Problem p03499 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>

//    #include <boost/multiprecision/cpp_int.hpp>
#define int long long
#define inf 1000000007
#define pa pair<int, int>
#define ll long long
#define pal pair<double, double>
#define ppap pair<pa, int>
//  #define PI 3.14159265358979323846
#define paa pair<int, char>
#define mp make_pair
#define pb push_back
#define EPS (1e-10)

int dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
int dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
using namespace std;
class pa3 {
public:
  int x, y, z;
  pa3(int x = 0, int y = 0, int z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    return z < p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    return z > p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};

class pa4 {
public:
  double x;
  int y, z, w;
  pa4(double x = 0, int y = 0, int z = 0, int w = 0) : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    if (z != p.z)
      return z < p.z;
    return w < p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    if (z != p.z)
      return z > p.z;
    return w > p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
public:
  int x, y;
  pa2(int x = 0, int y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2 &p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};

/*
                                            class Point{
                                                public:
                                                double x,y;
                                                Point(double x=0,double
   y=0):x(x),y(y) {} Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                                Point operator - (Point p)
   {return Point(x-p.x,y-p.y);} Point operator * (double a) {return
   Point(x*a,y*a);} Point operator / (double a) {return Point(x/a,y/a);} double
   absv() {return sqrt(norm());} double norm() {return x*x+y*y;} bool operator <
   (const Point &p) const{ return x != p.x ? x<p.x: y<p.y;
                                                }
                                                bool operator == (const Point
   &p) const{ return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                                }
                                            };
                                            typedef Point Vector;
                                     #define pl pair<int,pas>
                                            struct Segment{
                                            Point p1,p2;
                                            };
                                             double dot(Vector a,Vector b){
                                                return a.x*b.x+a.y*b.y;
                                            }
                                            double cross(Vector a,Vector b){
                                                return a.x*b.y-a.y*b.x;
                                            }

                bool parareru(Point a,Point b,Point c,Point d){
                //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd
   "<<cross(a-b,d-c)<<endl; return abs(cross(a-b,d-c))<EPS;
                }
                double distance_ls_p(Point a, Point b, Point c) {
                  if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
                  if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
                  return abs(cross(b-a, c-a)) / (b-a).absv();
                }
                bool is_intersected_ls(Segment a,Segment b) {
                        if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2)
   return false;
                        if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
                //		cout<<"sss"<<endl;
                                if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
                                if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
                                if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
                                if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
                                return false;
                        }
                  else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1,
   b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1,
   a.p2-b.p1) < EPS );
                }

                double segment_dis(Segment a,Segment b){
                        if(is_intersected_ls(a,b))return 0;
                        double r=distance_ls_p(a.p1, a.p2, b.p1);
                        r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
                        r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
                        r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
                        return r;
                }
                Point intersection_ls(Segment a, Segment b) {
                  Point ba = b.p2-b.p1;
                  double d1 = abs(cross(ba, a.p1-b.p1));
                  double d2 = abs(cross(ba, a.p2-b.p1));
                  double t = d1 / (d1 + d2);

                  return a.p1 + (a.p2-a.p1) * t;
                }
 */
string itos(int i) {
  ostringstream s;
  s << i;
  return s.str();
}

int gcd(int v, int b) {
  if (v > b)
    return gcd(b, v);
  if (v == b)
    return b;
  if (b % v == 0)
    return v;
  return gcd(v, b % v);
}

double distans(double x1, double y1, double x2, double y2) {
  double rr = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return sqrt(rr);
}
int mod;

int pr[500010];
int inv[500010];

int beki(int wa, int rr, int warukazu) {
  if (rr == 0)
    return 1 % warukazu;
  if (rr == 1)
    return wa % warukazu;
  if (rr % 2 == 1)
    return ((ll)beki(wa, rr - 1, warukazu) * (ll)wa) % warukazu;
  ll zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
double bekid(double w, int r) {
  if (r == 0)
    return 1.0;
  if (r == 1)
    return w;
  if (r % 2)
    return bekid(w, r - 1) * w;
  double f = bekid(w, r / 2);
  return f * f;
}

int comb(int nn, int rr) {
  int r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}
/*
void gya(int ert){
        pr[0]=1;
        for(int i=1;i<ert;i++){
                pr[i]=(pr[i-1]*i)%mod;
        }
        for(int i=0;i<ert;i++) inv[i]=beki(pr[i],mod-2,mod);

