답안 #776689

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
776689	2023-07-08T07:13:53 Z	mousebeaver	메기 농장 (IOI22_fish)	C++17	100 / 100	346 ms	55500 KB

fish

        #define ll long long
        #define pll pair<ll, ll>
        #define INF numeric_limits<ll>::max()
        #include "fish.h"
        #include <bits/stdc++.h>
        using namespace std;
         
        struct fish
        {
            ll height;
            ll weight;
            ll below;
            ll above; //Sums of weights in column
            ll bigPier; //No bigger pier in the previous column -> first one to be caught
            ll noPier; //No pier in this column -> first one to be caught
            ll smallPier; //Bigger pier in the previous column -> first one not below a pier
        };
         
        bool operator < (fish a, fish b)
        {
            return (a.height < b.height);
        }
     
        ll transitionBig(vector<vector<fish>>& dp, ll i, ll preind, ll index)
        {
            //Return dp[i][index].bigPier based on dp[i-1][preind]
            if(dp[i][index].height < dp[i-1][preind].height)
            {
                //The given pier is not bigger!
                return 0;
            }
     
            ll sum = 0; //Sum of the fish that get catched additionally
            if(dp[i][index].height > dp[i-1][preind].height)
            {
                //The piers have different size
                //Search for the last caught fish
                ll left = preind;
                ll right = dp[i-1].size()-1;
                while(left < right)
                {
                    ll mid = (left+right+1)/2;
                    if(dp[i-1][mid].height < dp[i][index].height)
                    {
                        left = mid;
                    }
                    else
                    {
                        right = mid-1;
                    }
                }
                sum = dp[i-1][left].below + dp[i-1][left].weight - dp[i-1][preind].below;
            }
     
            return max(dp[i-1][preind].bigPier, dp[i-1][preind].noPier) + sum;
        }

        ll intersectBig(vector<vector<fish>>& dp, ll i, ll first, ll second)
        {
            //First index in dp[i] with second (> first) being the at least as good as transition base in dp[i-1]
            if(transitionBig(dp, i, first, dp[i].size()-1) > transitionBig(dp, i, second, dp[i].size()-1))                                                                     
            {
                //It never happens!
                return INF;
            }

            ll left = 0;
            ll right = dp[i].size()-1;
            while(left < right)
            {
                ll mid = (left+right)/2;
                if(transitionBig(dp, i, first, mid) > transitionBig(dp, i, second, mid))
                {
                    left = mid+1;
                }
                else
                {
                    right = mid;
                }
            }
            return left;
        }
     
        ll transitionSmall(vector<vector<fish>>& dp, ll i, ll preind, ll index)
        {
            //Return dp[i][index].smallPier based on dp[i-1][preind]
            if(dp[i][index].height >= dp[i-1][preind].height)
            {
                //The given pier is not strictly smaller!
                return 0;
            }
     
            ll sum = 0; //Sum of the fish that get catched additionally
            //Search for the last caught fish
            ll left = index;
            ll right = dp[i].size()-1;
            while(left < right)
            {
                ll mid = (left+right+1)/2;
                if(dp[i][mid].height < dp[i-1][preind].height)
                {
                    left = mid;
                }
                else
                {
                    right = mid-1;
                }
            }
            sum = dp[i][left].below + dp[i][left].weight - dp[i][index].below;
     
            return max(dp[i-1][preind].bigPier, dp[i-1][preind].smallPier) + sum;
        }

        ll intersectSmall(vector<vector<fish>>& dp, ll i, ll high, ll low)
        {
            //Highest index in dp[i] with low being the at least as good as transition base in dp[i-1]
            if(transitionSmall(dp, i, high, 0) > transitionSmall(dp, i, low, 0))
            {
                //It never happens!
                return -1;
            }

            ll left = 0;
            ll right = dp[i].size()-1;
            while(left < right)
            {
                ll mid = (left+right+1)/2;
                if(transitionSmall(dp, i, low, mid) >= transitionSmall(dp, i, high, mid))
                {
                    left = mid;
                }
                else
                {
                    right = mid-1;
                }
            }
            return left;
        }        
         
        long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y, std::vector<int> W) 
        {
            bool sub1 = true;
            bool sub2 = true;
            bool sub3 = true;
         
            for(ll i = 0; i < M; i++)
            {
                if(X[i] % 2 == 1)
                {
                    sub1 = false;
                }
                if(X[i] > 1)
                {
                    sub2 = false;
                }
                if(Y[i] != 0)
                {
                    sub3 = false;
                }
            }
         
