Submission #550126

#	Time	Username	Problem	Language	Result	Execution time	Memory
550126		theshadow_04	Skyscraper (JOI16_skyscraper)	C++14	15 / 100	280 ms	269812 KiB

skyscraper

#include <bits/stdc++.h>

#define Task "CF"
#define MOD 1000000007
#define pb push_back

using namespace std;

const int maxn = 200005;

int n, l;
int a[maxn];

void Sub1() {
  vector<int> v;
  for(int i = 1; i <= n; ++i) v.pb(i);
  int ans = 0;
  do {
    long long res = 0;
    for(int i = 0; i < (int) v.size() - 1; ++ i) res += abs(a[v[i + 1]] - a[v[i]]);
    if(res <= l) ++ ans;
    if(ans > MOD) ans -= MOD;
  } while(next_permutation(v.begin(), v.end()));
  cout << ans << "\n";
}

namespace Sub2 {

  long long dp[(1 << 14) + 5][20][105];

  void solve() {
    memset(dp, 0, sizeof dp);
    for(int i = 0; i < n; ++ i) {
      dp[(1 << i)][i][0] = 1;
    }
    for(int mask = 0; mask < (1 << n); ++ mask) {
      for(int last = 0; last < n; ++ last) {
        for(int s = 0; s <= l; ++ s) {
          if(dp[mask][last][s] == 0 || !(mask >> last & 1)) continue;
          for(int nex = 0; nex < n; ++ nex) {
            if((mask >> nex & 1) || s + abs(a[last] - a[nex]) > l) continue;
            (dp[mask + (1 << nex)][nex][s + abs(a[last] - a[nex])] += dp[mask][last][s]) %= MOD;
          }
        }
      }
    }
    long long ans = 0;
    for(int last = 0; last < n; ++ last) {
      for(int s = 0; s <= l; ++ s) {
        (ans += dp[(1 << n) - 1][last][s]) %= MOD;
      }
    }
    cout << ans << "\n";
  }

}

// connected component DP / USACE code
namespace Full {

  long long dp[102][102][1002][3];

  /*
  dp[i][j][k][l] : 
  i - number of numbers placed
  j - number of connected components
  k - total sum currently (filling empty spaces with a_{i} (0-indexed)
  l - number of endpoints that are filled
  */

  void solve() {
    sort(a + 1, a + n + 1);
    a[n + 1] = 10000;
    dp[0][0][0][0] = 1;
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= i; j++) {
        for (int k = 0; k <= l; k++) {
          for (int m = 0; m <= 2; m++) {
            int cost_diff = (2 * j - m) * (a[i + 1] - a[i]);
            if (cost_diff > k || i + j + 1 - m > n) continue;

            // Case 1
            dp[i][j][k][m] += dp[i - 1][j - 1][k - cost_diff][m];
            // Case 2
            if (m) dp[i][j][k][m] += (3 - m) * dp[i - 1][j - 1][k - cost_diff][m - 1];
            // Case 3
            dp[i][j][k][m] += (2 * j - m) * dp[i - 1][j][k - cost_diff][m];
            // Case 4
            if (m == 1) dp[i][j][k][m] += 2 * j * dp[i - 1][j][k - cost_diff][m - 1];
            if (m == 2) {
              if (i == n) dp[i][j][k][m] += dp[i - 1][j][k - cost_diff][m - 1];
              else if (j > 1) dp[i][j][k][m] += (j - 1) * dp[i - 1][j][k - cost_diff][m - 1];
            }
            // Case 5
            if (m == 2) {
              if (i == n) dp[i][j][k][m] += dp[i - 1][j + 1][k - cost_diff][m];
              else dp[i][j][k][m] += j * (j - 1) * dp[i - 1][j + 1][k - cost_diff][m];
            } else if (m == 1) dp[i][j][k][m] += j * j * dp[i - 1][j + 1][k - cost_diff][m];
            else dp[i][j][k][m] += j * (j + 1) * dp[i - 1][j + 1][k - cost_diff][m];

            dp[i][j][k][m] %= MOD;
          }
        }
      }
    }

    long long ans = 0;
    for (int i = 0; i <= l; i++) ans += dp[n][1][i][2];
    cout << ans % MOD;
  }
}

void Solve(int Test) {
  cin >> n >> l;
  for(int i = 0; i < n; ++ i) cin >> a[i];
  if(n <= 8) {
    Sub1();
    return;
  }
  if(n <= 14 && l <= 100) {
    Sub2::solve();
  } else {
    Full::solve();
  }
}

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  if(fopen(Task".inp", "r")) {
    freopen(Task".inp", "r", stdin);
    freopen(Task".out", "w", stdout);
  }
  int test = 1;
  // cin >> test;
  for(int i = 1; i <= test; ++ i) {
    Solve(i);
  }
}

/*no pain no gain*/

Compilation message (stderr)

skyscraper.cpp: In function 'int main()':
skyscraper.cpp:131:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  131 |     freopen(Task".inp", "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
skyscraper.cpp:132:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  132 |     freopen(Task".out", "w", stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 0 / 5
• Subtask 2: 15 / 15
• Subtask 3: 0 / 80