oj.uz

Submission #150879

# Submission time Handle Problem Language Result Execution time Memory
150879 2019-09-01T09:52:16 Z percywtc Wine Tasting (FXCUP4_wine) C++17
57 / 100
 11 ms 1060 KB 
#include "bartender.h"
#include <bits/stdc++.h>
using namespace std;

const int LARGESTS_FILLED_UNTIL = 5;
const int RAND_SEED = 689;

int fill_largests(int K, vector<int>& R, vector<int>& magic, vector<int>& A, int pos[]) {
	int N = R.size();

	int cur_num = N;
	int cur_fill = K;
	int prv_magic = -1;

	while (cur_fill >= LARGESTS_FILLED_UNTIL && cur_num >= 1) {
		if (magic[pos[cur_num]] >= prv_magic) {
			A[pos[cur_num]] = cur_fill;
			prv_magic = magic[pos[cur_num]];
			cur_num--;
		} else {
			prv_magic = magic[pos[cur_num]];
			cur_fill--;
		}
	}

	return cur_num;
}

vector<int> BlendWines(int K, vector<int> R) {
	int N = R.size();

	srand(RAND_SEED);
	vector<int> magic;
	for (int i = 0; i < N; i++) {
		magic.push_back(i);
	}
	random_shuffle(magic.begin(), magic.end());

	int pos[35] = {};
	for (int i = 0; i < N; i++) {
		pos[R[i]] = i;
	}

	vector<int> A(N, 0);

	int unfilled_n = fill_largests(K, R, magic, A, pos);
	int filled_until = 0;

	for (int i = 1; i < LARGESTS_FILLED_UNTIL; i++) {
		int unfilled_cnt = (unfilled_n - filled_until);
		int group_size = min(unfilled_cnt, 6);
		if ((LARGESTS_FILLED_UNTIL - i) * 5 >= unfilled_cnt) {
			group_size = min(group_size, 5);
		}

		for (int j = filled_until + 1; j <= filled_until + group_size; j++) {
			A[pos[j]] = i;
		}

		filled_until += group_size;
	}
/*
	for (int i = 0; i < N; i++) {
		printf("%2d ", A[i]);
	}
	printf("\n");
*/
	return A;
}

#include "taster.h"
#include <bits/stdc++.h>
using namespace std;

const int LARGESTS_FILLED_UNTIL = 5;
const int RAND_SEED = 689;

// merge insertion sort ---- merge insertion sort ---- merge insertion sort ---- merge insertion sort
const bool CONSIDER_INSERTION = true;
const bool CONSIDER_MERGE = true;
const bool CONSIDER_MI = true;

const bool INSERTION_BS = true;
const bool INSERTION_TS = false;

const bool MERGE_OPTIMIZE = true;

const bool MI_HALF = true;
const bool MI_OPTIMIZE = true;

int cmp(int u, int v) {
	int result = Compare(u, v);
	return result == 1;
}

vector<int> operator+ (const vector<int>& u, const vector<int>& v) {
	vector<int> result(u.begin(), u.end());
	result.insert(result.end(), v.begin(), v.end());

	return result;
}

vector<int> operator+ (const vector<int>& u, const int& v) {
	return u + vector<int>(1, v);
}

vector<int> operator+ (const int& u, const vector<int>& v) {
	return vector<int>(1, u) + v;
}

tuple<vector<int>, vector<int>, vector<int>> split(const vector<int>& T, int size1, int size2 = -1, int size3 = -1) {
	if (size2 == -1) {
		size2 = T.size() - size1;
		size3 = 0;
	} else
	if (size3 == -1) {
		size3 = T.size() - size1 - size2;
	}

	return make_tuple(vector<int>(T.begin(), T.begin() + size1),
						vector<int>(T.begin() + size1, T.begin() + size1 + size2),
						vector<int>(T.begin() + size1 + size2, T.end()));
}

const int INF = 123456;
int N;
vector<int> sortDP;

map<int, int> memInsertionCost;
map<pair<int, int>, int> memMultiInsertionsCost;
map<pair<int, int>, vector<pair<int, int>>> memMultiInsertionsDP;

