Problem p03973 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <bitset>
#include <cassert>
#include <ciso646>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> T;
typedef vector<ll> vec;

inline bool check(ll x, ll y, ll xMax, ll yMax) {
  return x >= 0 && y >= 0 && xMax > x && yMax > y;
}
inline int toint(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string tostring(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T> inline T sqr(T x) { return x * x; }
template <class T> inline T mypow(T x, ll n) {
  T res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x;
    x = x * x;
    n >>= 1;
  }
  return res;
}
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

#define For(i, a, b) for (ll(i) = (a); i < (b); (i)++)
#define rep(i, n) For(i, 0, n)
#define rFor(i, a, b) for (ll(i) = (a - 1); i >= (b); (i)--)
#define rrep(i, n) rFor(i, n, 0)
#define each(i, n) for (auto &i : n)
#define clr(a) memset((a), 0, sizeof(a))
#define mclr(a) memset((a), -1, sizeof(a))
#define all(a) (a).begin(), (a).end()
#define sz(a) (sizeof(a))
#define tostr(a) tostring(a)
#define dump(val) cerr << #val " = " << val << endl;
#define Fill(a, v) fill((int *)a, (int *)(a + (sz(a) / sz(*(a)))), v)

const ll dx[8] = {1, 0, -1, 0, 1, 1, -1, -1},
         dy[8] = {0, -1, 0, 1, -1, 1, -1, 1};

const ll mod = 1e9 + 7;
const ll INF = 1e17 + 9;

#define int ll
#define double ld

int n;
map<int, int> dp[100001];
int a[100001];

int solve(int i, int ma) {
  if (dp[i].count(ma)) {
    return dp[i][ma];
  }
  if (i == n) {
    return 0;
  }
  if (a[i] <= ma + 1) {
    return dp[i][ma] = solve(i + 1, max(a[i], ma));
  }

  int res = 0;
  for (int t = 1; t <= ma + 1; t++) { // t残す
    int r = a[i] - t;
    int ad = r / (ma + 1);
    if (ad) {
      res = max(res, solve(i + 1, max(t, ma)) + ad);
    }
  }
  return dp[i][ma] = res;
}

signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  cin >> n;

  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  cout << solve(0, 0) << endl;

  return 0;
}

Fixed submission:
#include <algorithm>
#include <bitset>
#include <cassert>
#include <ciso646>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> T;
typedef vector<ll> vec;

inline bool check(ll x, ll y, ll xMax, ll yMax) {
  return x >= 0 && y >= 0 && xMax > x && yMax > y;
}
inline int toint(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string tostring(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T> inline T sqr(T x) { return x * x; }
template <class T> inline T mypow(T x, ll n) {
  T res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x;
    x = x * x;
    n >>= 1;
  }
  return res;
}
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

#define For(i, a, b) for (ll(i) = (a); i < (b); (i)++)
#define rep(i, n) For(i, 0, n)
#define rFor(i, a, b) for (ll(i) = (a - 1); i >= (b); (i)--)
#define rrep(i, n) rFor(i, n, 0)
#define each(i, n) for (auto &i : n)
#define clr(a) memset((a), 0, sizeof(a))
#define mclr(a) memset((a), -1, sizeof(a))
#define all(a) (a).begin(), (a).end()
#define sz(a) (sizeof(a))
#define tostr(a) tostring(a)
#define dump(val) cerr << #val " = " << val << endl;
#define Fill(a, v) fill((int *)a, (int *)(a + (sz(a) / sz(*(a)))), v)

const ll dx[8] = {1, 0, -1, 0, 1, 1, -1, -1},
         dy[8] = {0, -1, 0, 1, -1, 1, -1, 1};

const ll mod = 1e9 + 7;
const ll INF = 1e17 + 9;

#define int ll
#define double ld

int n;
map<int, int> dp[100001];
int a[100001];

int solve(int i, int ma) {
  if (dp[i].count(ma)) {
    return dp[i][ma];
  }
  if (i == n) {
    return 0;
  }
  if (a[i] <= ma + 1) {
    return dp[i][ma] = solve(i + 1, max(a[i], ma));
  }

  int res = 0;
  int r = a[i] - 1;
  int ad = r / (ma + 1);
  if (ad) {
    res = max(res, solve(i + 1, max(1ll, ma)) + ad);
  }
  return dp[i][ma] = res;
}

signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  cin >> n;

  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  cout << solve(0, 0) << endl;

  return 0;
}