Language: C++

// ref. https://ei1333.github.io/luzhiled/snippets/dp/hu-tucker.html
// ref. https://www.slideshare.net/secret/N435vV6yFDRsmK
 
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <unordered_map>
#include <vector>
#include <string.h>
#include <set>
 
using namespace std;
 
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
 
template<class T> void printvec(const vector<T>& v) {
  for (auto x : v) { cout << x << " "; }
  cout << endl;
}
template<class T> void printtree(const vector< vector<T> >& tree) {
  for (long long i = 0; i < tree.size(); ++i) {
    cout << i + 1 << ": "; printvec(tree[i]);
  }
}
template<class T, class U> void printmap(const map<T, U>& mp) {
  for (auto x : mp) { cout << x.first << "=>" << x.second << endl; }
}
 
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
 
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define all(s) s.begin(), s.end()
#define sz(x) (ll)(x).size()
#define fr first
#define sc second
#define mp make_pair
#define pb push_back
#define eb emplace_back
 
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> triple;
typedef double D;
typedef vector<ll> vl;
typedef vector<P> vp;
 
const ll INF = 1e18;
const ll MOD = 1000000007;  // 1e9 + 7
 
template<typename T, typename E = T>
struct SkewHeap {
  using G = function< T(T, E) >;
  using H = function< E(E, E) >;
 
  struct Node {
    T key;
    E lazy;
    Node *l, *r;
  };
 
  const bool rev;
  const G g;
  const H h;
 
  SkewHeap(bool rev = false) : g([](const T &a, const E &b) { return a + b; }),
                               h([](const E &a, const E &b) { return a + b; }), rev(rev) {}
 
  SkewHeap(const G &g, const H &h, bool rev = false) : g(g), h(h), rev(rev) {}
 
  Node *propagate(Node *t) {
    if(t->lazy != 0) {
      if(t->l) t->l->lazy = h(t->l->lazy, t->lazy);
      if(t->r) t->r->lazy = h(t->r->lazy, t->lazy);
      t->key = g(t->key, t->lazy);
      t->lazy = 0;
    }
    return t;
  }
 
  Node *merge(Node *x, Node *y) {
    if(!x || !y) return x ? x : y;
    propagate(x), propagate(y);
    if((x->key > y->key) ^ rev) swap(x, y);
    x->r = merge(y, x->r);
    swap(x->l, x->r);
    return x;
  }
 
  void push(Node *&root, const T &key) {
    root = merge(root, new Node({key, 0, nullptr, nullptr}));
  }
 
  T top(Node *root) {
    return propagate(root)->key;
  }
 
  T pop(Node *&root) {
    T top = propagate(root)->key;
    auto *temp = root;
    root = merge(root->l, root->r);
    delete temp;
    return top;
  }
 
  bool empty(Node *root) const {
    return !root;
  }
 
  void add(Node *root, const E &lazy) {
    if(root) {
      root->lazy = h(root->lazy, lazy);
      propagate(root);
    }
  }
 
  Node *makeheap() {
    return nullptr;
  }
};
 
// Hu-Tucker
template<typename Heap, typename T>
T hu_tucker(vector< T > vs, T INF) {
  int N = (int) vs.size();
  Heap heap;
  vector< typename Heap::Node * > hs(N - 1, heap.makeheap());
  vector< int > ls(N), rs(N);
  vector< T > cs(N - 1);
  using pi = pair< T, int >;
  priority_queue< pi, vector< pi >, greater< pi > > que;
  for(int i = 0; i + 1 < N; i++) {
    ls[i] = i - 1;
    rs[i] = i + 1;
    cs[i] = vs[i] + vs[i + 1];
    que.emplace(cs[i], i);
  }
  T ret = 0;
  for(int k = 0; k + 1 < N; k++) {
    T c;
    int i;
    do {
      tie(c, i) = que.top();
      que.pop();
    } while(rs[i] < 0 || cs[i] != c);
 
    bool ml = false, mr = false;
    if(!heap.empty(hs[i]) && vs[i] + heap.top(hs[i]) == c) {
      heap.pop(hs[i]);
      ml = true;
    } else if(vs[i] + vs[rs[i]] == c) {
      ml = mr = true;
    } else {
      auto top = heap.pop(hs[i]);
      if(!heap.empty(hs[i]) && heap.top(hs[i]) + top == c) {
        heap.pop(hs[i]);
      } else {
        mr = true;
      }
    }
    ret += c;
    heap.push(hs[i], c);
    if(ml) vs[i] = INF;
    if(mr) vs[rs[i]] = INF;
 
    if(ml && i > 0) {
      int j = ls[i];
      hs[j] = heap.merge(hs[j], hs[i]);
      rs[j] = rs[i];
      rs[i] = -1;
      ls[rs[j]] = j;
      i = j;
    }
 
    if(mr && rs[i] + 1 < N) {
      int j = rs[i];
      hs[i] = heap.merge(hs[i], hs[j]);
      rs[i] = rs[j];
      rs[j] = -1;
      ls[rs[i]] = i;
    }
    cs[i] = vs[i] + vs[rs[i]];
 