// cost for inserting ONE element into a SORTED array of "size - 1" elements
int insertionCost(int size) {
	if (memInsertionCost.count(size)) {
		return memInsertionCost[size];
	}
	int result = INF;
	if (INSERTION_BS) {
		result = min(result, 2 + insertionCost(size - size / 2));
	}
	if (INSERTION_TS) {
		result = min(result, 3 + insertionCost((size - 1) / 3 + 1));
	}
	return memInsertionCost[size] = result;
}

// cost to sort two SORTED arrays of "size1" and "size2" elements
int mergeCost(int size1, int size2) {
	if (!MERGE_OPTIMIZE || !INSERTION_TS) {
		return 2 * (size1 + size2 - 1);
	}
	if (size1 == 1 && size2 == 1) {
		return 2;
	}
	return 2 * (size1 + size2 - 3) + 3;
}


// dp[i].first = value
// dp[i].second = backtrack
vector<pair<int, int>> multiInsertionsDP(int size1, int size2) {
	if (memMultiInsertionsDP.count(make_pair(size1, size2))) {
		return memMultiInsertionsDP[make_pair(size1, size2)];
	}
	vector<int> guaranteedPos(size2, 0);

	for (int i = 0; i < size2; i++) {
		guaranteedPos[i] = min(i + 3, size1 + 1);
	}

	vector<pair<int, int>> dp(size2, make_pair(INF, -1));

	for (int i = 0; i < size2; i++) {
		for (int j = 0; j <= i; j++) {
			int cost = (j > 0) ? dp[j - 1].first : 0;
			for (int k = 0; k <= i - j; k++) {
				cost += insertionCost(guaranteedPos[i - k] + k + j);
			}
			dp[i] = min(dp[i], make_pair(cost, j));
		}
	}

	return memMultiInsertionsDP[make_pair(size1, size2)] = dp;
}

// https://en.wikipedia.org/wiki/Merge-insertion_sort
// "size1" is the size of X
// "size2" is the size of Y
int multiInsertionsCost(int size1, int size2) {
	if (size2 == 0) {
		return 0;
	}
	if (memMultiInsertionsCost.count(make_pair(size1, size2))) {
		return memMultiInsertionsCost[make_pair(size1, size2)];
	}
	
	vector<pair<int, int> > dp = multiInsertionsDP(size1, size2);

	return memMultiInsertionsCost[make_pair(size1, size2)] = dp[size2 - 1].first;
}

void precompute(int N) {
	memInsertionCost[1] = 0;

	sortDP.push_back(0);
	sortDP.push_back(0);

	for (int i = sortDP.size(); sortDP.size() <= N; i = sortDP.size()) {
		sortDP.push_back(INF);

		if (CONSIDER_INSERTION) {
			// inserting ONE element into "i - 1" SORTED elements
			sortDP[i] = min(sortDP[i], sortDP[i - 1] + insertionCost(i));
		}

		if (CONSIDER_MERGE) {
			// merging TWO SORTED arrays of "j" and "i - j" elements
			for (int j = 1; j <= i - j; j++) {
				sortDP[i] = min(sortDP[i], sortDP[j] + sortDP[i - j] + mergeCost(j, i - j));
			}
		}

		if (CONSIDER_MI) {
			// merge-insertion sort with parition of "j" and "i - j" elements
			for (int j = MI_HALF ? i / 2 : 1; j <= i - j; j++) {
				int sizeOfX = j + 1;
				int sizeOfY = i - j - 1;
				int costX = 2 * j + sortDP[j];
				int costY = multiInsertionsCost(sizeOfX, sizeOfY);

				sortDP[i] = min(sortDP[i], costX + costY);
			}
		}
	}
}

vector<int> solve(const vector<int>& arr);

vector<int> insertion(const vector<int>& arr, int extra) {
	int len = arr.size();

