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답안 #749807

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
749807 2023-05-28T14:03:59 Z happypotato 메기 농장 (IOI22_fish) C++17
100 / 100
 681 ms 119960 KB 
#include "fish.h"
 
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int, int>
#define ff first
#define ss second
#define pb push_back
#pragma GCC optimize("Ofast")
 
long long max_weights(int32_t n, int32_t m, vector<int32_t> X, vector<int32_t> Y,
					vector<int32_t> W) {
	
	for (int i = 0; i < m; i++) {
		X[i]++; Y[i]++;
	}

	// int olda[n + 1][n + 1];
	// for (int i = 0; i <= n; i++) {
	// 	for (int j = 0; j <= n; j++) {
	// 		olda[i][j] = 0;
	// 	}
	// }
	// for (int i = 0; i < m; i++) {
	// 	olda[X[i]][Y[i]] = W[i];
	// }
	// int oldps[n + 1][n + 1]; // ps[i][j] = a[i][1] + ... + a[i][j]
	// for (int i = 1; i <= n; i++) {
	// 	oldps[i][0] = 0;
	// 	for (int j = 1; j <= n; j++) {
	// 		oldps[i][j] = oldps[i][j - 1] + olda[i][j];
	// 	}
	// }

	vector<pii> a[n + 1], ps[n + 1];
	vector<int> critpts[n + 1];
	for (int i = 1; i <= n; i++) {
		a[i].pb({0, 0});
		ps[i].pb({0, 0});
		critpts[i].pb(0);
		critpts[i].pb(n);
	}
	for (int i = 0; i < m; i++) {
		a[X[i]].pb({Y[i], W[i]});
		// critical points: (X[i] +- 1, Y[i]), (X[i], Y[i] - 1)
		if (X[i] > 1) {
			critpts[X[i] - 1].pb(Y[i]);
		}
		if (X[i] < n) {
			critpts[X[i] + 1].pb(Y[i]);
		}
		critpts[X[i]].pb(Y[i] - 1);
	}
	for (int i = 1; i <= n; i++) {
		sort(a[i].begin(), a[i].end());
		for (pii &x : a[i]) {
			ps[i].pb({x.ff, ps[i].back().ss + x.ss});
		}
	}

	function<int(int, int)> GetPS = [&](int x, int y) -> int {
		int lb = 0, rb = (int)(ps[x].size()) - 1;
		while (lb < rb) {
			int mid = (lb + rb + 1) >> 1;
			if (ps[x][mid].ff <= y) lb = mid;
			else rb = mid - 1;
		}
		return ps[x][lb].ss;
	};
	
	// int olddp[2][n + 1][n + 1];
	// // olddp[increasing][pos][height] = max ans from 1 to pos with pos getting height, height must be increasing
	// for (int i = 0; i <= n; i++) {
	// 	olddp[0][0][i] = olddp[1][0][i] = (i == 0 ? 0 : -1e18);
	// 	olddp[0][1][i] = olddp[1][1][i] = 0;
	// }
	// int oldcur[n + 1];
	// function<void(void)> resetoldcur = [&]() {
	// 	for (int i = 0; i <= n; i++) oldcur[i] = 0;
	// };

	vector<vector<pii>> dp[2];
	dp[0].resize(n + 1); dp[1].resize(n + 1);
	for (int i = 0; i <= n; i++) {
		dp[0][0].pb({i, (i == 0 ? 0 : -1e18)});
		dp[1][0].pb({i, (i == 0 ? 0 : -1e18)});
		
		dp[0][1].pb({i, 0});
		dp[1][1].pb({i, 0});
	}
	for (int i = 2; i <= n; i++) {
		sort(critpts[i].begin(), critpts[i].end());
		for (int &x : critpts[i]) {
			if (!dp[0][i].empty() && x == dp[0][i].back().ff) continue;
			dp[0][i].pb({x, 0});
			dp[1][i].pb({x, 0});
		}
	}
	vector<pii> cur;
 
	for (int i = 2; i <= n; i++) {
		// for (int j = 0; j <= n; j++) {
		// 	olddp[0][i][j] = olddp[1][i][j] = 0;
		// }
		// Case 0: height of i is 0
		// resetoldcur();
		// olddp[0][i][0] = max(olddp[0][i - 1][0], olddp[1][i - 1][0]);
		// for (int j = 1; j <= n; j++) {
		// 	olddp[0][i][0] = max(olddp[0][i][0], max(olddp[0][i - 1][j], olddp[1][i - 1][j]) + oldps[i][j]);
		// }
		// olddp[1][i][0] = olddp[0][i][0];

