Submission #988436

#	Time	Username	Problem	Language	Result	Execution time	Memory
988436		GrindMachine	Skyscraper (JOI16_skyscraper)	C++17	100 / 100	563 ms	347016 KiB

skyscraper

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif

/*

refs:
https://usaco.guide/problems/joi-2016skyscraper/solution
read it long back, recollected the ideas from there when solving the problem

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

void solve(int test_case)
{
    ll n,m; cin >> n >> m;
    vector<ll> a(n+5);
    rep1(i,n) cin >> a[i];
    sort(a.begin()+1,a.begin()+n+1);
    a[n+1] = inf1;

    if(n == 1){
        cout << 1 << endl;
        return;
    }

    ll dp[n+5][n+5][m+5][2][2];
    memset(dp,0,sizeof dp);
    dp[1][0][0][0][0] = 1;

    rep1(i,n){
        ll d = a[i+1]-a[i];

        rep(j,n+1){
            rep(k,m+1){
                rep(x,2){
                    rep(y,2){
                        dp[i][j][k][x][y] %= MOD;
                        ll val = dp[i][j][k][x][y];

                        // new
                        {
                            ll spaces = 2*(j+1)-x-y;
                            ll k2 = k+spaces*d;
                            if(k2 >= 0 and k2 <= m){
                                dp[i+1][j+1][k2][x][y] += val;
                            }
                        }

                        // connect to 1 comp
                        {
                            ll spaces = 2*j-x-y;
                            ll k2 = k+spaces*d;
                            if(k2 >= 0 and k2 <= m){
                                dp[i+1][j][k2][x][y] += val*spaces;
                            }
                        }

                        // connect to 2 comps
                        {
                            ll spaces = 2*(j-1)-x-y;
                            ll k2 = k+spaces*d;
                            if(k2 >= 0 and k2 <= m){
                                ll ways = 0;

                                // both non-spl
                                ways += (j-x-y)*(j-x-y-1);
                                amax(ways,0ll);

                                // x
                                if(x){
                                    ways += j-1;
                                }

                                // y
                                if(y){
                                    ways += j-1;
                                }

                                // x and y
                                if(x and y){
                                    if(i == n) ways--;
                                    else ways -= 2;
                                }

                                dp[i+1][j-1][k2][x][y] += val*ways;
                            }
                        }

                        // left end
                        if(!x){
                            // new
                            {
                                ll spaces = 2*(j+1)-(x|1)-y;
                                ll k2 = k+spaces*d;
                                if(k2 >= 0 and k2 <= m){
                                    dp[i+1][j+1][k2][x|1][y] += val;
                                }
                            }

                            // connect to 1 comp
                            {
                                ll spaces = 2*j-(x|1)-y;
                                ll k2 = k+spaces*d;
                                ll ways = j;
                                if(y and i != n) ways--; 
                                if(k2 >= 0 and k2 <= m){
                                    dp[i+1][j][k2][x|1][y] += val*ways;
                                }
                            }
                        }

                        // right end
                        if(!y){
                            // new
                            {
                                ll spaces = 2*(j+1)-x-(y|1);
                                ll k2 = k+spaces*d;
                                if(k2 >= 0 and k2 <= m){
                                    dp[i+1][j+1][k2][x][y|1] += val;
                                }
                            }

                            // connect to 1 comp
                            {
                                ll spaces = 2*j-x-(y|1);
                                ll k2 = k+spaces*d;
                                ll ways = j;
                                if(x and i != n) ways--;
                                if(k2 >= 0 and k2 <= m){
                                    dp[i+1][j][k2][x][y|1] += val*ways;
                                }
                            }
                        }      
                    }
                }
            }
        }
    }

    ll ans = 0;
    rep(k,m+1){
        ans += dp[n+1][1][k][1][1];
    }

    ans %= MOD;
    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

• Subtask 1: 5 / 5
• Subtask 2: 15 / 15
• Subtask 3: 80 / 80