	if (len == 0) {
		return vector<int>{extra};
	}

	if (INSERTION_BS && 2 + insertionCost(len + 1 - (len + 1) / 2) == insertionCost(len + 1)) {
		int verdict = cmp(arr[len / 2], extra);

		vector<int> prefix(arr.begin(), arr.begin() + len / 2);
		vector<int> suffix(arr.begin() + len / 2 + 1, arr.end());
		
		if (verdict == 1) {
			prefix = insertion(prefix, extra);
		} else {
			suffix = insertion(suffix, extra);
		}

		return prefix + arr[len / 2] + suffix;
	}

	assert(false);
}

vector<int> merge(const vector<int>& u, const vector<int>& v) {
	vector<int> result;
	int pu = 0, pv = 0;
	while (pu + MERGE_OPTIMIZE < u.size() && pv + MERGE_OPTIMIZE < v.size()) {
		int verdict = cmp(u[pu], v[pv]);

		if (verdict == 0) {
			result.push_back(u[pu++]);
		} else {
			result.push_back(v[pv++]);
		}
	}

	if (MERGE_OPTIMIZE) {
		if (pu + 1 == u.size()) {
			vector<int> vsuffix;
			tie(ignore, vsuffix, ignore) = split(v, pv);
			return result + insertion(vsuffix, u[pu]);
		}
		if (pv + 1 == v.size()) {
			vector<int> usuffix;
			tie(ignore, usuffix, ignore) = split(u, pu);
			return result + insertion(usuffix, v[pv]);
		}
	}

	while (pu < u.size()) {
		result.push_back(u[pu++]);
	}

	while (pv < v.size()) {
		result.push_back(v[pv++]);
	}

	return result;
}

vector<int> reorder(const vector<int>& elements, const vector<int>& from, const vector<int>& to) {
	map<int, int> originalPosition;
	for (int i = 0; i < from.size(); i++) {
		originalPosition[from[i]] = i;
	}

	vector<int> result = elements;

	for (int i = 0; i < to.size(); i++) {
		result[i] = elements[originalPosition[to[i]]];
	}

	return result;
}

vector<int> mergeInsertion(const vector<int>& arr, int partitionSize) {
	assert(partitionSize * 2 <= arr.size());

	vector<int> partitionX(arr.begin(), arr.begin() + partitionSize);
	vector<int> partitionY(arr.begin() + partitionSize, arr.end());

	for (int i = 0; i < partitionSize; i++) {
		int verdict = cmp(partitionX[i], partitionY[i]);

		if (!verdict) { // swapping larger elements to X
			swap(partitionX[i], partitionY[i]);
		}
	}

	vector<int> newPartitionX = solve(partitionX);
	vector<int> newPartitionY = reorder(partitionY, partitionX, newPartitionX);
	newPartitionX.insert(newPartitionX.begin(), newPartitionY[0]);
	newPartitionY.erase(newPartitionY.begin());

	if (newPartitionY.size() == 0) {
		return newPartitionX;
	}

	vector<pair<int, int>> dp = multiInsertionsDP(newPartitionX.size(), newPartitionY.size());
	vector<int> insertionOrder;

	int cur = newPartitionY.size() - 1;

	while (cur >= 0) {
		int to = dp[cur].second;
		for (int i = to; i <= cur; i++) {
			insertionOrder.push_back(i);
		}
		cur = to - 1;
	}

	reverse(insertionOrder.begin(), insertionOrder.end());

	vector<int> result(newPartitionX.begin(), newPartitionX.end());

	for (int i = 0; i < newPartitionY.size(); i++) {
		vector<int> prefix, suffix;
		int prefixSize = min((int)result.size(), i + insertionOrder[i] + 2);

		if (MI_OPTIMIZE) {
			if (insertionOrder[i] + 2 < newPartitionX.size()) {
				int relativeX = newPartitionX[insertionOrder[i] + 2];
				for (int j = 0; j < result.size(); j++) {
					if (result[j] == relativeX) {
						prefixSize = j;
					}
				}
			}
		}