}
*/
//   cin.tie(0);
//	ios::sync_with_stdio(false);
// priority_queue<pa3,vector<pa3>,greater<pa3>> pq;
// sort(ve.begin(),ve.end(),greater<int>());
//----------------kokomade tenpure------------
// vector<double> ans(100000000),ans2(100000000)

int n;
int bu[202000] = {0};
// int dp[2020][2200][2];
deque<pa3> dp[202000];
vector<int> G[202000];
int dep[200200] = {0};
vector<pa> ve;
int fdfs(int r, int d) {
  ve.pb(mp(-d, r));
  int ans = 1;
  dep[r] = d;
  for (auto v : G[r])
    ans += fdfs(v, d + 1);
  bu[r] = ans;

  return ans;
}
int ni[300020];
pa3 marge(pa3 z1, pa3 z2) {
  int x = z1.x * z2.x % inf;
  int y = (z1.x * z2.y % inf + z1.y * z2.x % inf) % inf;

  int zen =
      ((z1.x + z1.y + z1.z) % inf * ((z2.x + z2.y + z2.z) % inf) % inf) % inf;
  int z = (zen + 5ll * inf - x - y) % inf;

  return {x, y, z};
}

void me(deque<pa3> &d0, deque<pa3> &d1, bool b) {
  int l0 = d0.size();
  // int l1=d1.size();

  auto it0 = d0.begin();
  auto it1 = d1.begin();

  for (int i = 0; i < l0; i++) {

    *it1 = marge(*it0, *it1);
    if (b) {
      (*it1).x += (*it1).z;
      (*it1).x %= inf;
      (*it1).z = 0;
    }
    it0++;
    it1++;
  }
  d0.clear();
}

bool hikaku(int l, int r) { return dp[l].size() < dp[r].size(); }

void dfs(int r) {
  if (G[r].size() == 0) {
    dp[r].pb({1, 1, 0});
    return;
  }
  // for(auto v:G[r])dfs(v);
  int l = G[r].size();
  int ima = 0;
  sort(G[r].begin(), G[r].end(), hikaku);
  for (int i = 0; i < l - 1; i++) {
    me(dp[G[r][i]], dp[G[r][i + 1]], i == l - 2);
  }

  swap(dp[r], dp[G[r][l - 1]]);
  for (auto it = dp[r].begin(); it != dp[r].end(); it++) {
    (*it).x += (*it).z;
    (*it).x %= inf;
    (*it).z = 0;
  }
  dp[r].push_front({1, 1, 0});
}
int ko[200020] = {0};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin >> n;
  // assert(n<=2000);

  for (int i = 1; i <= n; i++) {
    int y;
    cin >> y;
    G[y].pb(i);
  }
  ni[0] = 1;
  for (int i = 1; i <= 300000; i++)
    ni[i] = ni[i - 1] * 2 % inf;
  fdfs(0, 0);
  for (int i = 0; i <= n; i++)
    ko[dep[i]]++;
  //  	for(int i=0;i<=n;i++)cout<<bu[i]<<endl;
  sort(ve.begin(), ve.end());
  for (auto v : ve) {
    dfs(v.second);
  }
  // 	dfs(0);
  int ans = 0;
  int r = 0;
  for (auto it = dp[0].begin(); it != dp[0].end(); it++) {
    int ka = (*it).y * ni[n + 1 - ko[r]] % inf;
    ans += ka;
    ans %= inf;

    r++;
  }
  cout << ans << endl;

