Problem p02603 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <iostream>
using namespace std;

long long N, A[87];
long long dp[87];

int main() {
  cin >> N;
  for (int i = 1; i <= N; i++)
    cin >> A[i];

  dp[1] = 1000;
  for (int i = 2; i <= N; i++) {
    dp[i] = dp[i - 1];
    for (int j = 1; j <= i - 1; j++) {
      long long V = dp[j] / A[j];
      long long W = dp[j] + (A[i] - A[j]) * V;
      dp[i] = max(dp[i], W);
    }
  }
  cout << dp[N] << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#include <functional> // for less
#include <iostream>
#define ll long long
#define ull unsigned long long
#define ld long double
#define all(ar) ar.begin(), ar.end()
#define mp make_pair
#define sot(bello) bello.begin(), bello.end()
#define bitc __builtin_popcountl
#define fr(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define frr(i, a, b) for (int i = (a), _b = (b); i >= _b; i--)
#define rep(i, n) for (int i = 0, _n = (n); i < _n; i++)
#define repr(i, n) for (int i = n - 1; i >= 0; i--)
#define fill(ar, val) rep(i, sizeof(ar) / sizeof(ll)) ar[i] = val
#define fill0(ar) fill((ar), 0)
#define foreach(it, ar)                                                        \\
  for (typeof(ar.begin()) it = ar.begin(); it != ar.end(); it++)
#define fillinf(ar, n) fr(i, 0, (n)) ar[i] = INF
#define MOD 1000000007
#define MOD1 998244353
#define print(x)                                                               \\
  {                                                                            \\
    cout << x << endl;                                                         \\
    cerr << endl;                                                              \\
    return;                                                                    \\
  }
#define debug(x) cerr << #x << ": " << x << endl
#define arr1d(a, n)                                                            \\
  cout << #a << " : ";                                                         \\
  fr(_, 1, n) cout << a[_] << ' ';                                             \\
  cout << endl;
#define arr1d0(a, n)                                                           \\
  cout << #a << " : ";                                                         \\
  rep(_, n) cout << a[_] << ' ';                                               \\
  cout << endl;
#define arr2d(a, n, m)                                                         \\
  cout << #a << " :" << endl;                                                  \\
  fr(_, 1, n) {                                                                \\
    fr(__, 1, m) cout << a[_][__] << ' ';                                      \\
    cout << endl;                                                              \\
  }
#define arr2d0(a, n, m)                                                        \\
  cout << #a << " :" << endl;                                                  \\
  rep(_, n) {                                                                  \\
    rep(__, m) cout << a[_][__] << ' ';                                        \\
    cout << endl;                                                              \\
  }
#define clr(a) memset(a, 0, sizeof(a))
#define dbug(x) cerr << #x << ": " << x << " "
auto clk = clock();
#define PI 3.1415926535897932385
#define fi first
#define se second
#define arr1d(a, n)                                                            \\
  cout << #a << " : ";                                                         \\
  fr(_, 1, n) cout << a[_] << ' ';                                             \\
  cout << endl;
#define arr1d0(a, n)                                                           \\
  cout << #a << " : ";                                                         \\
  rep(_, n) cout << a[_] << ' ';                                               \\
  cout << endl;
#define arr2d(a, n, m)                                                         \\
  cout << #a << " :" << endl;                                                  \\
  fr(_, 1, n) {                                                                \\
    fr(__, 1, m) cout << a[_][__] << ' ';                                      \\
    cout << endl;                                                              \\
  }
#define arr2d0(a, n, m)                                                        \\
  cout << #a << " :" << endl;                                                  \\
  rep(_, n) {                                                                  \\
    rep(__, m) cout << a[_][__] << ' ';                                        \\
    cout << endl;                                                              \\
  }

#define INF 1000000000000000000
const ld PI2 = acos(-1) / 2.0l;
const int dx[] = {0, 0, -1, 1}, dy[] = {-1, 1, 0, 0};
const int dx8[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          dy8[] = {-1, 0, 1, 1, 1, 0, -1, -1};
/* This Template is authored by Ankit Anvesh */

using namespace std;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// gcd for negatives too
/* ll gcd(ll a, ll b) {
 if (a == 0) return b;
 if (b == 0) return a;
 if (b < 0) return gcd(a, -1 * b);
 if (a < 0) return gcd(-1 * a, b);
 if (a > b) return gcd(b, a);
 return gcd(b%a, a);
}
 */

