Submission #757470

#	Time	Username	Problem	Language	Result	Execution time	Memory
757470		happypotato	Catfish Farm (IOI22_fish)	C++17	100 / 100	708 ms	123664 KiB

fish

#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]++;
	}

	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;
	};

	// O(n^2): dp[increasing][pos][height] = max ans from 1 to [pos] with [pos] getting [height], height must be [increasing]
 
	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;
	int ptr = 0, curans = 0;

	for (int i = 2; i <= n; i++) {

		// Case 0: height of i is 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
		
		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);
		}
		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
		
		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);
		}
		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
		
		cur.clear();
		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
 
		cur.clear();
		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 = 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 / 3
• Subtask 2: 6 / 6
• Subtask 3: 9 / 9
• Subtask 4: 14 / 14
• Subtask 5: 21 / 21
• Subtask 6: 17 / 17
• Subtask 7: 14 / 14
• Subtask 8: 16 / 16