This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#include "fish.h"
using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
typedef long double ld;
const ll I = 1000LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL;
const int II = 2 * 1000 * 1000 * 1000;
const ll M = 1000LL * 1000LL * 1000LL + 7LL;
const int N = 1000 * 1000 + 7;
vector<pair<int, ll>> cat[N];
vector<int> dpv[N];
vector<ll> dp[N][2], sl[N], as[N], sr[N];
void CntS(int n)
{
for(int l = 0; l <= n; ++l)
{
int j1 = 0, j2 = 0, j3 = 0, s1 = 0, s2 = 0, s3 = 0;
//cerr << l << " " << dpv[l].size() << " " << as[l].size() << "\n";
for(int i = 1; i < (int)dpv[l].size(); ++i)
{
while(l > 0 && j1 < (int)cat[l - 1].size() - 1 && cat[l - 1][j1 + 1].st <= dpv[l][i])
{
++j1;
s1 += cat[l - 1][j1].nd;
}
while(j2 < (int)cat[l].size() - 1 && cat[l][j2 + 1].st <= dpv[l][i])
{
++j2;
s2 += cat[l][j2].nd;
}
while(j3 < (int)cat[l + 1].size() - 1 && cat[l + 1][j3 + 1].st <= dpv[l][i])
{
++j3;
s3 += cat[l + 1][j3].nd;
}
//cerr << i << " ";
sl[l][i] = s1; as[l][i] = s2; sr[l][i] = s3;
}
}
}
void Do1()
{
for(int i = 1; i < (int)dpv[1].size(); ++i)
{
dp[1][0][i] = sr[1][i];
//dp[1][2][i] = sr[1][i];
}
}
void CntDP(int n)
{
Do1();
for(int l = 2; l <= n; ++l)
{
for(int i = 1; i < (int)dpv[l].size(); ++i)
{
for(int j = 0; j < (int)dpv[l - 2].size(); ++j)
{
if(dpv[l - 2][j] <= dpv[l][i])
dp[l][0][i] = max(dp[l][0][i], dp[l - 2][0][j] - sr[l - 2][j] + sl[l][i]);
else
dp[l][0][i] = max(dp[l][0][i], dp[l - 2][0][j]);
}
dp[l][1][i] = dp[l][0][i];
for(int j = 0; j < (int)dpv[l - 1].size(); ++j)
{
if(dpv[l - 1][j] <= dpv[l][i])
dp[l][1][i] = max(dp[l][1][i], dp[l - 1][1][j] + sl[l][i] - as[l - 1][j]);
if(dpv[l - 1][j] >= dpv[l][i])
dp[l][0][i] = max(dp[l][0][i], dp[l - 1][0][j] - as[l][i]);
}
dp[l][0][i] = max(dp[l][0][i], dp[l][1][i]) + sr[l][i];
//cerr << l << " " << i << " " << dp[l][0][i] << " " << dp[l][1][i] << "\n";
}
}
}
long long max_weights(int _N, int _M, vector<int> X, vector<int> Y, vector<int> W)
{
int n = _N, m = _M;
for(int i = 0; i < m; ++i)
{X[i] += 1; Y[i] += 1;}
for(int i = 0; i <= n + 1; ++i)
{
dpv[i].pb(0);
cat[i].pb(make_pair(0, 0LL));
}
for(int i = 0; i < m; ++i)
{
cat[X[i]].pb(make_pair(Y[i], W[i]));
if(X[i] > 1)
dpv[X[i] - 1].pb(Y[i]);
if(X[i] < N)
dpv[X[i] + 1].pb(Y[i]);
}
for(int l = 0; l <= n; ++l)
{
sort(cat[l].begin(), cat[l].end());
sort(dpv[l].begin(), dpv[l].end());
vector<int> nw;
for(int i = 0; i < (int)dpv[l].size(); ++i)
if(i == 0 || dpv[l][i] != dpv[l][i - 1])
nw.pb(dpv[l][i]);
dpv[l] = nw;
for(int i = 0; i < (int)dpv[l].size(); ++i)
dp[l][0].pb(0);
dp[l][1] = dp[l][0];
sl[l] = dp[l][0]; as[l] = dp[l][0]; sr[l] = dp[l][0];
}
CntS(n);
CntDP(n);
//cerr << "XD\n";
ll ans = 0LL;
for(int i = 1; i <= n; ++i)
for(int j = 0; j < (int)dpv[i].size(); ++j)
ans = max(ans, dp[i][0][j]);
return ans;
}
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