Problem p03301 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <bitset>
#include <cassert>
#include <ciso646>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;

// #define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop                                                                   \
  char nyaa;                                                                   \
  cin >> nyaa;
#define rep(i, n) for (int i = 0; i < n; i++)
#define per(i, n) for (int i = n - 1; i >= 0; i--)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define per1(i, n) for (int i = n; i >= 1; i--)
#define Rep1(i, sta, n) for (int i = sta; i <= n; i++)
#define all(v) (v).begin(), (v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n) {
  ll res = 1;
  while (n) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}
struct modint {
  ll n;
  modint() : n(0) { ; }
  modint(ll m) : n(m) {
    if (n >= mod)
      n %= mod;
    else if (n < 0)
      n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint &a, modint b) {
  a.n += b.n;
  if (a.n >= mod)
    a.n -= mod;
  return a;
}
modint operator-=(modint &a, modint b) {
  a.n -= b.n;
  if (a.n < 0)
    a.n += mod;
  return a;
}
modint operator*=(modint &a, modint b) {
  a.n = ((ll)a.n * b.n) % mod;
  return a;
}
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
  if (n == 0)
    return modint(1);
  modint res = (a * a) ^ (n / 2);
  if (n % 2)
    res = res * a;
  return res;
}

ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); }
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
  fact[0] = modint(1);
  for (int i = 0; i < max_n - 1; i++) {
    fact[i + 1] = fact[i] * modint(i + 1);
  }
  factinv[max_n - 1] = modint(1) / fact[max_n - 1];
  for (int i = max_n - 2; i >= 0; i--) {
    factinv[i] = factinv[i + 1] * modint(i + 1);
  }
}
modint comb(int a, int b) {
  if (a < 0 || b < 0 || a < b)
    return 0;
  return fact[a] * factinv[b] * factinv[a - b];
}

struct Node {
  Node *lch, *rch;
  int l, r;
  P cl, cr;
  Node(int l, int r) : l(l), r(r), cl({l, mod}), lch(NULL), rch(NULL){};
};

void add(Node *nd, int x, int y) {
  int l = nd->l, r = nd->r;
  if (r - l == 1) {
    if (nd->cl.second == mod) {
      nd->cl = {x, y};
      nd->cr = {x, y};
    } else {
      if (nd->cl.second < y) {
        nd->cl = {x, y};
        nd->cr = {x, y};
      }
    }
    return;
  }
  int m = (l + r) / 2;
  if (x < m) {
    if (nd->lch == NULL) {
      nd->lch = new Node(l, m);
    }
    add(nd->lch, x, y);
  } else {
    if (nd->rch == NULL) {
      nd->rch = new Node(m, r);
    }
    add(nd->rch, x, y);
  }
  if (nd->lch == NULL) {
    nd->cl = nd->rch->cl;
    nd->cr = nd->rch->cr;
  } else if (nd->rch == NULL) {
    nd->cl = nd->lch->cl;
    nd->cr = nd->lch->cr;
  } else {
    vector<P> vs;
    vector<P> v = {nd->lch->cl, nd->lch->cr, nd->rch->cl, nd->rch->cr};
    rep(i, 4) {
      while (vs.size() && vs.back().second <= v[i].second)
        vs.pop_back();
      vs.push_back(v[i]);
    }
    nd->cl = vs[0];
    nd->cr = vs.back();
  }
}
int query(Node *nd, int ad) {
  if (nd->r - nd->l == 1) {
    return min(nd->l, nd->cl.second + ad);
  }

  if (nd->lch == NULL)
    return query(nd->rch, ad);
  else if (nd->rch == NULL)
    return query(nd->lch, ad);
  else {
    return max(query(nd->lch, ad), query(nd->rch, ad));
  }
}

void solve() {
  int n;
  cin >> n;
  vector<int> a(n);
  int sum = 0;
  rep(i, n) {
    cin >> a[i];
    sum += a[i];
  }
  if (n % 2 == 0) {
    int s1 = 0, s2 = 0;
    for (int i = 0; i < n; i += 2) {
      s1 += a[i];
    }
    for (int i = 1; i < n; i += 2) {
      s2 += a[i];
    }
    int ans1 = max(s1, s2);
    cout << ans1 << " " << sum - ans1 << "\n";
    return;
  }

  int ad = 0;
  Node *nd = new Node(0, mod + 1);
  add(nd, mod, 0);

  vector<int> memo(n + 2);
  memo[0] = mod;

  int ex = 0;
  for (int i = 1; i < n; i += 2)
    ex += a[i];

  for (int i = 2; i <= n + 1; i += 2) {
    if (i >= 4) {
      ad += a[i - 2] - a[i - 3];
    }
    memo[i] = min(memo[i - 2], ex + a[i - 2]);
    memo[i] = max(memo[i], query(nd, ad));
    add(nd, memo[i - 2], ex + a[i - 2] - ad);
  }

  int ans = memo[n + 1];
  cout << ans << " " << sum - ans << "\n";
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  // cout << fixed << setprecision(10);
  // init();
  // int t; cin >> t; rep(i, t)
  solve();
  return 0;
}


Fixed submission:
#include <algorithm>
#include <bitset>
#include <cassert>
#include <ciso646>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;