		tie(prefix, suffix, ignore) = split(result, prefixSize);
		result = insertion(prefix, newPartitionY[insertionOrder[i]]) + suffix;
	}

	return result;
}

vector<int> solve(const vector<int>& arr) {
	int len = arr.size();

	if (len <= 1) {
		return arr;
	}

	if (CONSIDER_INSERTION) {
		if (sortDP[len] == sortDP[len - 1] + insertionCost(len)) {
			vector<int> prefix(arr.begin(), arr.end() - 1);
			return insertion(solve(prefix), arr[len - 1]);
		}
	}

	if (CONSIDER_MERGE) {
		for (int i = 1; i <= len - i; i++) {
			if (sortDP[len] == sortDP[i] + sortDP[len - i] + mergeCost(i, len - i)) {
				vector<int> prefix(arr.begin(), arr.begin() + i);
				vector<int> suffix(arr.begin() + i, arr.end());
				return merge(solve(prefix), solve(suffix));
			}
		}
	}

	if (CONSIDER_MI) {
		for (int i = MI_HALF ? len / 2 : 1; i <= len - i; i++) {
			int sizeOfX = i + 1;
			int sizeOfY = len - i - 1;
			int costX = 2 * i + sortDP[i];
			int costY = multiInsertionsCost(sizeOfX, sizeOfY);

			if (sortDP[len] == costX + costY) {
				return mergeInsertion(arr, i);
			}
		}
	}

	assert(false);
}
// merge insertion sort ---- merge insertion sort ---- merge insertion sort ---- merge insertion sort

int handle_largests(int K, vector<int>& A, vector<int>& magic, vector<int>& R) {
	int N = A.size();
	int next_num = N;
	for (int filled_as = K; filled_as >= LARGESTS_FILLED_UNTIL; filled_as--) {
		vector<pair<int, int> > filled_bingo;
		for (int i = 0; i < N; i++) {
			if (A[i] == filled_as) {
				filled_bingo.push_back(make_pair(magic[i], i));
			}
		}
		sort(filled_bingo.begin(), filled_bingo.end());

		for (int i = 0; i < filled_bingo.size(); i++) {
			R[filled_bingo[i].second] = next_num--;
		}
	}

	return next_num;
}

void handle_smallests(vector<int>& A, vector<int>& R) {
	int N = A.size();
	int next_num = 1;
	for (int filled_as = 1; filled_as < LARGESTS_FILLED_UNTIL; filled_as++) {
		vector<int> filled_bingo;
		for (int i = 0; i < N; i++) {
			if (A[i] == filled_as) {
				filled_bingo.push_back(i);
			}
		}

		random_shuffle(filled_bingo.begin(), filled_bingo.end());
		filled_bingo = solve(filled_bingo);

		for (int i = 0; i < filled_bingo.size(); i++) {
			R[filled_bingo[i]] = next_num++;
		}
	}
}

vector<int> SortWines(int K, vector<int> A) {
	int N = A.size();
	precompute(N);

	srand(RAND_SEED);
	vector<int> magic;
	for (int i = 0; i < N; i++) {
		magic.push_back(i);
	}
	random_shuffle(magic.begin(), magic.end());

	vector<int> R(N, 0);

	handle_largests(K, A, magic, R);
	handle_smallests(A, R);
/*
	for (int i = 0; i < N; i++) {
		printf("%2d ", R[i]);
	}
	printf("\n");
*/
	return R;
}