// gcd

const ll MAXN = 100010;

ll Gcd(ll a, ll b) {
  if (a % b == 0)
    return b;
  return Gcd(b, a % b);
}
// max
ll Max(ll a, ll b) {
  if (a > b)
    return a;
  return b;
}
// min
ll Min(ll a, ll b) {
  if (a < b)
    return a;
  return b;
}

void kickstartFormat() {
  static int tno = 1;
  cout << "Case #" << tno++ << ": ";
}

void printvector(std::vector<ll> v) {
  for (int i = 0; i < v.size(); ++i) {
    cout << v[i] << " ";
  }
  cout << "" << endl;
}
void printarray(ll a[], ll n) {
  for (ll i = 0; i < n; ++i) {
    cout << a[i] << " ";
  }
  cout << "" << endl;
}

ll findlcm(vector<ll> arr, ll n) {
  // Initialize result
  ll ans = arr[0];

  // ans contains LCM of arr[0], ..arr[i]
  // after i'th iteration,
  for (int i = 1; i < n; i++)
    ans = (((arr[i] * ans)) / (Gcd(arr[i], ans)));

  return ans;
}

ll power(ll x, ll y, ll p) {
  ll res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1)
      res = (res * x) % p;

    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}

ll lowerbound(ll k, vector<ll> v) {
  // lowerbound to be used when first index such that
  //  ar[index]>=k is needed

  ll l = 0;
  ll size = v.size();
  ll r = size - 1;
  ll mid;
  while (l <= r) {
    mid = (l + r) / 2;
    if (v[mid] < k)
      l = mid + 1;
    else {
      r = mid - 1;
    }
  }
  return l;
}

ll upperbound(ll k, vector<ll> v) {
  // lowerbound to be used when first index such that
  //  ar[index]>k is needed
  ll l = 0;
  ll size = v.size();
  ll r = size - 1;
  ll mid;
  while (l <= r) {
    mid = (l + r) / 2;
    if (v[mid] > k)
      r = mid - 1;
    else {
      l = mid + 1;
    }
  }
  return l;
}

ll spf[MAXN];

void sieve() {
  spf[1] = 1;
  for (int i = 2; i < MAXN; i++)
    spf[i] = i;
  for (int i = 4; i < MAXN; i += 2)
    spf[i] = 2;

  for (int i = 3; i * i < MAXN; i++) {
    if (spf[i] == i) {
      for (int j = i * i; j < MAXN; j += i)
        if (spf[j] == j)
          spf[j] = i;
    }
  }
}

// Segment Tree Implementation

// const ll N = 100000;

ll n, m;

// BIT tree
/*
start indexing from 1
ll BIT[100010];
void update(ll x,ll val){

  for (; x <=n ; x +=(x&(-x)) )
     BIT[x]+=val;

}
ll query(ll x){
  ll sum=0;
  for(;x>0;x -= (x&(-x)) )
    sum+=BIT[x];
  return sum;

}*/

// Dijkstra's Algorithm
//  if x->y (weight=w) then v[x].push_back(mp(y,w));

vector<ll> shortPath(vector<pair<ll, ll>> v[], ll src, ll V = 0) {
  set<pair<ll, ll>> setds;

  ll sizee = V;
  ll IN = INF;
  vector<ll> dist(sizee, IN);
  vector<bool> vis(sizee, false);
  setds.insert(make_pair(0, src));
  dist[src] = 0;

  while (!setds.empty()) {
    pair<ll, ll> tmp = *(setds.begin());
    setds.erase(setds.begin());

    ll u = tmp.second;
    if (vis[u])
      continue;
    vis[u] = true;
    vector<pair<ll, ll>>::iterator i;
    for (auto i = v[u].begin(); i != v[u].end(); ++i) {
      ll v = (*i).first;
      ll weight = (*i).second;
      if (dist[v] > dist[u] + weight) {
        if (dist[v] != INF)
          setds.erase(setds.find(make_pair(dist[v], v)));

        dist[v] = dist[u] + weight;
        setds.insert(make_pair(dist[v], v));
      }
    }
  }
  return dist;
}

ll root(ll a[], ll r) {
  if (a[r] == r) {
    return r;
  } else {
    ll x = root(a, a[r]);
    a[r] = x;
    return x;
  }
}

void unio(ll a[], ll size[], ll x, ll y) {
  x = root(a, x);
  y = root(a, y);
  if (x == y) {
    return;
  }
  if (size[x] >= size[y]) {
    a[y] = x;
    size[x] += size[y];
  } else {
    a[x] = y;
    size[y] += size[x];
  }
}

