Problem p02709 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;

/**** Type Define ****/

typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<ll, P> Q;

/**** Const List   ****/

const ll INF = 1LL << 60;
const ll mod = 1000000007;
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, -1, 0, 1};
const ll NCK_MAX = 510000;
/**** General Functions ****/
ll ketawa(ll n) {
  ll a = 0;
  while (n != 0) {
    a += n % 10;
    n /= 10;
  }
  return a;
}
ll RepeatSquaring(ll N, ll P, ll M) { // pow->double
  if (P == 0)
    return 1;
  if (P % 2 == 0) {
    ll t = RepeatSquaring(N, P / 2, M);
    return (t % M) * (t % M) % M;
  }
  return (N * RepeatSquaring(N, P - 1, M)) % M;
}
ll RS(ll N, ll P) { // modがだるいときにつかう
  if (P == 0)
    return 1;
  if (P % 2 == 0) {
    ll t = RS(N, P / 2);
    return t * t;
  }
  return (N * RS(N, P - 1));
}
map<ll, int> prime_factor(ll n) {
  map<ll, int> ret;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1)
    ret[n] = 1;
  return ret;
}
bool IsPrime(ll a) { // order root a
  if (a == 1)
    return false;
  for (int i = 2; i * i <= a; i++) {
    if (a % i == 0 && a != i) {
      return false;
    }
  }
  return true;
}
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

ll extgcd(ll a, ll b, ll &x, ll &y) {
  if (b == 0) {
    x = 1, y = 0;
    return a;
  }
  ll q = a / b, g = extgcd(b, a - q * b, x, y);
  ll z = x - q * y;
  x = y;
  y = z;
  return g;
}

ll invmod(ll a, ll m) { // a^-1 mod m
  ll x, y;
  extgcd(a, m, x, y);
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

ll *fac, *finv, *inv;

void nCk_init(ll mod) {
  fac = new ll[NCK_MAX];
  finv = new ll[NCK_MAX];
  inv = new ll[NCK_MAX];
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (ll i = 2; i < NCK_MAX; i++) {
    fac[i] = fac[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    finv[i] = finv[i - 1] * inv[i] % mod;
  }
}

ll nCk(ll n, ll k, ll mod) {
  if (fac == NULL)
    nCk_init(mod);
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

ll lmin(ll a, ll b) { return a > b ? b : a; };

ll lmax(ll a, ll b) { return a > b ? a : b; };

ll lsum(ll a, ll b) { return a + b; };

/**** Zip ****/

template <typename T> class Zip {
  vector<T> d;
  bool flag;

public:
  Zip() { flag = false; }
  void add(T x) {
    d.push_back(x);
    flag = true;
  }
  ll getNum(T x) { // T need to have operator < !!
    if (flag) {
      sort(d.begin(), d.end());
      d.erase(unique(d.begin(), d.end()), d.end());
      flag = false;
    }
    return lower_bound(d.begin(), d.end(), x) - d.begin();
  }
  ll size() {
    if (flag) {
      sort(d.begin(), d.end());
      d.erase(unique(d.begin(), d.end()), d.end());
      flag = false;
    }
    return (ll)d.size();
  }
};

/**** Union Find ****/

class UnionFind {
  vector<ll> par, rank; // par > 0: number, par < 0: -par
public:
  void init(ll n) {
    par.resize(n, 1);
    rank.resize(n, 0);
  }
  ll getSize(ll x) { return par[find(x)]; }
  ll find(ll x) {
    if (par[x] > 0)
      return x;
    return -(par[x] = -find(-par[x]));
  }
  void merge(ll x, ll y) {
    x = find(x);
    y = find(y);
    if (x == y)
      return;
    if (rank[x] < rank[y]) {
      par[y] += par[x];
      par[x] = -y;
    } else {
      par[x] += par[y];
      par[y] = -x;
      if (rank[x] == rank[y])
        rank[x]++;
    }
  }
  bool isSame(ll x, ll y) { return find(x) == find(y); }
};

/**** Segment Tree ****/
class SegmentTree {
public:
  vector<pair<double, double>> node; // node[0]は使用しない
  ll n; // データの個数(nodeの最下層には何個並んでいるか)
  pair<double, double> initial_value; // 初期値
public:
  void Init(ll n_, pair<double, double> initial_value_) {
    n = 1;
    while (n < n_)
      n *= 2;
    node.resize(2 * n);
    for (ll i = 0; i < 2 * n; i++) {
      node[i] = initial_value_;
    }
    initial_value = initial_value_;
  }
  void Update(ll k, pair<double, double> a) {
    // node[k]をaにする
    // それに従って先祖も変わっていく
    k += n;
    node[k] = a;
    while (k > 1) {
      k = k / 2;
      node[k] = pair<double, double>(
          node[k * 2].first * node[k * 2 + 1].first,
          node[k * 2].second * node[k * 2 + 1].first + node[k * 2 + 1].second);
    }
  }
  /*void Watch(){
    for(ll i=0;i<2*n;i++){
      cout<<node[i]<<endl;
    }
  }*/
  double Query() { //[a,b)
    return node[1].first + node[1].second;
  }
};