Compilation message

taster.cpp: In function 'void precompute(int)':
taster.cpp:139:44: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i = sortDP.size(); sortDP.size() <= N; i = sortDP.size()) {
                              ~~~~~~~~~~~~~~^~~~
taster.cpp: In function 'std::vector<int> merge(const std::vector<int>&, const std::vector<int>&)':
taster.cpp:198:29: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (pu + MERGE_OPTIMIZE < u.size() && pv + MERGE_OPTIMIZE < v.size()) {
         ~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~
taster.cpp:198:63: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (pu + MERGE_OPTIMIZE < u.size() && pv + MERGE_OPTIMIZE < v.size()) {
                                           ~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~
taster.cpp:209:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if (pu + 1 == u.size()) {
       ~~~~~~~^~~~~~~~~~~
taster.cpp:214:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if (pv + 1 == v.size()) {
       ~~~~~~~^~~~~~~~~~~
taster.cpp:221:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (pu < u.size()) {
         ~~~^~~~~~~~~~
taster.cpp:225:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (pv < v.size()) {
         ~~~^~~~~~~~~~
taster.cpp: In function 'std::vector<int> reorder(const std::vector<int>&, const std::vector<int>&, const std::vector<int>&)':
taster.cpp:234:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i = 0; i < from.size(); i++) {
                  ~~^~~~~~~~~~~~~
taster.cpp:240:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i = 0; i < to.size(); i++) {
                  ~~^~~~~~~~~~~
In file included from /usr/include/c++/7/cassert:44:0,
                 from /usr/include/x86_64-linux-gnu/c++/7/bits/stdc++.h:33,
                 from taster.cpp:2:
taster.cpp: In function 'std::vector<int> mergeInsertion(const std::vector<int>&, int)':
taster.cpp:248:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  assert(partitionSize * 2 <= arr.size());
         ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~
taster.cpp:287:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i = 0; i < newPartitionY.size(); i++) {
                  ~~^~~~~~~~~~~~~~~~~~~~~~
taster.cpp:292:30: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    if (insertionOrder[i] + 2 < newPartitionX.size()) {
taster.cpp:294:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int j = 0; j < result.size(); j++) {
                     ~~^~~~~~~~~~~~~~~
taster.cpp: In function 'int handle_largests(int, std::vector<int>&, std::vector<int>&, std::vector<int>&)':
taster.cpp:362:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for (int i = 0; i < filled_bingo.size(); i++) {
                   ~~^~~~~~~~~~~~~~~~~~~~~
taster.cpp: In function 'void handle_smallests(std::vector<int>&, std::vector<int>&)':
taster.cpp:384:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for (int i = 0; i < filled_bingo.size(); i++) {
                   ~~^~~~~~~~~~~~~~~~~~~~~