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>

//    #include <boost/multiprecision/cpp_int.hpp>
#define int long long
#define inf 1000000007
#define pa pair<int, int>
#define ll long long
#define pal pair<double, double>
#define ppap pair<pa, int>
//  #define PI 3.14159265358979323846
#define paa pair<int, char>
#define mp make_pair
#define pb push_back
#define EPS (1e-10)

int dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
int dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
using namespace std;
class pa3 {
public:
  int x, y, z;
  pa3(int x = 0, int y = 0, int z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    return z < p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    return z > p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};

class pa4 {
public:
  double x;
  int y, z, w;
  pa4(double x = 0, int y = 0, int z = 0, int w = 0) : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    if (z != p.z)
      return z < p.z;
    return w < p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    if (z != p.z)
      return z > p.z;
    return w > p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
public:
  int x, y;
  pa2(int x = 0, int y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2 &p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};

/*
                                            class Point{
                                                public:
                                                double x,y;
                                                Point(double x=0,double
   y=0):x(x),y(y) {} Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                                Point operator - (Point p)
   {return Point(x-p.x,y-p.y);} Point operator * (double a) {return
   Point(x*a,y*a);} Point operator / (double a) {return Point(x/a,y/a);} double
   absv() {return sqrt(norm());} double norm() {return x*x+y*y;} bool operator <
   (const Point &p) const{ return x != p.x ? x<p.x: y<p.y;
                                                }
                                                bool operator == (const Point
   &p) const{ return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                                }
                                            };
                                            typedef Point Vector;
                                     #define pl pair<int,pas>
                                            struct Segment{
                                            Point p1,p2;
                                            };
                                             double dot(Vector a,Vector b){
                                                return a.x*b.x+a.y*b.y;
                                            }
                                            double cross(Vector a,Vector b){
                                                return a.x*b.y-a.y*b.x;
                                            }

                bool parareru(Point a,Point b,Point c,Point d){
                //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd
   "<<cross(a-b,d-c)<<endl; return abs(cross(a-b,d-c))<EPS;
                }
                double distance_ls_p(Point a, Point b, Point c) {
                  if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
                  if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
                  return abs(cross(b-a, c-a)) / (b-a).absv();
                }
                bool is_intersected_ls(Segment a,Segment b) {
                        if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2)
   return false;
                        if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
                //		cout<<"sss"<<endl;
                                if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
                                if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
                                if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
                                if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
                                return false;
                        }
                  else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1,
   b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1,
   a.p2-b.p1) < EPS );
                }

                double segment_dis(Segment a,Segment b){
                        if(is_intersected_ls(a,b))return 0;
                        double r=distance_ls_p(a.p1, a.p2, b.p1);
                        r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
                        r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
                        r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
                        return r;
                }
                Point intersection_ls(Segment a, Segment b) {
                  Point ba = b.p2-b.p1;
                  double d1 = abs(cross(ba, a.p1-b.p1));
                  double d2 = abs(cross(ba, a.p2-b.p1));
                  double t = d1 / (d1 + d2);

                  return a.p1 + (a.p2-a.p1) * t;
                }
 */
string itos(int i) {
  ostringstream s;
  s << i;
  return s.str();
}

int gcd(int v, int b) {
  if (v > b)
    return gcd(b, v);
  if (v == b)
    return b;
  if (b % v == 0)
    return v;
  return gcd(v, b % v);
}

double distans(double x1, double y1, double x2, double y2) {
  double rr = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return sqrt(rr);
}
int mod;

int pr[500010];
int inv[500010];