/**** LIS ****/
ll lis(ll *a, ll n, ll *dp) {
  fill(dp, dp + n, INF); // INFを代入
  for (ll i = 0; i < n; i++)
    *lower_bound(dp, dp + n, a[i]) = a[i];
  return (ll)(lower_bound(dp, dp + n, INF) - dp);
}

/**** main function ****/
ll n, k;
ll ans;
ll seki[2000];
ll saidaiti[2001][2001];
vector<P> ch;
ll tansaku(ll hidari, ll migi, ll value) {
  // cout<<hidari<<" "<<migi<<" "<<value<<endl;
  if (saidaiti[hidari][migi] > value) {
    return 0;
  } else {
    saidaiti[hidari][migi] = value;
  }
  if (hidari + migi == n) {
    ans = lmax(ans, value);
    return 0;
  }
  ll index = hidari + migi;
  tansaku(hidari + 1, migi,
          value + ch[index].first * labs(ch[index].second - hidari));
  tansaku(hidari, migi + 1,
          value + ch[index].first * labs(ch[index].second - (n - 1 - migi)));
  return 0;
}
int main() {
  cin >> n;
  for (ll i = 0; i < n; i++) {
    ll aa;
    cin >> aa;
    ch.push_back(P(aa, i));
  }
  sort(ch.begin(), ch.end(), greater<P>());
  // tansaku(0,0,0);
  for (ll i = 0; i < n; i++) {
    for (ll j = 0; j <= i; j++) { // hidari j migi i-j
      saidaiti[j + 1][i - j] =
          lmax(saidaiti[j + 1][i - j],
               saidaiti[j][i - j] + ch[i].first * labs(ch[i].second - j));
      saidaiti[j][i - j + 1] =
          lmax(saidaiti[j][i - j + 1],
               saidaiti[j][i - j] +
                   ch[i].first * labs(ch[i].second - (n - 1 - i + j)));
    }
  }
  for (ll i = 0; i <= n; i++) {
    ans = lmax(ans, saidaiti[i][n - i]);
  }
  cout << ans << endl;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;

/**** Type Define ****/

typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<ll, P> Q;

/**** Const List   ****/

const ll INF = 1LL << 60;
const ll mod = 1000000007;
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, -1, 0, 1};
const ll NCK_MAX = 510000;
/**** General Functions ****/
ll ketawa(ll n) {
  ll a = 0;
  while (n != 0) {
    a += n % 10;
    n /= 10;
  }
  return a;
}
ll RepeatSquaring(ll N, ll P, ll M) { // pow->double
  if (P == 0)
    return 1;
  if (P % 2 == 0) {
    ll t = RepeatSquaring(N, P / 2, M);
    return (t % M) * (t % M) % M;
  }
  return (N * RepeatSquaring(N, P - 1, M)) % M;
}
ll RS(ll N, ll P) { // modがだるいときにつかう
  if (P == 0)
    return 1;
  if (P % 2 == 0) {
    ll t = RS(N, P / 2);
    return t * t;
  }
  return (N * RS(N, P - 1));
}
map<ll, int> prime_factor(ll n) {
  map<ll, int> ret;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1)
    ret[n] = 1;
  return ret;
}
bool IsPrime(ll a) { // order root a
  if (a == 1)
    return false;
  for (int i = 2; i * i <= a; i++) {
    if (a % i == 0 && a != i) {
      return false;
    }
  }
  return true;
}
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

ll extgcd(ll a, ll b, ll &x, ll &y) {
  if (b == 0) {
    x = 1, y = 0;
    return a;
  }
  ll q = a / b, g = extgcd(b, a - q * b, x, y);
  ll z = x - q * y;
  x = y;
  y = z;
  return g;
}

ll invmod(ll a, ll m) { // a^-1 mod m
  ll x, y;
  extgcd(a, m, x, y);
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

ll *fac, *finv, *inv;

void nCk_init(ll mod) {
  fac = new ll[NCK_MAX];
  finv = new ll[NCK_MAX];
  inv = new ll[NCK_MAX];
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (ll i = 2; i < NCK_MAX; i++) {
    fac[i] = fac[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    finv[i] = finv[i - 1] * inv[i] % mod;
  }
}

ll nCk(ll n, ll k, ll mod) {
  if (fac == NULL)
    nCk_init(mod);
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

ll lmin(ll a, ll b) { return a > b ? b : a; };

ll lmax(ll a, ll b) { return a > b ? a : b; };

ll lsum(ll a, ll b) { return a + b; };

