Problem p01545 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define INF 1 << 27
#define all(n) n.begin(), n.end()
#define insert(a, b, c, d) PP(P(a, b), P(c, d))
#define F first
#define S second
#define pb push_back
#define MAX_N 100100
#define foreach(i, c) for (iter(c) i = (c).begin(); i != (c).end(); ++i)
using namespace std;
typedef pair<int, int> P;
typedef pair<P, P> PP;
typedef long long ll;

template <class T> class RMQ_segment {
private:
  int n;
  T dat[2 * MAX_N - 1];

public:
  void init(int n_) {
    n = 1;
    while (n < n_)
      n *= 2;
    for (int i = 0; i < 2 * n - 1; i++)
      dat[i] = 0;
  }

  void update(int k, T a) {
    k += n - 1;
    dat[k] = a;
    while (k > 0) {
      k = (k - 1) / 2;
      dat[k] = max(dat[k * 2 + 1], dat[k * 2 + 2]);
    }
  }

  T query(int a, int b, int k, int l, int r) {
    if (r <= a || b <= l)
      return 0;
    else if (a <= l && r <= b)
      return dat[k];

    T vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
    T vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
    return max(vl, vr);
  }

  T _query(int a, int b) { // nの範囲でミスしないように極力こっちを利用
    return query(a, b, 0, 0, n);
  }
};

int x[1000010];
RMQ_segment<ll> rmq;
int main() {
  int n;
  cin >> n;

  rmq.init(n + 1);

  rep(i, n) cin >> x[i];
  ll mex = 0;
  ll sum = 0;

  for (int i = 0; i < n; i++) {
    sum += x[i];
    ll premex = rmq._query(0, x[i]) + x[i];
    rmq.update(x[i], premex);
    mex = max(mex, premex);
  }

  cout << sum - mex << endl;

  return 0;
}

Fixed submission:
#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define INF 1 << 27
#define all(n) n.begin(), n.end()
#define insert(a, b, c, d) PP(P(a, b), P(c, d))
#define F first
#define S second
#define pb push_back
#define MAX_N (1 << 18)
#define foreach(i, c) for (iter(c) i = (c).begin(); i != (c).end(); ++i)
using namespace std;
typedef pair<int, int> P;
typedef pair<P, P> PP;
typedef long long ll;

template <class T> class RMQ_segment {
private:
  int n;
  T dat[2 * MAX_N - 1];

public:
  void init(int n_) {
    n = 1;
    while (n < n_)
      n *= 2;
    for (int i = 0; i < 2 * n - 1; i++)
      dat[i] = 0;
  }

  void update(int k, T a) {
    k += n - 1;
    dat[k] = a;
    while (k > 0) {
      k = (k - 1) / 2;
      dat[k] = max(dat[k * 2 + 1], dat[k * 2 + 2]);
    }
  }

  T query(int a, int b, int k, int l, int r) {
    if (r <= a || b <= l)
      return 0;
    else if (a <= l && r <= b)
      return dat[k];

    T vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
    T vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
    return max(vl, vr);
  }

  T _query(int a, int b) { // nの範囲でミスしないように極力こっちを利用
    return query(a, b, 0, 0, n);
  }
};

int x[1000010];
RMQ_segment<ll> rmq;
int main() {
  int n;
  cin >> n;

  rmq.init(n + 1);

  rep(i, n) cin >> x[i];
  ll mex = 0;
  ll sum = 0;

  for (int i = 0; i < n; i++) {
    sum += x[i];
    ll premex = rmq._query(0, x[i]) + x[i];
    rmq.update(x[i], premex);
    mex = max(mex, premex);
  }

  cout << sum - mex << endl;

  return 0;
}