// Sieve Implementation
/*
for (ll i=2;i<=100005;i++)
        if (p[i]==0)
        for (ll j=2*i;j<=100005;j+=i) p[j]=1; */

// Dfs search

// do not use n , m , N , C

// Using iterators in C++
// set<ll>:: iterator it;
// string to integer stuuu()
// string to long long stoll()
// string to float stof
// string.substr(position,length);
// integer to string to_string();
// intialize 2d vector vector<vector<ll>> dp(105,vector<ll>(105));
// for taking ceil use (num+den-1)/den
// for declaring min heap use this complicated shit
// priority_queue<ll,vector<ll>,greater<ll>> q;

struct as {
  ll a;
  ll b;
  ll c;
};

vector<ll> ar(82);
map<pair<pair<ll, ll>, ll>, ll> ma;

ll f(ll in, ll st, ll cash) {
  if (ma.count({{in, st}, cash})) {
    return ma[{{in, st}, cash}];
  }
  if (in >= n) {
    return cash;
  }
  ll sto = cash / ar[in];
  ll change;
  change = cash % ar[in];
  ll casho = st * ar[in];
  if (in == n - 1) {
    return ma[{{in, st}, cash}] =
               max(f(in + 1, st, cash),
                   max(f(in + 1, sto, change), f(in + 1, 0, casho + cash)));
  }
  return ma[{{in, st}, cash}] =
             max(f(in + 1, st, cash),
                 max(f(in + 1, sto, change), f(in + 1, 0, casho + cash)));

  if (cash == -1) {

    ll cs = st * ar[in];
    if (in == n - 1) {
      return ma[{{in, st}, cash}] = cs;
    }
    ll oi = in;
    return ma[{{in, st}, cash}] = max(f(in + 1, -1, cs), f(in + 1, st, -1));
  }
  if (st == -1) {
    if (in >= n) {
      return ma[{{in, st}, cash}] = cash;
    }
    ll sto = cash / ar[in];
    ll change = cash % ar[in];
    ll oi = in;
    if (in == n - 1) {
      return ma[{{in, st}, cash}] = cash;
    }
    return ma[{{in, st}, cash}] = max(f(in + 1, -1, cash), f(in + 1, sto, -1));
  }
}

void CV(ll txt) {
  cin >> n;
  // ll k;cin>>k;

  fr(i, 0, n - 1) { cin >> ar[i]; }

  ll mx = -1;
  vector<ll> mxx(n);
  repr(i, n) {
    mxx[i] = max(mx, ar[i]);
    mx = max(mx, ar[i]);
  }

  cout << (max(f(1, 1000 / ar[0], 1000 % ar[0]), f(1, 0, 1000))) << endl;
  // debug(f(1,1000/ar[0],-1));
  return;
  vector<ll> prof(n + 4, 0);

  /* repr(i,n){
      if(i==n-1){
          continue;
      }
      ll pro=mxx[i]-ar[i];
      if(pro>0){
          prof[i]=max(prof[i+1],pro);
      }
      else
      {
          prof[i]=prof[i+1];
      }
  } */
  ll mxp = 1000;
  repr(i, n) {
    // buying here first
    ll st = 1;
    ll mxa = 0;
    for (ll j = i + 1; j < n; j++) {
      if (ar[j] > ar[i]) {
        ll po = (ar[j] - ar[i]) * st;
        po += prof[j + 1];
        mxa = max(mxa, po);
        /* for(ll k=j+1;k<n;k++){
           ll st1=po/ar[k];
           ll prf=mxx[k]-ar[k];
           ll po1=mxx[k]*st1;
           mxp=max(mxp,po1);
        } */
      }
    }
    prof[i] = max(prof[i + 1], mxa);
    st = 1000 / ar[i];
    mxp = max((st * prof[i]), mxp);
  }
  print(mxp);

  return;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ll x68 = 1;
  // cin >> x68;
  for (ll vi = 1; vi <= x68; vi++) {
    CV(vi);
  }

  return 0;
}