Subtask #1
57.0 / 100.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 908 KB Correct
2 Correct 9 ms 884 KB Correct
3 Correct 10 ms 908 KB Correct
4 Correct 8 ms 644 KB Correct
5 Correct 8 ms 772 KB Correct
6 Correct 10 ms 772 KB Correct
7 Correct 10 ms 908 KB Correct
8 Correct 11 ms 772 KB Correct
9 Correct 10 ms 908 KB Correct
10 Correct 10 ms 780 KB Correct
11 Correct 10 ms 644 KB Correct
12 Correct 9 ms 780 KB Correct
13 Correct 10 ms 772 KB Correct
14 Correct 10 ms 804 KB Correct
15 Correct 10 ms 772 KB Correct
16 Correct 10 ms 900 KB Correct
17 Correct 10 ms 908 KB Correct
18 Correct 10 ms 772 KB Correct
19 Correct 10 ms 908 KB Correct
20 Correct 10 ms 780 KB Correct
21 Correct 9 ms 664 KB Correct
22 Correct 10 ms 908 KB Correct
23 Correct 9 ms 900 KB Correct
24 Correct 9 ms 732 KB Correct
25 Correct 10 ms 908 KB Correct
26 Correct 9 ms 772 KB Correct
27 Correct 9 ms 772 KB Correct
28 Correct 10 ms 812 KB Correct
29 Correct 10 ms 772 KB Correct
30 Correct 10 ms 780 KB Correct
31 Correct 10 ms 780 KB Correct
32 Correct 9 ms 908 KB Correct
33 Correct 10 ms 772 KB Correct
34 Correct 9 ms 908 KB Correct
35 Correct 10 ms 980 KB Correct
36 Correct 10 ms 644 KB Correct
37 Correct 9 ms 884 KB Correct
38 Correct 10 ms 908 KB Correct
39 Correct 8 ms 772 KB Correct
40 Correct 9 ms 780 KB Correct
41 Correct 9 ms 772 KB Correct
42 Correct 10 ms 816 KB Correct
43 Correct 10 ms 772 KB Correct
44 Correct 9 ms 644 KB Correct
45 Correct 9 ms 772 KB Correct
46 Correct 10 ms 772 KB Correct
47 Correct 9 ms 908 KB Correct
48 Correct 9 ms 772 KB Correct
49 Correct 10 ms 1060 KB Correct
50 Correct 11 ms 780 KB Correct
51 Correct 10 ms 908 KB Correct
52 Correct 10 ms 908 KB Correct
53 Correct 8 ms 772 KB Correct
54 Correct 11 ms 676 KB Correct
55 Correct 11 ms 772 KB Correct
56 Correct 10 ms 772 KB Correct
57 Correct 10 ms 644 KB Correct
58 Correct 11 ms 644 KB Correct
59 Correct 10 ms 964 KB Correct
60 Correct 10 ms 908 KB Correct
61 Correct 8 ms 772 KB Correct
62 Correct 10 ms 772 KB Correct
63 Correct 9 ms 884 KB Correct
64 Correct 10 ms 908 KB Correct
65 Correct 10 ms 908 KB Correct
66 Correct 10 ms 772 KB Correct
67 Correct 10 ms 780 KB Correct
68 Correct 10 ms 908 KB Correct
69 Correct 10 ms 772 KB Correct
70 Correct 10 ms 908 KB Correct
71 Correct 9 ms 772 KB Correct
72 Correct 10 ms 908 KB Correct
73 Correct 10 ms 940 KB Correct
74 Partially correct 10 ms 988 KB Wrong
75 Correct 10 ms 884 KB Correct
76 Correct 9 ms 772 KB Correct
77 Correct 8 ms 772 KB Correct
78 Correct 9 ms 644 KB Correct
79 Correct 10 ms 644 KB Correct
80 Correct 10 ms 772 KB Correct
81 Correct 9 ms 644 KB Correct
82 Partially correct 10 ms 908 KB Wrong
83 Correct 10 ms 908 KB Correct
84 Correct 10 ms 972 KB Correct
85 Correct 9 ms 772 KB Correct
86 Correct 10 ms 908 KB Correct
87 Correct 9 ms 772 KB Correct
88 Correct 10 ms 644 KB Correct
89 Correct 9 ms 772 KB Correct
90 Correct 9 ms 772 KB Correct
91 Correct 9 ms 772 KB Correct
92 Correct 9 ms 772 KB Correct
93 Correct 10 ms 908 KB Correct
94 Partially correct 10 ms 1024 KB Wrong
95 Correct 10 ms 1020 KB Correct
96 Partially correct 10 ms 888 KB Wrong
97 Partially correct 10 ms 908 KB Wrong
98 Partially correct 10 ms 908 KB Wrong
99 Partially correct 10 ms 960 KB Wrong
100 Partially correct 10 ms 780 KB Wrong
101 Partially correct 10 ms 1016 KB Wrong
102 Partially correct 10 ms 1024 KB Wrong
103 Correct 10 ms 772 KB Correct
104 Correct 10 ms 892 KB Correct
105 Correct 11 ms 772 KB Correct
106 Correct 10 ms 772 KB Correct
107 Correct 10 ms 956 KB Correct
108 Correct 8 ms 748 KB Correct
109 Partially correct 9 ms 908 KB Wrong
110 Partially correct 9 ms 772 KB Wrong
111 Partially correct 10 ms 848 KB Wrong
112 Partially correct 10 ms 772 KB Wrong
113 Partially correct 10 ms 772 KB Wrong
114 Partially correct 10 ms 772 KB Wrong
115 Partially correct 9 ms 772 KB Wrong
116 Partially correct 8 ms 1016 KB Wrong
117 Partially correct 9 ms 1020 KB Wrong
118 Partially correct 11 ms 780 KB Wrong
119 Partially correct 11 ms 940 KB Wrong
120 Partially correct 10 ms 884 KB Wrong