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poi06_est.cpp
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poi06_est.cpp
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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <time.h>
#include <iostream>
#include <functional>
#include <numeric>
#include <algorithm>
#include <stack>
#include <queue>
#include <deque>
#include <vector>
#include <string>
#include <bitset>
#include <map>
#include <set>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<lint, int> pi;
lint a[2005], dp[2005][2005];
int n, m;
priority_queue<pi, vector<pi>, greater<pi> > pq1[2005], pq2[2005];
int pnt[2005];
int main(){
cin >> m >> n;
m++;
for(int i=1; i<=n; i++){
cin >> a[i];
a[i]++;
a[i] += a[i-1];
}
for(int i=n; i; i--){
for(int j=i; j<=n; j++){
dp[i][j] = 1e18;
if(a[j] - a[i-1] > m) continue;
if(j == n){
dp[i][j] = 0;
continue;
}
while(pnt[j+1] <= n && 2ll * a[j] - a[i-1] > a[pnt[j+1]]){
int k = pnt[j+1];
pq1[j+1].push(pi(dp[j+1][k] - a[k] + 2ll * a[j], k));
pnt[j+1]++;
}
if(!pq1[j+1].empty()){
dp[i][j] = pq1[j+1].top().first - a[i-1];
}
while(!pq2[j+1].empty() && pq2[j+1].top().second < pnt[j+1]){
pq2[j+1].pop();
}
if(!pq2[j+1].empty()){
dp[i][j] = min(dp[i][j], pq2[j+1].top().first + a[i-1]);
}
}
pnt[i] = i;
for(int j=i; j<=n; j++){
pq2[i].push(pi(dp[i][j] + a[j] - 2ll * a[i-1], j));
}
/*for(int j=i; j<=n; j++){
seg1[i].add(j, dp[i][j] - a[j] + 2ll * a[i-1]);
seg2[i].add(j, dp[i][j] + a[j] - 2ll * a[i-1]);
}*/
}
cout << *min_element(dp[1] + 1, dp[1] + n + 1);
}