Box Stack II

// #ifdef ONLINE_JUDGE
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// #endif
#include "bits/stdc++.h"
#define fast ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define fill(arr,val) memset(arr,val,sizeof(arr))
#define FOR(i, a, b) for(__typeof(b) i = a, _b = b; i <= _b; ++i)
#define FORD(i, a, b) for(__typeof(a) i = a, _b = b; i >= _b; --i)
#define ALL(a) (a).begin(), (a).end()
#define YES cout << "YES\n"
#define NO cout << "NO\n"
#define ll long long
#define fi first
#define se second
#define pb push_back
#define pf push_front
#define ii pair<int,int>
#define iii pair<int,pair<int,int>>
#define dq deque<int>
#define nend '\n'
using namespace std;

const ll inf = 1e18;
const int dx[] = {1,0,-1,0};
const int dy[] = {0,1,0,-1};
const int MOD = 1e9 + 7;
const ll hashi = 2e9 + 11;

inline ll add(ll a, ll b) { return (a + b) % MOD; }
inline ll sub(ll a, ll b) { return ((a - b) % MOD + MOD) % MOD; }
inline ll mul(ll a, ll b) { return (a * b) % MOD; }

inline ll binpow(ll a, ll b) {
    ll res = 1;
    a %= MOD;
    while (b > 0) {
        if (b & 1) res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return res;
}

inline ll modInverse(ll n) {
    return binpow(n, MOD - 2);
}

inline ll modDivide(ll a, ll b) {
    return (a % MOD * modInverse(b)) % MOD;
}

ll extended_gcd(ll a, ll b, ll& x, ll& y) {
    if (b == 0) {
        x = 1; y = 0;
        return a;
    }
    ll x1, y1;
    ll d = extended_gcd(b, a % b, x1, y1);
    x = y1;
    y = x1 - y1 * (a / b);
    return d;
}

void init_code() {
    fast;
    // #ifndef ONLINE_JUDGE
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    // #endif
}
/// boxes Stack II: pick boxess that can sit on each other (x and y both
/// non-decreasing going up), maximize sum of heights z
/// -> sort by x asc, then it is "max weight non-decreasing
///    subsequence in y": dp[i] = z[i] + max{ dp[j] : j before i, y[j] <= y[i] }
/// ties in x are safe: xi <= xj allows equal x, and inside the same x we
/// sorted by y asc, so any earlier j in that block has y[j] <= y[i]
/// Segment tree point update = max, query = prefmax
const int N=2e5+5;
const int S=N*4+5;
int n,m;
ll st[S];
struct boxes {
    int x,y;
    ll z;
} b[N];
bool cmp(const boxes &p, const boxes &q) {
    if (p.x!=q.x) return p.x<q.x;
    return p.y<q.y;
}
void update(int pos, ll val, int id=1, int l=1, int r=m) {
    if (pos<l||pos>r) return;
    if (l==r) {
        st[id]=max(st[id],val); ///keep the best tower ending with this y
        return;
    }
    int mid=(l+r)>>1;
    update(pos,val,id*2,l,mid);
    update(pos,val,id*2+1,mid+1,r);
    st[id]=max(st[id*2],st[id*2+1]);
}
ll get(int u, int v, int id=1, int l=1, int r=m) {
    if (r<u||l>v) return 0;
    if (l>=u&&r<=v) return st[id];
    int mid=(l+r)>>1;
    return max(get(u,v,id*2,l,mid),get(u,v,id*2+1,mid+1,r));
}
void solve() {
    cin >> n;
    vector<int> ys;
    FOR(i,1,n) {
        cin >> b[i].x >> b[i].y >> b[i].z;
        ys.pb(b[i].y);
    }
    sort(ALL(ys));
    ys.erase(unique(ALL(ys)),ys.end());
    m=ys.size();
    sort(b+1,b+n+1,cmp);
    ll res=0;
    FOR(i,1,n) {
        int p=lower_bound(ALL(ys),b[i].y)-ys.begin()+1;
        ll dp=b[i].z+get(1,p); ///best tower that hav top boxes has y <= this y
        update(p,dp);
        res=max(res,dp);
    }
    cout << res << nend;
}
int main() {
    init_code();

    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }

}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED

Test 70

Verdict: ACCEPTED

Test 71

Verdict: ACCEPTED

Test 72

Verdict: ACCEPTED

Test 73

Verdict: ACCEPTED