Submission #652284

#	Time	Username	Problem	Language	Result	Execution time	Memory
652284		alvinpiter	Gondola (IOI14_gondola)	C++17	65 / 100	58 ms	5348 KiB

gondola

#include "gondola.h"
#include<bits/stdc++.h>
using namespace std;
#define LL long long int
#define MOD 1000000009

LL fastExponentiation(LL base, LL p) {
  if (p == 0)
    return 1;

  LL half = fastExponentiation(base, p/2);
  LL halfhalf = (half * half)%MOD;

  if (p % 2 == 0)
    return halfhalf;
  else
    return (halfhalf * base)%MOD;
}

/*
* If there is a duplicated gondola, return 0.
* If all gondolas are > n, return 1.
* Otherwise, find the position of one of the original gondola, let this be idxOfOriginalGondola.
  Start from idxOfOriginalGondola, go around the circle and make sure all other original gondolas
  are in place.
*/
int valid(int n, int gondolas[]) {
  set<int> uniqGondolas;
  int idxOfOriginalGondola = -1;

  for (int i = 0; i < n; i++) {
    uniqGondolas.insert(gondolas[i]);
    if (gondolas[i] <= n) {
      idxOfOriginalGondola = i;
    }
  }

  if (uniqGondolas.size() < n) {
    return 0;
  }

  if (idxOfOriginalGondola == -1) {
    return 1;
  }

  for (int i = idxOfOriginalGondola, step = 0; step < n; i = (i + 1)%n, step++) {
    if (gondolas[i] <= n && gondolas[i] != (gondolas[idxOfOriginalGondola] - 1 + step)%n + 1) {
      return 0;
    }
  }

  return 1;
}

/*
* For each of the given gondola, find the original gondola that it replaces. Here's how:
  - If there is an original gondola, then just go around the circle starting from it.
  - If there is no original gondola, then we assume the original gondolas were ordered from 1 to n.
* Process the new gondolas starting from the smallest-numbered one. For example, there is a gondola numbered
  10 which replaces gondola 4. Then the replacement sequence will be:
  4 -> <lastUsedGondola + 1> -> <lastUsedGondola + 2> -> ... -> 9

  lastUsedGondola initially equals to n, and updated accordingly.
*/
int replacement(int n, int gondolas[], int replacementSeq[])
{
  int idxOfOriginalGondola = -1;
  for (int i = 0; i < n; i++) {
    if (gondolas[i] <= n) {
      idxOfOriginalGondola = i;
      break;
    }
  }

  vector<pair<int, int> > newGondolasWithOriginal;
  if (idxOfOriginalGondola == -1) {
    for (int i = 0; i < n; i++) {
      newGondolasWithOriginal.push_back({gondolas[i], i + 1});
    }
  } else {
    for (int i = idxOfOriginalGondola, step = 0; step < n - 1; i = (i + 1)%n, step++) {
      if (gondolas[i] > n) {
        newGondolasWithOriginal.push_back({gondolas[i], (gondolas[idxOfOriginalGondola] - 1 + step)%n + 1});
      }
    }
  }

  sort(newGondolasWithOriginal.begin(), newGondolasWithOriginal.end());

  int cntReplacement = 0;
  int lastUsedGondola = n;
  for (auto [newGondola, originalGondola]: newGondolasWithOriginal) {
    replacementSeq[cntReplacement++] = originalGondola;
    for (int g = lastUsedGondola + 1; g < newGondola; g++) {
      replacementSeq[cntReplacement++] = g;
    }

    lastUsedGondola = newGondola;
  }

  return cntReplacement;
}

int countReplacement(int n, int gondolas[]) {
  if (!valid(n, gondolas)) {
    return 0;
  }

  vector<int> largerThanN;
  for (int i = 0; i < n; i++) {
    if (gondolas[i] > n) {
      largerThanN.push_back(gondolas[i]);
    }
  }

  int cntReplaced = largerThanN.size();

  sort(largerThanN.begin(), largerThanN.end());

  vector<int> gapSizes;
  for (int i = 0; i < largerThanN.size(); i++) {
    int prev = (i == 0 ? n : largerThanN[i - 1]);
    int gapSize = largerThanN[i] - prev - 1;
    gapSizes.push_back(gapSize);
  }

  // cout << "cntReplaced: " << cntReplaced << endl;
  // cout << "gapSizes:"; for (auto gapSize: gapSizes) cout << " " << gapSize;
  // cout << endl;

  LL result = 1;
  for (int i = 0; i < gapSizes.size(); i++) {
    // cout << "hihi " << cntReplaced - i << " " << gapSizes[i] << endl;
    LL numWays = fastExponentiation(cntReplaced - i, gapSizes[i]);
    // cout << "numWays: " << numWays << endl;
    result = (result * numWays)%MOD;
  }

  if (cntReplaced == n) {
    result = (result * n)%MOD;
  }

  return result;
}

Compilation message (stderr)

gondola.cpp: In function 'int valid(int, int*)':
gondola.cpp:38:27: warning: comparison of integer expressions of different signedness: 'std::set<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   38 |   if (uniqGondolas.size() < n) {
      |       ~~~~~~~~~~~~~~~~~~~~^~~
gondola.cpp: In function 'int countReplacement(int, int*)':
gondola.cpp:121:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  121 |   for (int i = 0; i < largerThanN.size(); i++) {
      |                   ~~^~~~~~~~~~~~~~~~~~~~
gondola.cpp:132:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  132 |   for (int i = 0; i < gapSizes.size(); i++) {
      |                   ~~^~~~~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 5 / 5
• Subtask 3: 10 / 10
• Subtask 4: 0 / 5
• Subtask 5: 0 / 10
• Subtask 6: 0 / 20
• Subtask 7: 5 / 5
• Subtask 8: 15 / 15
• Subtask 9: 15 / 15
• Subtask 10: 10 / 10