		{
			// dp[flag][i][0].ff is always 0
			for (int j = 0; j < (int)(dp[0][i - 1].size()); j++) {
				dp[0][i][0].ss = max(dp[0][i][0].ss, max(dp[0][i - 1][j].ss, dp[1][i - 1][j].ss) + GetPS(i, dp[0][i - 1][j].ff));
			}
			dp[1][i][0].ss = dp[0][i][0].ss;
		}
 
		// Case 1: height of i-1 is 0
		// Case 1.1: height of i-2 <= height of i
		// resetoldcur();
		// oldcur[0] = olddp[0][i - 2][0];
		// for (int j = 1; j <= n; j++) {
		// 	oldcur[j] = max(oldcur[j - 1], max(olddp[0][i - 2][j], olddp[1][i - 2][j]));
		// }
		// for (int j = 0; j <= n; j++) {
		// 	olddp[0][i][j] = max(olddp[0][i][j], oldcur[j] + oldps[i - 1][j]);
		// 	olddp[1][i][j] = max(olddp[1][i][j], oldcur[j] + oldps[i - 1][j]);
		// }

		{
			cur.clear();
			for (int j = 0; j < (int)(dp[0][i - 2].size()); j++) {
				cur.pb({dp[0][i - 2][j].ff, max(dp[0][i - 2][j].ss, dp[1][i - 2][j].ss)});
			}
			for (int j = 1; j < (int)(cur.size()); j++) {
				cur[j].ss = max(cur[j].ss, cur[j - 1].ss);
			}
			int ptr = 0, curans = 0;
			for (int j = 0; j < (int)(dp[0][i].size()); j++) {
				while (ptr < (int)(cur.size()) && cur[ptr].ff <= dp[0][i][j].ff) {
					curans = max(curans, cur[ptr].ss);
					ptr++;
				}
				dp[0][i][j].ss = max(dp[0][i][j].ss, curans + GetPS(i - 1, dp[0][i][j].ff));
				dp[1][i][j].ss = max(dp[1][i][j].ss, curans + GetPS(i - 1, dp[0][i][j].ff));
			}
		}

		// Case 1.2: height of i-2 >= height of i
		// resetoldcur();
		// oldcur[n] = olddp[0][i - 2][n] + oldps[i - 1][n];
		// for (int j = n - 1; j >= 0; j--) {
		// 	oldcur[j] = max(oldcur[j + 1], max(olddp[0][i - 2][j], olddp[1][i - 2][j]) + oldps[i - 1][j]);
		// }
		// for (int j = 0; j <= n; j++) {
		// 	olddp[0][i][j] = max(olddp[0][i][j], oldcur[j]);
		// 	olddp[1][i][j] = max(olddp[1][i][j], oldcur[j]);
		// }

		{
			cur.clear();
			for (int j = 0; j < (int)(dp[0][i - 2].size()); j++) {
				cur.pb({dp[0][i - 2][j].ff, max(dp[0][i - 2][j].ss, dp[1][i - 2][j].ss) + GetPS(i - 1, dp[0][i - 2][j].ff)});
			}
			for (int j = (int)(cur.size()) - 2; j >= 0; j--) {
				cur[j].ss = max(cur[j].ss, cur[j + 1].ss);
			}
			int ptr = (int)(cur.size()) - 1, curans = 0;
			for (int j = (int)(dp[0][i].size()) - 1; j >= 0; j--) {
				while (ptr >= 0 && cur[ptr].ff >= dp[0][i][j].ff) {
					curans = max(curans, cur[ptr].ss);
					ptr--;
				}
				dp[0][i][j].ss = max(dp[0][i][j].ss, curans);
				dp[1][i][j].ss = max(dp[1][i][j].ss, curans);
			}
		}
 