    if(!heap.empty(hs[i])) {
      T top = heap.pop(hs[i]);
      cs[i] = min(cs[i], min(vs[i], vs[rs[i]]) + top);
      if(!heap.empty(hs[i])) cs[i] = min(cs[i], top + heap.top(hs[i]));
      heap.push(hs[i], top);
    }
    que.emplace(cs[i], i);
  }
  return ret;
}
 
int main(int argc, char** argv) {
  cin.tie(NULL);
  cout.tie(NULL);
  ios_base::sync_with_stdio(false);
  //cout << setprecision(10) << fixed;
 
  ll n;
  cin >> n;
  vector<ll> a(n);
  rep(i,n) {
    cin >> a[i];
  }
  cout << hu_tucker<SkewHeap<ll>>(a,INF) << endl;
}
// ref. https://ei1333.github.io/luzhiled/snippets/dp/hu-tucker.html
// ref. https://www.slideshare.net/secret/N435vV6yFDRsmK

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <unordered_map>
#include <vector>
#include <string.h>
#include <set>

using namespace std;

#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl

template<class T> void printvec(const vector<T>& v) {
  for (auto x : v) { cout << x << " "; }
  cout << endl;
}
template<class T> void printtree(const vector< vector<T> >& tree) {
  for (long long i = 0; i < tree.size(); ++i) {
    cout << i + 1 << ": "; printvec(tree[i]);
  }
}
template<class T, class U> void printmap(const map<T, U>& mp) {
  for (auto x : mp) { cout << x.first << "=>" << x.second << endl; }
}

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

#define rep(i, n) for(ll i = 0; i < n; ++i)
#define all(s) s.begin(), s.end()
#define sz(x) (ll)(x).size()
#define fr first
#define sc second
#define mp make_pair
#define pb push_back
#define eb emplace_back

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> triple;
typedef double D;
typedef vector<ll> vl;
typedef vector<P> vp;

const ll INF = 1e18;
const ll MOD = 1000000007;  // 1e9 + 7

template<typename T, typename E = T>
struct SkewHeap {
  using G = function< T(T, E) >;
  using H = function< E(E, E) >;

  struct Node {
    T key;
    E lazy;
    Node *l, *r;
  };

  const bool rev;
  const G g;
  const H h;

  SkewHeap(bool rev = false) : g([](const T &a, const E &b) { return a + b; }),
                               h([](const E &a, const E &b) { return a + b; }), rev(rev) {}

  SkewHeap(const G &g, const H &h, bool rev = false) : g(g), h(h), rev(rev) {}

  Node *propagate(Node *t) {
    if(t->lazy != 0) {
      if(t->l) t->l->lazy = h(t->l->lazy, t->lazy);
      if(t->r) t->r->lazy = h(t->r->lazy, t->lazy);
      t->key = g(t->key, t->lazy);
      t->lazy = 0;
    }
    return t;
  }

  Node *merge(Node *x, Node *y) {
    if(!x || !y) return x ? x : y;
    propagate(x), propagate(y);
    if((x->key > y->key) ^ rev) swap(x, y);
    x->r = merge(y, x->r);
    swap(x->l, x->r);
    return x;
  }

  void push(Node *&root, const T &key) {
    root = merge(root, new Node({key, 0, nullptr, nullptr}));
  }

  T top(Node *root) {
    return propagate(root)->key;
  }

  T pop(Node *&root) {
    T top = propagate(root)->key;
    auto *temp = root;
    root = merge(root->l, root->r);
    delete temp;
    return top;
  }

  bool empty(Node *root) const {
    return !root;
  }

  void add(Node *root, const E &lazy) {
    if(root) {
      root->lazy = h(root->lazy, lazy);
      propagate(root);
    }
  }

  Node *makeheap() {
    return nullptr;
  }
};

// Hu-Tucker
template<typename Heap, typename T>
T hu_tucker(vector< T > vs, T INF) {
  int N = (int) vs.size();
  Heap heap;
  vector< typename Heap::Node * > hs(N - 1, heap.makeheap());
  vector< int > ls(N), rs(N);
  vector< T > cs(N - 1);
  using pi = pair< T, int >;
  priority_queue< pi, vector< pi >, greater< pi > > que;
  for(int i = 0; i + 1 < N; i++) {
    ls[i] = i - 1;
    rs[i] = i + 1;
    cs[i] = vs[i] + vs[i + 1];
    que.emplace(cs[i], i);
  }
  T ret = 0;
  for(int k = 0; k + 1 < N; k++) {
    T c;
    int i;
    do {
      tie(c, i) = que.top();
      que.pop();
    } while(rs[i] < 0 || cs[i] != c);

    bool ml = false, mr = false;
    if(!heap.empty(hs[i]) && vs[i] + heap.top(hs[i]) == c) {
      heap.pop(hs[i]);
      ml = true;
    } else if(vs[i] + vs[rs[i]] == c) {
      ml = mr = true;
    } else {
      auto top = heap.pop(hs[i]);
      if(!heap.empty(hs[i]) && heap.top(hs[i]) + top == c) {
        heap.pop(hs[i]);
      } else {
        mr = true;
      }
    }
    ret += c;
    heap.push(hs[i], c);
    if(ml) vs[i] = INF;
    if(mr) vs[rs[i]] = INF;