            if(sub1)
            {
                ll sum = 0;
                for(int i : W)
                {
                    sum += (ll) i;
                }
                return sum;
            }
         
            if(sub2)
            {
                vector<pll> left(0);
                vector<pll> right(0); //Height, weight
                ll lsum = 0;
                ll rsum = 0;
         
                for(ll i = 0; i < M; i++)
                {
                    if(X[i] == 0)
                    {
                        left.push_back({Y[i], W[i]});
                        lsum += W[i];
                    }
                    else
                    {
                        right.push_back({Y[i], W[i]});
                        rsum += W[i];
                    }
                }
                sort(left.begin(), left.end());
                sort(right.begin(), right.end());
         
                ll output = max(lsum, rsum);
         
                if(N > 2)
                {
                    ll lindex = -1;
                    ll rindex = -1;
                    ll shadow = 0;
                    ll roof = 0;
                    for(ll i = 0; i < N; i++)
                    {
                        while(lindex+1 < (ll) left.size() && left[lindex+1].first <= i)
                        {
                            lindex++;
                            shadow += left[lindex].second;
                        }
                        while(rindex+1 < (ll) right.size() && right[rindex+1].first <= i)
                        {
                            rindex++;
                            roof += right[rindex].second;
                        }
                        output = max(output, shadow + rsum - roof);
                    }
                }
         
                return output;
            }
            
            if(sub3)
            {
                vector<ll> w(N, 0);
                for(ll i = 0; i < M; i++)
                {
                    w[X[i]] = W[i];
                }
         
                vector<vector<ll>> dp(N, vector<ll> (3, 0)); //Pier, no pier + uncaught, no pier + caught
                for(ll i = 1; i < N; i++)
                {
                    //Pier:
                    dp[i][0] = dp[i-1][0];
                    dp[i][0] = max(dp[i][0], dp[i-1][1]+w[i-1]);
                    dp[i][0] = max(dp[i][0], dp[i-1][2]);
         
                    //no pier + uncaught:
                    dp[i][1] = dp[i-1][1];
                    dp[i][1] = max(dp[i][1], dp[i-1][2]);
         
                    //no pier + caught:
                    dp[i][2] = dp[i-1][0]+w[i];
                }
         
                return max(max(dp[N-1][0], dp[N-1][1]), dp[N-1][2]);
            }
         
            vector<vector<fish>> grid(N, vector<fish> (0));
            for(ll i = 0; i < M; i++)
            {
                fish f;
                f.height = Y[i];
                f.weight = W[i];
                f.bigPier = 0;
                f.smallPier = 0;
                f.noPier = 0;
                grid[X[i]].push_back(f);
            }
         
            fish top, bottom;
            top.height = N;
            top.weight = 0;
            top.noPier = 0;
            top.bigPier = 0;
            top.smallPier = 0;
            bottom.height = -1;
            bottom.weight = 0;
            bottom.smallPier = 0;
            bottom.bigPier = 0;
            bottom.noPier = 0;
            for(ll i = 0; i < N; i++)
            {
                grid[i].push_back(top);
                grid[i].push_back(bottom);
                sort(grid[i].begin(), grid[i].end());
                ll sum = 0;
                for(ll j = 0; j < (ll) grid[i].size(); j++)
                {
                    grid[i][j].below = sum;
                    sum += grid[i][j].weight;
                }
                sum = 0;
                for(ll j = grid[i].size()-1; j >= 0; j--)
                {
                    grid[i][j].above = sum;
                    sum += grid[i][j].weight;
                }
            }
         
            for(ll i = 0; i < (ll) grid[0].size(); i++)
            {
                grid[0][i].bigPier = 0;
                grid[0][i].smallPier = 0;
                grid[0][i].noPier = 0;
            }
         
            for(ll i = 1; i < N; i++)
            {   
                //no pier:
                ll preind = 0;
                ll postind = 0;
                ll premax = 0;
                while(preind < (ll) grid[i-1].size())
                {
                    while(postind < (ll) grid[i].size() && grid[i-1][preind].height >= grid[i][postind].height)
                    {
                        grid[i][postind].noPier = max(grid[i-1][preind].bigPier, grid[i-1][preind].smallPier)+grid[i][postind].below;
                        postind++;
                    }
                    premax = max(premax, grid[i-1][preind].noPier);
                    preind++;
                }
                for(ll j = 0; j < (ll) grid[i].size(); j++)
                {
                    grid[i][j].noPier = max(grid[i][j].noPier, premax);
                }
                
