제출 #652057

#제출 시각아이디문제언어결과실행 시간메모리
652057alvinpiterDetecting Molecules (IOI16_molecules)C++14
100 / 100
64 ms8656 KiB
/* WLOG, the weight of the molecules are sorted in non-decreasing order. Lemma: If there is a subset of molecules with size k whose total weight is between l and u (inclusive), then there is also a subarray of molecules with size k whose total weight is between l and u (inclusive). Proof: Let's see a prefix of size k. If the total weight is >= l, then we are done. Otherwise, let's shift this prefix by 1 position to the right. The change in the total weight will be w[k + 1] - w[1] (or w[b + 1] - w[a] if our subarray are currently from index a to b). By the constraint of the problem, this change must be <= u - l. There are two cases to consider: * The sum of the last suffix of size k is >= l and <= u. Then this is the subarray that we are looking for. * The sum of the last suffix of size k is > u. Because the total weight changes by at most (u - l), at some point during our shift we must have a total sum of >= l and <= u. Note: the sum of the last suffix of size k can't be < l because it will contradict our first premise, i.e there is a subset of molecules of size k whose total weight is between l and u. */ #include "molecules.h" #include<bits/stdc++.h> using namespace std; #define LL long long int std::vector<int> find_subset(int l, int u, std::vector<int> w) { vector<pair<int, int> > indexedWeights; for (int i = 0; i < w.size(); i++) { indexedWeights.push_back({w[i], i}); } sort(indexedWeights.begin(), indexedWeights.end()); vector<LL> prefixSum; prefixSum.push_back(indexedWeights[0].first); for (int i = 1; i < indexedWeights.size(); i++) { prefixSum.push_back(indexedWeights[i].first + prefixSum.back()); } for (int i = 0; i < indexedWeights.size(); i++) { int lo = i, hi = indexedWeights.size() - 1, mid; while (hi >= lo) { mid = (lo + hi)/2; LL sum = prefixSum[mid] - (i == 0 ? 0 : prefixSum[i - 1]); if (sum < l) { lo = mid + 1; } else { hi = mid - 1; } } LL sum = prefixSum[lo] - (i == 0 ? 0 : prefixSum[i - 1]); if (sum >= l && sum <= u) { vector<int> result; for (int j = i; j <= lo; j++) { result.push_back(indexedWeights[j].second); } return result; } } vector<int> result; return result; }

컴파일 시 표준 에러 (stderr) 메시지

molecules.cpp: In function 'std::vector<int> find_subset(int, int, std::vector<int>)':
molecules.cpp:29:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   29 |   for (int i = 0; i < w.size(); i++) {
      |                   ~~^~~~~~~~~~
molecules.cpp:38:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   38 |   for (int i = 1; i < indexedWeights.size(); i++) {
      |                   ~~^~~~~~~~~~~~~~~~~~~~~~~
molecules.cpp:42:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   42 |   for (int i = 0; i < indexedWeights.size(); i++) {
      |                   ~~^~~~~~~~~~~~~~~~~~~~~~~
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