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답안 #629811

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
629811 2022-08-15T08:11:28 Z spacewalker 메기 농장 (IOI22_fish) C++17
70 / 100
 750 ms 2097152 KB 
#include "fish.h"

#include <vector>
#include <bits/stdc++.h>

using namespace std;
using ll = long long;
constexpr ll INF = 1000000000000000000;

long long subtask_bypass(int N, int M, std::vector<int> X, std::vector<int> Y,
                      std::vector<int> W) {
    if (all_of(begin(X), end(X), [] (int v) {return v%2 == 0;})) {
        // subtask 1
        return accumulate(begin(W), end(W), 0LL);
    }
    return -1; // this is full problem
}
/*
    to make life easier, the value of a pier is (wt of fish behind/in front) - (wt of fish on pier)
    the path can be in a few states;
        - back-facing (pier at x=i that catches some fish at i-1)
        - front-facing (pier at x=i-1 that catches some fish at i)
    
    a back-facing path at y=h can move to
        - a back-facing path at some higher/same y value
        - a front-facing path at the same y value (do NOT count the - value of this pier, and ADD it to cancel the - of the ff path)

    a front-facing path at y=h can move to
        - a front-facing path at some lower/(same) y value
        - a back-facing path at some lower/same y value (do NOT count the + value of the first back-facing pier)
        - a back-facing path at a higher/(same) y value (do NOT count the + value of this pier)
        - stasis

    stasis can move to any back-facing path, or to stasis

    start the x-coordinates at 1; starting state is stasis at x=0
    pad 2 columns to the right; end state is stasis on last column

    then dp to get max weight path from start to end state
*/

long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
                      std::vector<int> _W) {

    // solve subtask 1 manually
    ll bypass = subtask_bypass(N, M, X, Y, _W);
    if (bypass != -1) return bypass;

    // otherwise
    int W = min(N, *max_element(begin(X), end(X)) + 2);
    int H = *max_element(begin(Y), end(Y)) + 1;
    

    vector<vector<ll>> weights(W + 3, vector<ll>(H));
    for (int i = 0; i < M; ++i) {
        weights[X[i] + 1][Y[i]] = _W[i];
    }
    vector<vector<ll>> columnSum = weights;
    for (int xc = 0; xc < columnSum.size(); ++xc) {
        for (int yc = 1; yc < H; ++yc) {
            columnSum[xc][yc] += columnSum[xc][yc-1];
        }
    }
    // needs xc > 0
    auto pierValue = [&] (int xc, int yc, int c1, int c2) {
        return c1 * columnSum[xc-1][yc] + c2 * columnSum[xc][yc];
    };
    vector<ll> stasisOpt(W + 3, -INF);
    vector<vector<ll>> backFaceOpt(W+3, vector<ll>(H, -INF)), frontFaceOpt(W+3, vector<ll>(H, -INF));
    // mod = -pierValue(xc, yc, 1, 0) is added to the entries
    vector<ll> nxtBackFaceModPrefMax(H, -INF), nxtBackFaceSufMax(H, -INF), nxtFrontFacePrefMax(H, -INF);
    stasisOpt[W+2] = 0;
    for (int xc = W+1; xc >= 0; --xc) {
        ll &s = stasisOpt[xc];
        for (int yc = 0; yc < H; ++yc) {
            ll &b = backFaceOpt[xc][yc], &f = frontFaceOpt[xc][yc];
            if (0 < xc && xc <= W) {
                // find value for the back-facing path here
                b = max(b, frontFaceOpt[xc+1][yc] + pierValue(xc, yc, 1, 1));
                /*
                for (int nyc = yc; nyc < N; ++nyc) {
                    b = max(b, backFaceOpt[xc+1][nyc] + pierValue(xc, yc, 1, -1));
                }
                */
                b = max(b, nxtBackFaceSufMax[yc] + pierValue(xc, yc, 1, -1));
            }
            if (2 <= xc && xc <= W + 1) {
                // find value for the front-facing path here
                f = max(f, stasisOpt[xc+1] + pierValue(xc, yc, -1, 1));
                /*
                for (int nyc = 0; nyc <= yc; ++nyc) {
                    f = max(f, frontFaceOpt[xc+1][nyc] + pierValue(xc, yc, -1, 1));
                    f = max(f, backFaceOpt[xc+1][nyc] + pierValue(xc, yc, -1, 1) - pierValue(xc+1, nyc, 1, 0));
                }
                */
                f = max(f, nxtFrontFacePrefMax[yc] + pierValue(xc, yc, -1, 1));
                f = max(f, nxtBackFaceModPrefMax[yc] + pierValue(xc, yc, -1, 1));
                /*
                for (int nyc = yc; nyc < N; ++nyc) {
                    f = max(f, backFaceOpt[xc+1][nyc] + pierValue(xc, yc, -1, 0));
                }
                */
                f = max(f, nxtBackFaceSufMax[yc] + pierValue(xc, yc, -1, 0));
            }
        }
        // find value for the stasis path here
        s = max(s, stasisOpt[xc+1]);
        for (int nyc = 0; nyc < H; ++nyc) {
            s = max(s, backFaceOpt[xc+1][nyc]);
        }
        // compute the prefix/suffix max arrays
        if (xc > 0) {
            nxtFrontFacePrefMax = frontFaceOpt[xc];
            for (int i = 1; i < H; ++i) nxtFrontFacePrefMax[i] = max(nxtFrontFacePrefMax[i-1], nxtFrontFacePrefMax[i]);
            nxtBackFaceModPrefMax = backFaceOpt[xc];
            for (int i = 0; i < H; ++i) nxtBackFaceModPrefMax[i] -= pierValue(xc, i, 1, 0);
            for (int i = 1; i < H; ++i) nxtBackFaceModPrefMax[i] = max(nxtBackFaceModPrefMax[i-1], nxtBackFaceModPrefMax[i]);
            nxtBackFaceSufMax = backFaceOpt[xc];
            for (int i = H - 2; i >= 0; --i) nxtBackFaceSufMax[i] = max(nxtBackFaceSufMax[i+1], nxtBackFaceSufMax[i]);
        }
    }
    return stasisOpt[0];
}