		// now height of i-1 > 0
		// Case 2: height of i-1 <= height of i
		// resetoldcur();
		// oldcur[1] = olddp[0][i - 1][1];
		// for (int j = 2; j <= n; j++) {
		// 	oldcur[j] = max(oldcur[j - 1] + olda[i - 1][j], olddp[0][i - 1][j]);
		// }
		// for (int j = 1; j <= n; j++) {
		// 	olddp[0][i][j] = max(olddp[0][i][j], oldcur[j]);
		// }

		{
			cur.clear();
			int ptr = 1, curans = 0;
			for (int j = 1; j < (int)(dp[0][i].size()); j++) {
				curans += (GetPS(i - 1, dp[0][i][j].ff) - GetPS(i - 1, (j == 1 ? 1 : dp[0][i][j - 1].ff)));
				while (ptr < (int)(dp[0][i - 1].size()) && dp[0][i - 1][ptr].ff <= dp[0][i][j].ff) {
					curans = max(curans, dp[0][i - 1][ptr].ss + (GetPS(i - 1, dp[0][i][j].ff) - GetPS(i - 1, dp[0][i - 1][ptr].ff)));
					ptr++;
				}
				dp[0][i][j].ss = max(dp[0][i][j].ss, curans);
			}
		}
 
		// Case 3: height of i-1 >= height of i
		// resetoldcur();
		// oldcur[n] = max(olddp[0][i - 1][n], olddp[1][i - 1][n]);
		// for (int j = n - 1; j >= 1; j--) {
		// 	oldcur[j] = max(oldcur[j + 1] + olda[i][j + 1], max(olddp[0][i - 1][j], olddp[1][i - 1][j]));
		// }
		// for (int j = 1; j <= n; j++) {
		// 	olddp[1][i][j] = max(olddp[1][i][j], oldcur[j]);
		// }

		{
			cur.clear();
			int ptr = (int)(dp[1][i - 1].size()) - 1, curans = 0;
			for (int j = (int)(dp[1][i].size()) - 1; j >= 1; j--) {
				curans += (GetPS(i, (j + 1 == (int)(dp[1][i].size()) ? n : dp[1][i][j + 1].ff)) - GetPS(i, dp[1][i][j].ff));
				while (ptr >= 0 && dp[1][i - 1][ptr].ff >= dp[0][i][j].ff) {
					curans = max(curans, max(dp[0][i - 1][ptr].ss, dp[1][i - 1][ptr].ss) + (GetPS(i, dp[1][i - 1][ptr].ff) - GetPS(i, dp[1][i][j].ff)));
					ptr--;
				}
				dp[1][i][j].ss = max(dp[1][i][j].ss, curans);
			}
		}
	}
 
	// int ans = max(dp[0][n][0].ss, dp[1][n][0].ss);
	// for (int i = 1; i <= n; i++) {
	// 	// cerr << olddp[0][n][i] << ' ' << olddp[1][n][i] << endl;
	// 	ans = max(ans, max(olddp[0][n][i], olddp[1][n][i]));
	// }
	// return ans;

	// for (int i = 1; i <= n; i++) {
	// 	cerr << i << ": ";
	// 	for (pii &x : dp[1][i]) cerr << "(" << x.ff << ", " << x.ss << ") ";
	// 	cerr << endl;
	// }

	int ans = 0;
	for (pii &x : dp[0][n]) ans = max(ans, x.ss);
	for (pii &x : dp[1][n]) ans = max(ans, x.ss);
	return ans;
}
 
#undef int

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 163 ms 49576 KB Output is correct
2 Correct 185 ms 55508 KB Output is correct
3 Correct 97 ms 44828 KB Output is correct
4 Correct 98 ms 44792 KB Output is correct
5 Correct 573 ms 103696 KB Output is correct
6 Correct 665 ms 117044 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 304 ms 58720 KB Output is correct
3 Correct 363 ms 66476 KB Output is correct
4 Correct 171 ms 49604 KB Output is correct
5 Correct 253 ms 55464 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 93 ms 44820 KB Output is correct
11 Correct 92 ms 44868 KB Output is correct
12 Correct 200 ms 52772 KB Output is correct
13 Correct 218 ms 59472 KB Output is correct
14 Correct 187 ms 51316 KB Output is correct
15 Correct 213 ms 54620 KB Output is correct
16 Correct 186 ms 51380 KB Output is correct
17 Correct 213 ms 56360 KB Output is correct