                //calculate DP[i][j]:
                vector<pll> opt = {{0, 0}}; //Index in dp[i], index in dp[i-1]
                for(ll j = 1; j < (ll) grid[i-1].size(); j++)
                {
                    while(opt.size() && intersectBig(grid, i, opt.back().second, j) <= opt.back().first)
                    {
                        opt.pop_back();
                    }
                    if(opt.size())
                    {
                        opt.push_back({intersectBig(grid, i, opt.back().second, j), j});
                    }
                    else
                    {
                        opt.push_back({0, j});
                    }
                }
                ll optind = 0;
                for(ll j = 0; j < (ll) grid[i].size(); j++)
                {
                    //bigPier
                    while(optind < (ll) opt.size()-1 && opt[optind+1].first <= j)
                    {
                        optind++;
                    }
                    grid[i][j].bigPier = transitionBig(grid, i, opt[optind].second, j);
                }

                opt = {{grid[i].size()-1, grid[i-1].size()-1}}; //Index in dp[i], index in dp[i-1]
                for(ll j = grid[i-1].size()-2; j >= 0; j--)
                {
                    while(opt.size() && intersectSmall(grid, i, opt.back().second, j) >= opt.back().first)
                    {
                        opt.pop_back();
                    }
                    if(opt.size())
                    {
                        opt.push_back({intersectSmall(grid, i, opt.back().second, j), j});
                    }
                    else
                    {
                        opt.push_back({grid[i].size()-1, j});
                    }
                }
                optind = 0;
                for(ll j = grid[i].size()-1; j >= 0; j--)
                {
                    //smallPier
                    while(optind < (ll) opt.size()-1 && opt[optind+1].first >= j)
                    {
                        optind++;
                    }
                    grid[i][j].smallPier = transitionSmall(grid, i, opt[optind].second, j);
                }
            }
         
            ll output = 0;
            for(fish f : grid[N-1])
            {
                ll val = max(max(f.noPier, f.bigPier), f.smallPier);
                output = max(output, val);
            }
            
            return output;
        }

Subtask #1
3.0 / 3.0

#	결과	실행 시간	메모리	Grader output
1	Correct	19 ms	3540 KB	Output is correct
2	Correct	23 ms	4276 KB	Output is correct
3	Correct	0 ms	296 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	71 ms	12588 KB	Output is correct
6	Correct	79 ms	12884 KB	Output is correct

Subtask #2
6.0 / 6.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	60 ms	10048 KB	Output is correct
3	Correct	65 ms	11488 KB	Output is correct
4	Correct	18 ms	3548 KB	Output is correct
5	Correct	22 ms	4264 KB	Output is correct
6	Correct	0 ms	212 KB	Output is correct
7	Correct	0 ms	212 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Correct	1 ms	212 KB	Output is correct
10	Correct	1 ms	212 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	30 ms	5780 KB	Output is correct
13	Correct	32 ms	6572 KB	Output is correct
14	Correct	26 ms	5248 KB	Output is correct
15	Correct	28 ms	5696 KB	Output is correct
16	Correct	26 ms	5336 KB	Output is correct
17	Correct	28 ms	5684 KB	Output is correct

Subtask #3
9.0 / 9.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	6 ms	6484 KB	Output is correct
3	Correct	17 ms	8092 KB	Output is correct
4	Correct	14 ms	8020 KB	Output is correct
5	Correct	27 ms	10560 KB	Output is correct
6	Correct	28 ms	9920 KB	Output is correct
7	Correct	26 ms	10420 KB	Output is correct
8	Correct	27 ms	10432 KB	Output is correct

Subtask #4
14.0 / 14.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	296 KB	Output is correct
2	Correct	1 ms	300 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	296 KB	Output is correct
5	Correct	1 ms	304 KB	Output is correct
6	Correct	1 ms	300 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	0 ms	212 KB	Output is correct
9	Correct	1 ms	340 KB	Output is correct
10	Correct	2 ms	596 KB	Output is correct
11	Correct	1 ms	340 KB	Output is correct
12	Correct	1 ms	468 KB	Output is correct
13	Correct	1 ms	212 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	1 ms	296 KB	Output is correct
2	Correct	1 ms	300 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	296 KB	Output is correct
5	Correct	1 ms	304 KB	Output is correct
6	Correct	1 ms	300 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	0 ms	212 KB	Output is correct
9	Correct	1 ms	340 KB	Output is correct
10	Correct	2 ms	596 KB	Output is correct
11	Correct	1 ms	340 KB	Output is correct
12	Correct	1 ms	468 KB	Output is correct
13	Correct	1 ms	212 KB	Output is correct
14	Correct	1 ms	468 KB	Output is correct
15	Correct	1 ms	340 KB	Output is correct
16	Correct	2 ms	552 KB	Output is correct
17	Correct	38 ms	5072 KB	Output is correct
18	Correct	31 ms	6356 KB	Output is correct
19	Correct	28 ms	6484 KB	Output is correct
20	Correct	28 ms	6584 KB	Output is correct
21	Correct	26 ms	6352 KB	Output is correct
22	Correct	66 ms	11688 KB	Output is correct
23	Correct	6 ms	1492 KB	Output is correct
24	Correct	19 ms	3796 KB	Output is correct
25	Correct	1 ms	468 KB	Output is correct
26	Correct	5 ms	1364 KB	Output is correct