    if(ml && i > 0) {
      int j = ls[i];
      hs[j] = heap.merge(hs[j], hs[i]);
      rs[j] = rs[i];
      rs[i] = -1;
      ls[rs[j]] = j;
      i = j;
    }

    if(mr && rs[i] + 1 < N) {
      int j = rs[i];
      hs[i] = heap.merge(hs[i], hs[j]);
      rs[i] = rs[j];
      rs[j] = -1;
      ls[rs[i]] = i;
    }
    cs[i] = vs[i] + vs[rs[i]];

    if(!heap.empty(hs[i])) {
      T top = heap.pop(hs[i]);
      cs[i] = min(cs[i], min(vs[i], vs[rs[i]]) + top);
      if(!heap.empty(hs[i])) cs[i] = min(cs[i], top + heap.top(hs[i]));
      heap.push(hs[i], top);
    }
    que.emplace(cs[i], i);
  }
  return ret;
}

int main(int argc, char** argv) {
  cin.tie(NULL);
  cout.tie(NULL);
  ios_base::sync_with_stdio(false);
  //cout << setprecision(10) << fixed;

  ll n;
  cin >> n;
  vector<ll> a(n);
  rep(i,n) {
    cin >> a[i];
  }
  cout << hu_tucker<SkewHeap<ll>>(a,INF) << endl;
}

Compiler output:
a.cc:239:24: error: redefinition of 'template<class T> void printvec(const std::vector<_Tp>&)'
  239 | template<class T> void printvec(const vector<T>& v) {
      |                        ^~~~~~~~
a.cc:23:24: note: 'template<class T> void printvec(const std::vector<_Tp>&)' previously declared here
   23 | template<class T> void printvec(const vector<T>& v) {
      |                        ^~~~~~~~
a.cc:243:24: error: redefinition of 'template<class T> void printtree(const std::vector<std::vector<_Tp> >&)'
  243 | template<class T> void printtree(const vector< vector<T> >& tree) {
      |                        ^~~~~~~~~
a.cc:27:24: note: 'template<class T> void printtree(const std::vector<std::vector<_Tp> >&)' previously declared here
   27 | template<class T> void printtree(const vector< vector<T> >& tree) {
      |                        ^~~~~~~~~
a.cc:248:33: error: redefinition of 'template<class T, class U> void printmap(const std::map<T, U>&)'
  248 | template<class T, class U> void printmap(const map<T, U>& mp) {
      |                                 ^~~~~~~~
a.cc:32:33: note: 'template<class T, class U> void printmap(const std::map<T, U>&)' previously declared here
   32 | template<class T, class U> void printmap(const map<T, U>& mp) {
      |                                 ^~~~~~~~
a.cc:252:31: error: redefinition of 'template<class T> bool chmax(T&, T)'
  252 | template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
      |                               ^~~~~
a.cc:36:31: note: 'template<class T> bool chmax(T&, T)' previously declared here
   36 | template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
      |                               ^~~~~
a.cc:253:31: error: redefinition of 'template<class T> bool chmin(T&, T)'
  253 | template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
      |                               ^~~~~
a.cc:37:31: note: 'template<class T> bool chmin(T&, T)' previously declared here
   37 | template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
      |                               ^~~~~
a.cc:272:10: error: redefinition of 'const ll INF'
  272 | const ll INF = 1e18;
      |          ^~~
a.cc:56:10: note: 'const ll INF' previously defined here
   56 | const ll INF = 1e18;
      |          ^~~
a.cc:273:10: error: redefinition of 'const ll MOD'
  273 | const ll MOD = 1000000007;  // 1e9 + 7
      |          ^~~
a.cc:57:10: note: 'const ll MOD' previously defined here
   57 | const ll MOD = 1000000007;  // 1e9 + 7
      |          ^~~
a.cc:275:22: error: redefinition of default argument for 'class E'
  275 | template<typename T, typename E = T>
      |                      ^~~~~~~~
a.cc:59:22: note: original definition appeared here
   59 | template<typename T, typename E = T>
      |                      ^~~~~~~~
a.cc:348:3: error: redefinition of 'template<class Heap, class T> T hu_tucker(std::vector<_ValT>, T)'
  348 | T hu_tucker(vector< T > vs, T INF) {
      |   ^~~~~~~~~
a.cc:132:3: note: 'template<class Heap, class T> T hu_tucker(std::vector<_ValT>, T)' previously declared here
  132 | T hu_tucker(vector< T > vs, T INF) {
      |   ^~~~~~~~~
a.cc:419:5: error: redefinition of 'int main(int, char**)'
  419 | int main(int argc, char** argv) {
      |     ^~~~
a.cc:203:5: note: 'int main(int, char**)' previously defined here
  203 | int main(int argc, char** argv) {
      |     ^~~~