Subtask #3
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 90 ms 44760 KB Output is correct
2 Correct 90 ms 44768 KB Output is correct
3 Correct 171 ms 50364 KB Output is correct
4 Correct 151 ms 51836 KB Output is correct
5 Correct 255 ms 61588 KB Output is correct
6 Correct 262 ms 61560 KB Output is correct
7 Correct 251 ms 61448 KB Output is correct
8 Correct 262 ms 61588 KB Output is correct

Subtask #4
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 4 ms 852 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 468 KB Output is correct

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 4 ms 852 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 3 ms 596 KB Output is correct
17 Correct 52 ms 7776 KB Output is correct
18 Correct 54 ms 8512 KB Output is correct
19 Correct 50 ms 8140 KB Output is correct
20 Correct 43 ms 7788 KB Output is correct
21 Correct 42 ms 7628 KB Output is correct
22 Correct 96 ms 14928 KB Output is correct
23 Correct 14 ms 2516 KB Output is correct
24 Correct 49 ms 6020 KB Output is correct
25 Correct 2 ms 596 KB Output is correct
26 Correct 13 ms 2404 KB Output is correct

Subtask #6
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 4 ms 852 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 3 ms 596 KB Output is correct
17 Correct 52 ms 7776 KB Output is correct
18 Correct 54 ms 8512 KB Output is correct
19 Correct 50 ms 8140 KB Output is correct
20 Correct 43 ms 7788 KB Output is correct
21 Correct 42 ms 7628 KB Output is correct
22 Correct 96 ms 14928 KB Output is correct
23 Correct 14 ms 2516 KB Output is correct
24 Correct 49 ms 6020 KB Output is correct
25 Correct 2 ms 596 KB Output is correct
26 Correct 13 ms 2404 KB Output is correct
27 Correct 6 ms 2132 KB Output is correct
28 Correct 276 ms 34252 KB Output is correct
29 Correct 381 ms 46956 KB Output is correct
30 Correct 508 ms 81004 KB Output is correct
31 Correct 512 ms 86100 KB Output is correct
32 Correct 340 ms 51444 KB Output is correct
33 Correct 531 ms 86692 KB Output is correct
34 Correct 567 ms 86544 KB Output is correct
35 Correct 156 ms 27640 KB Output is correct
36 Correct 533 ms 71028 KB Output is correct

Subtask #7
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 90 ms 44760 KB Output is correct
2 Correct 90 ms 44768 KB Output is correct
3 Correct 171 ms 50364 KB Output is correct
4 Correct 151 ms 51836 KB Output is correct
5 Correct 255 ms 61588 KB Output is correct
6 Correct 262 ms 61560 KB Output is correct
7 Correct 251 ms 61448 KB Output is correct
8 Correct 262 ms 61588 KB Output is correct
9 Correct 296 ms 61460 KB Output is correct
10 Correct 151 ms 33084 KB Output is correct
11 Correct 349 ms 65968 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 90 ms 44848 KB Output is correct
19 Correct 101 ms 44844 KB Output is correct
20 Correct 110 ms 44856 KB Output is correct
21 Correct 92 ms 44812 KB Output is correct
22 Correct 325 ms 67468 KB Output is correct
23 Correct 372 ms 78096 KB Output is correct
24 Correct 411 ms 78560 KB Output is correct