int beki(int wa, int rr, int warukazu) {
  if (rr == 0)
    return 1 % warukazu;
  if (rr == 1)
    return wa % warukazu;
  if (rr % 2 == 1)
    return ((ll)beki(wa, rr - 1, warukazu) * (ll)wa) % warukazu;
  ll zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
double bekid(double w, int r) {
  if (r == 0)
    return 1.0;
  if (r == 1)
    return w;
  if (r % 2)
    return bekid(w, r - 1) * w;
  double f = bekid(w, r / 2);
  return f * f;
}

int comb(int nn, int rr) {
  int r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}
/*
void gya(int ert){
        pr[0]=1;
        for(int i=1;i<ert;i++){
                pr[i]=(pr[i-1]*i)%mod;
        }
        for(int i=0;i<ert;i++) inv[i]=beki(pr[i],mod-2,mod);

}
*/
//   cin.tie(0);
//	ios::sync_with_stdio(false);
// priority_queue<pa3,vector<pa3>,greater<pa3>> pq;
// sort(ve.begin(),ve.end(),greater<int>());
//----------------kokomade tenpure------------
// vector<double> ans(100000000),ans2(100000000)

int n;
int bu[202000] = {0};
// int dp[2020][2200][2];
deque<pa3> dp[202000];
vector<int> G[202000];
int dep[200200] = {0};
vector<pa> ve;
int fdfs(int r, int d) {
  ve.pb(mp(-d, r));
  int ans = 1;
  dep[r] = d;
  for (auto v : G[r])
    ans += fdfs(v, d + 1);
  bu[r] = ans;

  return ans;
}
int ni[300020];
pa3 marge(pa3 z1, pa3 z2) {
  int x = z1.x * z2.x % inf;
  int y = (z1.x * z2.y % inf + z1.y * z2.x % inf) % inf;

  int zen =
      ((z1.x + z1.y + z1.z) % inf * ((z2.x + z2.y + z2.z) % inf) % inf) % inf;
  int z = (zen + 5ll * inf - x - y) % inf;

  return {x, y, z};
}

void me(deque<pa3> &d0, deque<pa3> &d1, bool b) {
  int l0 = d0.size();
  // int l1=d1.size();

  auto it0 = d0.begin();
  auto it1 = d1.begin();

  for (int i = 0; i < l0; i++) {

    *it1 = marge(*it0, *it1);
    if (b) {
      (*it1).x += (*it1).z;
      (*it1).x %= inf;
      (*it1).z = 0;
    }
    it0++;
    it1++;
  }
  d0.clear();
}

bool hikaku(int l, int r) { return dp[l].size() < dp[r].size(); }

void dfs(int r) {
  if (G[r].size() == 0) {
    dp[r].pb({1, 1, 0});
    return;
  }
  // for(auto v:G[r])dfs(v);
  int l = G[r].size();
  int ima = 0;
  sort(G[r].begin(), G[r].end(), hikaku);
  for (int i = 0; i < l - 1; i++) {
    me(dp[G[r][i]], dp[G[r][i + 1]], i == l - 2);
  }

  swap(dp[r], dp[G[r][l - 1]]);

  dp[r].push_front({1, 1, 0});
}
int ko[200020] = {0};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin >> n;
  // assert(n<=2000);

  for (int i = 1; i <= n; i++) {
    int y;
    cin >> y;
    G[y].pb(i);
  }
  ni[0] = 1;
  for (int i = 1; i <= 300000; i++)
    ni[i] = ni[i - 1] * 2 % inf;
  fdfs(0, 0);
  for (int i = 0; i <= n; i++)
    ko[dep[i]]++;
  //  	for(int i=0;i<=n;i++)cout<<bu[i]<<endl;
  sort(ve.begin(), ve.end());
  for (auto v : ve) {
    dfs(v.second);
  }
  // 	dfs(0);
  int ans = 0;
  int r = 0;
  for (auto it = dp[0].begin(); it != dp[0].end(); it++) {
    int ka = (*it).y * ni[n + 1 - ko[r]] % inf;
    ans += ka;
    ans %= inf;

    r++;
  }
  cout << ans << endl;

  return 0;
}