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Sonya and Problem Wihtout a Legend
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
分析：要使得严格递增，a[i]=a[i]-i，dp使得他单调不增即可；
代码：
#include <iostream>#include <cstdio>#include <cstdlib>#include <cmath>#include <algorithm>#include <climits>#include <cstring>#include <string>#include <set>#include <map>#include <queue>#include <stack>#include <vector>#include <list>#define rep(i,m,n) for(i=m;i<=n;i++)#define rsp(it,s) for(set<int>::iterator it=s.begin();it!=s.end();it++)#define mod 1000000007#define inf 0x3f3f3f3f#define vi vector<int>#define pb push_back#define mp make_pair#define fi first#define se second#define ll long long#define pi acos(-1.0)#define pii pair<int,int>#define Lson L, mid, rt<<1#define Rson mid+1, R, rt<<1|1const int maxn=3e3+10;using namespace std;ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);}ll qpow(ll p,ll q){ll f=1;while(q){if(q&1)f=f*p;p=p*p;q>>=1;}return f;}int n,m,k,t,a[maxn],b[maxn];ll dp[maxn][maxn];int main(){ int i,j; scanf("%d",&n); rep(i,1,n)scanf("%d",&a[i]),a[i]-=i,b[i]=a[i]; sort(b+1,b+n+1); rep(i,1,n) { ll p=1e18; rep(j,1,n) { p=min(p,dp[i-1][j]); dp[i][j]=p+abs(a[i]-b[j]); } } ll ans=1e18; rep(i,1,n)ans=min(ans,dp[n][i]); printf("%lld\n",ans); //system("Pause"); return 0;}
Sonya and Problem Wihtout a Legend