Subtask #6
17.0 / 17.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	296 KB	Output is correct
2	Correct	1 ms	300 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	296 KB	Output is correct
5	Correct	1 ms	304 KB	Output is correct
6	Correct	1 ms	300 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	0 ms	212 KB	Output is correct
9	Correct	1 ms	340 KB	Output is correct
10	Correct	2 ms	596 KB	Output is correct
11	Correct	1 ms	340 KB	Output is correct
12	Correct	1 ms	468 KB	Output is correct
13	Correct	1 ms	212 KB	Output is correct
14	Correct	1 ms	468 KB	Output is correct
15	Correct	1 ms	340 KB	Output is correct
16	Correct	2 ms	552 KB	Output is correct
17	Correct	38 ms	5072 KB	Output is correct
18	Correct	31 ms	6356 KB	Output is correct
19	Correct	28 ms	6484 KB	Output is correct
20	Correct	28 ms	6584 KB	Output is correct
21	Correct	26 ms	6352 KB	Output is correct
22	Correct	66 ms	11688 KB	Output is correct
23	Correct	6 ms	1492 KB	Output is correct
24	Correct	19 ms	3796 KB	Output is correct
25	Correct	1 ms	468 KB	Output is correct
26	Correct	5 ms	1364 KB	Output is correct
27	Correct	2 ms	1236 KB	Output is correct
28	Correct	158 ms	25604 KB	Output is correct
29	Correct	266 ms	37244 KB	Output is correct
30	Correct	210 ms	36048 KB	Output is correct
31	Correct	197 ms	36260 KB	Output is correct
32	Correct	216 ms	39512 KB	Output is correct
33	Correct	212 ms	36176 KB	Output is correct
34	Correct	198 ms	36224 KB	Output is correct
35	Correct	72 ms	15972 KB	Output is correct
36	Correct	211 ms	39412 KB	Output is correct

Subtask #7
14.0 / 14.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	6 ms	6484 KB	Output is correct
3	Correct	17 ms	8092 KB	Output is correct
4	Correct	14 ms	8020 KB	Output is correct
5	Correct	27 ms	10560 KB	Output is correct
6	Correct	28 ms	9920 KB	Output is correct
7	Correct	26 ms	10420 KB	Output is correct
8	Correct	27 ms	10432 KB	Output is correct
9	Correct	68 ms	30796 KB	Output is correct
10	Correct	57 ms	17712 KB	Output is correct
11	Correct	132 ms	34180 KB	Output is correct
12	Correct	1 ms	220 KB	Output is correct
13	Correct	1 ms	212 KB	Output is correct
14	Correct	0 ms	212 KB	Output is correct
15	Correct	1 ms	212 KB	Output is correct
16	Correct	0 ms	212 KB	Output is correct
17	Correct	0 ms	300 KB	Output is correct
18	Correct	0 ms	212 KB	Output is correct
19	Correct	0 ms	212 KB	Output is correct
20	Correct	6 ms	6484 KB	Output is correct
21	Correct	22 ms	15060 KB	Output is correct
22	Correct	72 ms	25984 KB	Output is correct
23	Correct	132 ms	33956 KB	Output is correct
24	Correct	151 ms	33768 KB	Output is correct