Subtask #8
16.0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 163 ms 49576 KB Output is correct
2 Correct 185 ms 55508 KB Output is correct
3 Correct 97 ms 44828 KB Output is correct
4 Correct 98 ms 44792 KB Output is correct
5 Correct 573 ms 103696 KB Output is correct
6 Correct 665 ms 117044 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 304 ms 58720 KB Output is correct
9 Correct 363 ms 66476 KB Output is correct
10 Correct 171 ms 49604 KB Output is correct
11 Correct 253 ms 55464 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 93 ms 44820 KB Output is correct
17 Correct 92 ms 44868 KB Output is correct
18 Correct 200 ms 52772 KB Output is correct
19 Correct 218 ms 59472 KB Output is correct
20 Correct 187 ms 51316 KB Output is correct
21 Correct 213 ms 54620 KB Output is correct
22 Correct 186 ms 51380 KB Output is correct
23 Correct 213 ms 56360 KB Output is correct
24 Correct 90 ms 44760 KB Output is correct
25 Correct 90 ms 44768 KB Output is correct
26 Correct 171 ms 50364 KB Output is correct
27 Correct 151 ms 51836 KB Output is correct
28 Correct 255 ms 61588 KB Output is correct
29 Correct 262 ms 61560 KB Output is correct
30 Correct 251 ms 61448 KB Output is correct
31 Correct 262 ms 61588 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 0 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 0 ms 212 KB Output is correct
36 Correct 0 ms 212 KB Output is correct
37 Correct 1 ms 212 KB Output is correct
38 Correct 0 ms 212 KB Output is correct
39 Correct 0 ms 212 KB Output is correct
40 Correct 1 ms 468 KB Output is correct
41 Correct 4 ms 852 KB Output is correct
42 Correct 1 ms 468 KB Output is correct
43 Correct 2 ms 596 KB Output is correct
44 Correct 1 ms 340 KB Output is correct
45 Correct 1 ms 468 KB Output is correct
46 Correct 1 ms 468 KB Output is correct
47 Correct 3 ms 596 KB Output is correct
48 Correct 52 ms 7776 KB Output is correct
49 Correct 54 ms 8512 KB Output is correct
50 Correct 50 ms 8140 KB Output is correct
51 Correct 43 ms 7788 KB Output is correct
52 Correct 42 ms 7628 KB Output is correct
53 Correct 96 ms 14928 KB Output is correct
54 Correct 14 ms 2516 KB Output is correct
55 Correct 49 ms 6020 KB Output is correct
56 Correct 2 ms 596 KB Output is correct
57 Correct 13 ms 2404 KB Output is correct
58 Correct 6 ms 2132 KB Output is correct
59 Correct 276 ms 34252 KB Output is correct
60 Correct 381 ms 46956 KB Output is correct
61 Correct 508 ms 81004 KB Output is correct
62 Correct 512 ms 86100 KB Output is correct
63 Correct 340 ms 51444 KB Output is correct
64 Correct 531 ms 86692 KB Output is correct
65 Correct 567 ms 86544 KB Output is correct
66 Correct 156 ms 27640 KB Output is correct
67 Correct 533 ms 71028 KB Output is correct
68 Correct 296 ms 61460 KB Output is correct
69 Correct 151 ms 33084 KB Output is correct
70 Correct 349 ms 65968 KB Output is correct
71 Correct 0 ms 212 KB Output is correct
72 Correct 0 ms 212 KB Output is correct
73 Correct 0 ms 212 KB Output is correct
74 Correct 0 ms 212 KB Output is correct
75 Correct 1 ms 212 KB Output is correct
76 Correct 0 ms 212 KB Output is correct
77 Correct 90 ms 44848 KB Output is correct
78 Correct 101 ms 44844 KB Output is correct
79 Correct 110 ms 44856 KB Output is correct
80 Correct 92 ms 44812 KB Output is correct
81 Correct 325 ms 67468 KB Output is correct
82 Correct 372 ms 78096 KB Output is correct
83 Correct 411 ms 78560 KB Output is correct
84 Correct 672 ms 96144 KB Output is correct
85 Correct 681 ms 100884 KB Output is correct
86 Correct 640 ms 114328 KB Output is correct
87 Correct 638 ms 119960 KB Output is correct
88 Correct 0 ms 212 KB Output is correct
89 Correct 627 ms 119840 KB Output is correct
90 Correct 518 ms 108704 KB Output is correct
91 Correct 380 ms 98468 KB Output is correct