// #define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop                                                                   \
  char nyaa;                                                                   \
  cin >> nyaa;
#define rep(i, n) for (int i = 0; i < n; i++)
#define per(i, n) for (int i = n - 1; i >= 0; i--)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define per1(i, n) for (int i = n; i >= 1; i--)
#define Rep1(i, sta, n) for (int i = sta; i <= n; i++)
#define all(v) (v).begin(), (v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n) {
  ll res = 1;
  while (n) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}
struct modint {
  ll n;
  modint() : n(0) { ; }
  modint(ll m) : n(m) {
    if (n >= mod)
      n %= mod;
    else if (n < 0)
      n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint &a, modint b) {
  a.n += b.n;
  if (a.n >= mod)
    a.n -= mod;
  return a;
}
modint operator-=(modint &a, modint b) {
  a.n -= b.n;
  if (a.n < 0)
    a.n += mod;
  return a;
}
modint operator*=(modint &a, modint b) {
  a.n = ((ll)a.n * b.n) % mod;
  return a;
}
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
  if (n == 0)
    return modint(1);
  modint res = (a * a) ^ (n / 2);
  if (n % 2)
    res = res * a;
  return res;
}

ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); }
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
  fact[0] = modint(1);
  for (int i = 0; i < max_n - 1; i++) {
    fact[i + 1] = fact[i] * modint(i + 1);
  }
  factinv[max_n - 1] = modint(1) / fact[max_n - 1];
  for (int i = max_n - 2; i >= 0; i--) {
    factinv[i] = factinv[i + 1] * modint(i + 1);
  }
}
modint comb(int a, int b) {
  if (a < 0 || b < 0 || a < b)
    return 0;
  return fact[a] * factinv[b] * factinv[a - b];
}

struct Node {
  Node *lch, *rch;
  int l, r;
  P cl, cr;
  Node(int l, int r) : l(l), r(r), cl({l, mod}), lch(NULL), rch(NULL){};
};

void add(Node *nd, int x, int y) {
  int l = nd->l, r = nd->r;
  if (r - l == 1) {
    if (nd->cl.second == mod) {
      nd->cl = {x, y};
      nd->cr = {x, y};
    } else {
      if (nd->cl.second < y) {
        nd->cl = {x, y};
        nd->cr = {x, y};
      }
    }
    return;
  }
  int m = (l + r) / 2;
  if (x < m) {
    if (nd->lch == NULL) {
      nd->lch = new Node(l, m);
    }
    add(nd->lch, x, y);
  } else {
    if (nd->rch == NULL) {
      nd->rch = new Node(m, r);
    }
    add(nd->rch, x, y);
  }
  if (nd->lch == NULL) {
    nd->cl = nd->rch->cl;
    nd->cr = nd->rch->cr;
  } else if (nd->rch == NULL) {
    nd->cl = nd->lch->cl;
    nd->cr = nd->lch->cr;
  } else {
    vector<P> vs;
    vector<P> v = {nd->lch->cl, nd->lch->cr, nd->rch->cl, nd->rch->cr};
    rep(i, 4) {
      while (vs.size() && vs.back().second <= v[i].second)
        vs.pop_back();
      vs.push_back(v[i]);
    }
    nd->cl = vs[0];
    nd->cr = vs.back();
  }
}
int query(Node *nd, int ad) {
  if (nd->cr.first <= nd->cr.second + ad) {
    return nd->cr.first;
  }
  if (nd->cl.first >= nd->cl.second + ad) {
    return nd->cl.second + ad;
  }
  if (nd->r - nd->l == 1) {
    return min(nd->l, nd->cl.second + ad);
  }

  if (nd->lch == NULL)
    return query(nd->rch, ad);
  else if (nd->rch == NULL)
    return query(nd->lch, ad);
  else {
    return max(query(nd->lch, ad), query(nd->rch, ad));
  }
}

void solve() {
  int n;
  cin >> n;
  vector<int> a(n);
  int sum = 0;
  rep(i, n) {
    cin >> a[i];
    sum += a[i];
  }
  if (n % 2 == 0) {
    int s1 = 0, s2 = 0;
    for (int i = 0; i < n; i += 2) {
      s1 += a[i];
    }
    for (int i = 1; i < n; i += 2) {
      s2 += a[i];
    }
    int ans1 = max(s1, s2);
    cout << ans1 << " " << sum - ans1 << "\n";
    return;
  }

  int ad = 0;
  Node *nd = new Node(0, mod + 1);
  add(nd, mod, 0);

  vector<int> memo(n + 2);
  memo[0] = mod;

  int ex = 0;
  for (int i = 1; i < n; i += 2)
    ex += a[i];

  for (int i = 2; i <= n + 1; i += 2) {
    if (i >= 4) {
      ad += a[i - 2] - a[i - 3];
    }
    memo[i] = min(memo[i - 2], ex + a[i - 2]);
    memo[i] = max(memo[i], query(nd, ad));
    add(nd, memo[i - 2], ex + a[i - 2] - ad);
  }

  int ans = memo[n + 1];
  cout << ans << " " << sum - ans << "\n";
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  // cout << fixed << setprecision(10);
  // init();
  // int t; cin >> t; rep(i, t)
  solve();
  return 0;
}