/**** Zip ****/

template <typename T> class Zip {
  vector<T> d;
  bool flag;

public:
  Zip() { flag = false; }
  void add(T x) {
    d.push_back(x);
    flag = true;
  }
  ll getNum(T x) { // T need to have operator < !!
    if (flag) {
      sort(d.begin(), d.end());
      d.erase(unique(d.begin(), d.end()), d.end());
      flag = false;
    }
    return lower_bound(d.begin(), d.end(), x) - d.begin();
  }
  ll size() {
    if (flag) {
      sort(d.begin(), d.end());
      d.erase(unique(d.begin(), d.end()), d.end());
      flag = false;
    }
    return (ll)d.size();
  }
};

/**** Union Find ****/

class UnionFind {
  vector<ll> par, rank; // par > 0: number, par < 0: -par
public:
  void init(ll n) {
    par.resize(n, 1);
    rank.resize(n, 0);
  }
  ll getSize(ll x) { return par[find(x)]; }
  ll find(ll x) {
    if (par[x] > 0)
      return x;
    return -(par[x] = -find(-par[x]));
  }
  void merge(ll x, ll y) {
    x = find(x);
    y = find(y);
    if (x == y)
      return;
    if (rank[x] < rank[y]) {
      par[y] += par[x];
      par[x] = -y;
    } else {
      par[x] += par[y];
      par[y] = -x;
      if (rank[x] == rank[y])
        rank[x]++;
    }
  }
  bool isSame(ll x, ll y) { return find(x) == find(y); }
};

/**** Segment Tree ****/
class SegmentTree {
public:
  vector<pair<double, double>> node; // node[0]は使用しない
  ll n; // データの個数(nodeの最下層には何個並んでいるか)
  pair<double, double> initial_value; // 初期値
public:
  void Init(ll n_, pair<double, double> initial_value_) {
    n = 1;
    while (n < n_)
      n *= 2;
    node.resize(2 * n);
    for (ll i = 0; i < 2 * n; i++) {
      node[i] = initial_value_;
    }
    initial_value = initial_value_;
  }
  void Update(ll k, pair<double, double> a) {
    // node[k]をaにする
    // それに従って先祖も変わっていく
    k += n;
    node[k] = a;
    while (k > 1) {
      k = k / 2;
      node[k] = pair<double, double>(
          node[k * 2].first * node[k * 2 + 1].first,
          node[k * 2].second * node[k * 2 + 1].first + node[k * 2 + 1].second);
    }
  }
  /*void Watch(){
    for(ll i=0;i<2*n;i++){
      cout<<node[i]<<endl;
    }
  }*/
  double Query() { //[a,b)
    return node[1].first + node[1].second;
  }
};

/**** LIS ****/
ll lis(ll *a, ll n, ll *dp) {
  fill(dp, dp + n, INF); // INFを代入
  for (ll i = 0; i < n; i++)
    *lower_bound(dp, dp + n, a[i]) = a[i];
  return (ll)(lower_bound(dp, dp + n, INF) - dp);
}

/**** main function ****/
ll n, k;
ll ans;
ll seki[2000];
ll saidaiti[2000][2000];
vector<P> ch;
ll tansaku(ll hidari, ll migi, ll value) {
  // cout<<hidari<<" "<<migi<<" "<<value<<endl;
  if (saidaiti[hidari][migi] > value) {
    return 0;
  } else {
    saidaiti[hidari][migi] = value;
  }
  if (hidari + migi == n) {
    ans = lmax(ans, value);
    return 0;
  }
  ll index = hidari + migi;
  tansaku(hidari + 1, migi,
          value + ch[index].first * labs(ch[index].second - hidari));
  tansaku(hidari, migi + 1,
          value + ch[index].first * labs(ch[index].second - (n - 1 - migi)));
  return 0;
}
int main() {
  cin >> n;
  for (ll i = 0; i < n; i++) {
    ll aa;
    cin >> aa;
    ch.push_back(P(aa, i));
  }
  sort(ch.begin(), ch.end(), greater<P>());
  tansaku(0, 0, 0);
  cout << ans << endl;
}