Subtask #8
16.0 / 16.0

#	결과	실행 시간	메모리	Grader output
1	Correct	19 ms	3540 KB	Output is correct
2	Correct	23 ms	4276 KB	Output is correct
3	Correct	0 ms	296 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	71 ms	12588 KB	Output is correct
6	Correct	79 ms	12884 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	60 ms	10048 KB	Output is correct
9	Correct	65 ms	11488 KB	Output is correct
10	Correct	18 ms	3548 KB	Output is correct
11	Correct	22 ms	4264 KB	Output is correct
12	Correct	0 ms	212 KB	Output is correct
13	Correct	0 ms	212 KB	Output is correct
14	Correct	1 ms	212 KB	Output is correct
15	Correct	1 ms	212 KB	Output is correct
16	Correct	1 ms	212 KB	Output is correct
17	Correct	1 ms	212 KB	Output is correct
18	Correct	30 ms	5780 KB	Output is correct
19	Correct	32 ms	6572 KB	Output is correct
20	Correct	26 ms	5248 KB	Output is correct
21	Correct	28 ms	5696 KB	Output is correct
22	Correct	26 ms	5336 KB	Output is correct
23	Correct	28 ms	5684 KB	Output is correct
24	Correct	1 ms	212 KB	Output is correct
25	Correct	6 ms	6484 KB	Output is correct
26	Correct	17 ms	8092 KB	Output is correct
27	Correct	14 ms	8020 KB	Output is correct
28	Correct	27 ms	10560 KB	Output is correct
29	Correct	28 ms	9920 KB	Output is correct
30	Correct	26 ms	10420 KB	Output is correct
31	Correct	27 ms	10432 KB	Output is correct
32	Correct	1 ms	296 KB	Output is correct
33	Correct	1 ms	300 KB	Output is correct
34	Correct	0 ms	212 KB	Output is correct
35	Correct	1 ms	296 KB	Output is correct
36	Correct	1 ms	304 KB	Output is correct
37	Correct	1 ms	300 KB	Output is correct
38	Correct	1 ms	212 KB	Output is correct
39	Correct	0 ms	212 KB	Output is correct
40	Correct	1 ms	340 KB	Output is correct
41	Correct	2 ms	596 KB	Output is correct
42	Correct	1 ms	340 KB	Output is correct
43	Correct	1 ms	468 KB	Output is correct
44	Correct	1 ms	212 KB	Output is correct
45	Correct	1 ms	468 KB	Output is correct
46	Correct	1 ms	340 KB	Output is correct
47	Correct	2 ms	552 KB	Output is correct
48	Correct	38 ms	5072 KB	Output is correct
49	Correct	31 ms	6356 KB	Output is correct
50	Correct	28 ms	6484 KB	Output is correct
51	Correct	28 ms	6584 KB	Output is correct
52	Correct	26 ms	6352 KB	Output is correct
53	Correct	66 ms	11688 KB	Output is correct
54	Correct	6 ms	1492 KB	Output is correct
55	Correct	19 ms	3796 KB	Output is correct
56	Correct	1 ms	468 KB	Output is correct
57	Correct	5 ms	1364 KB	Output is correct
58	Correct	2 ms	1236 KB	Output is correct
59	Correct	158 ms	25604 KB	Output is correct
60	Correct	266 ms	37244 KB	Output is correct
61	Correct	210 ms	36048 KB	Output is correct
62	Correct	197 ms	36260 KB	Output is correct
63	Correct	216 ms	39512 KB	Output is correct
64	Correct	212 ms	36176 KB	Output is correct
65	Correct	198 ms	36224 KB	Output is correct
66	Correct	72 ms	15972 KB	Output is correct
67	Correct	211 ms	39412 KB	Output is correct
68	Correct	68 ms	30796 KB	Output is correct
69	Correct	57 ms	17712 KB	Output is correct
70	Correct	132 ms	34180 KB	Output is correct
71	Correct	1 ms	220 KB	Output is correct
72	Correct	1 ms	212 KB	Output is correct
73	Correct	0 ms	212 KB	Output is correct
74	Correct	1 ms	212 KB	Output is correct
75	Correct	0 ms	212 KB	Output is correct
76	Correct	0 ms	300 KB	Output is correct
77	Correct	0 ms	212 KB	Output is correct
78	Correct	0 ms	212 KB	Output is correct
79	Correct	6 ms	6484 KB	Output is correct
80	Correct	22 ms	15060 KB	Output is correct
81	Correct	72 ms	25984 KB	Output is correct
82	Correct	132 ms	33956 KB	Output is correct
83	Correct	151 ms	33768 KB	Output is correct
84	Correct	346 ms	43096 KB	Output is correct
85	Correct	342 ms	44120 KB	Output is correct
86	Correct	221 ms	54036 KB	Output is correct
87	Correct	217 ms	55384 KB	Output is correct
88	Correct	1 ms	212 KB	Output is correct
89	Correct	226 ms	55500 KB	Output is correct
90	Correct	214 ms	51680 KB	Output is correct
91	Correct	199 ms	52388 KB	Output is correct

답안 #776689

Compilation message