) memset((x),0,sizeof(x))
#define MMI(x) memset((x), INF, sizeof(x))
using namespace std; const int INF = 0x3f3f3f3f;
const int N = 1e5+2000; int a[3030];
int b[3030];
LL dp[3030][3030];
int main()
{
int n;
while(~scanf("%d", &n))
{
MMF(dp);
for(int i = 1; i <= n; i++)
{
scanf("%d", a + i);
a[i] -= i;
b[i] = a[i];
}
sort(b + 1, b + 1 + n);
for(int i = 1; i <= n; i++)
{
dp[i][1] = dp[i - 1][1] + abs(a[i] - b[1]);
for(int j = 2; j <= n; j++)
{
dp[i][j] = min(dp[i - 1][j] + abs(a[i] - b[j]), dp[i][j - 1]);
}
}
printf("%lld\n", dp[n][n]);
}
return 0;
}