Submission #653004

#TimeUsernameProblemLanguageResultExecution timeMemory
653004vladutpieleBigger segments (IZhO19_segments)C++17
13 / 100
1 ms340 KiB
#include <bits/stdc++.h>

#define int long long

using namespace std;

const int nmax = 500000;

int n;
int v[nmax + 5], sume[nmax + 5];

struct elem
{
    int maxSeg; /// in cate segmente impart prefixul [1 ... i]
    int maxPrv; /// capatul stanga al ultimului segment
};

elem dp[nmax + 5];

void update(int a,int b)
{
    if(dp[a].maxSeg < dp[b].maxSeg)
    {
        dp[a] = dp[b];
    }
    else
    {
        if(dp[a].maxSeg == dp[b].maxSeg && dp[a].maxPrv < dp[b].maxPrv)
        {
            dp[a] = dp[b];
        }
    }
}

signed main()
{
    cin >> n;
    for(int i = 1; i <= n; i ++)
    {
        cin >> v[i];
        sume[i] = sume[i - 1] + v[i];
    }
    /// initializare
    for(int i = 1; i <= n; i ++)
    {
        dp[i] = {1, 1};
    }
    /// cum pot sa calculez cel mai usor dp[i].maxPrv?
    /// segmentul [a .... b] este un segment care imbunatateste solutia
    /// daca sume[b] - sume[a - 1] >= sume[a - 1] - sume[dp[a].maxPrv]
    /// relatie echivalenta cu : sume[b] >= 2 * sume[a - 1] - sume[dp[a - 1].maxPrv]
    /// astfel pot sa caut binar valoarea a (cel mai mare a)
    for(int i = 2; i <= n; i ++)
    {
        update(i, i - 1);
        int st = 1, dr = i - 1;
        int maxPrv = 0;
        while(st <= dr)
        {
            int mid = (st + dr) >> 1;
            if(sume[i] >= 2 * sume[mid] - sume[dp[mid].maxPrv - 1])
            {
                maxPrv = mid;
                st = mid + 1;
            }
            else
            {
                dr = mid - 1;
            }
        }
        dp[i].maxSeg = 1 + dp[maxPrv].maxSeg;
        dp[i].maxPrv = maxPrv + 1;
    }
    cout << dp[n].maxSeg << '\n';
    return 0;
}
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