Compilation message

fish.cpp: In function 'long long int max_weights(int, int, std::vector<int>, std::vector<int>, std::vector<int>)':
fish.cpp:59:25: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   59 |     for (int xc = 0; xc < columnSum.size(); ++xc) {
      |                      ~~~^~~~~~~~~~~~~~~~~~

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 23 ms 3344 KB Output is correct
2 Correct 29 ms 5556 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 87 ms 12592 KB Output is correct
6 Correct 84 ms 12620 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 70 ms 23476 KB Output is correct
3 Correct 84 ms 28720 KB Output is correct
4 Correct 22 ms 4436 KB Output is correct
5 Correct 29 ms 5556 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 41 ms 22604 KB Output is correct
13 Correct 53 ms 25488 KB Output is correct
14 Correct 47 ms 22604 KB Output is correct
15 Correct 45 ms 25176 KB Output is correct
16 Correct 40 ms 22620 KB Output is correct
17 Correct 48 ms 25104 KB Output is correct

Subtask #3
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 35 ms 22904 KB Output is correct
3 Correct 43 ms 21852 KB Output is correct
4 Correct 41 ms 21992 KB Output is correct
5 Correct 58 ms 25420 KB Output is correct
6 Correct 60 ms 26292 KB Output is correct
7 Correct 59 ms 26900 KB Output is correct
8 Correct 61 ms 26804 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 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 1 ms 340 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 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 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 1 ms 340 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 4 ms 3156 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 16 ms 4272 KB Output is correct
18 Correct 17 ms 4164 KB Output is correct
19 Correct 16 ms 4148 KB Output is correct
20 Correct 15 ms 4164 KB Output is correct
21 Correct 17 ms 2740 KB Output is correct
22 Correct 26 ms 5300 KB Output is correct
23 Correct 6 ms 3412 KB Output is correct
24 Correct 11 ms 3828 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 5 ms 3284 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 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 1 ms 340 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 4 ms 3156 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 16 ms 4272 KB Output is correct
18 Correct 17 ms 4164 KB Output is correct
19 Correct 16 ms 4148 KB Output is correct
20 Correct 15 ms 4164 KB Output is correct
21 Correct 17 ms 2740 KB Output is correct
22 Correct 26 ms 5300 KB Output is correct
23 Correct 6 ms 3412 KB Output is correct
24 Correct 11 ms 3828 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 5 ms 3284 KB Output is correct
27 Correct 302 ms 282800 KB Output is correct
28 Correct 73 ms 23088 KB Output is correct
29 Correct 342 ms 245840 KB Output is correct
30 Correct 388 ms 289984 KB Output is correct
31 Correct 389 ms 289980 KB Output is correct
32 Correct 84 ms 16828 KB Output is correct
33 Correct 394 ms 289976 KB Output is correct
34 Correct 370 ms 289908 KB Output is correct
35 Correct 49 ms 18380 KB Output is correct
36 Correct 193 ms 115744 KB Output is correct

Subtask #7
0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 35 ms 22904 KB Output is correct
3 Correct 43 ms 21852 KB Output is correct
4 Correct 41 ms 21992 KB Output is correct
5 Correct 58 ms 25420 KB Output is correct
6 Correct 60 ms 26292 KB Output is correct
7 Correct 59 ms 26900 KB Output is correct
8 Correct 61 ms 26804 KB Output is correct
9 Runtime error 750 ms 2097152 KB Execution killed with signal 9
10 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 23 ms 3344 KB Output is correct
2 Correct 29 ms 5556 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 87 ms 12592 KB Output is correct
6 Correct 84 ms 12620 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 70 ms 23476 KB Output is correct
9 Correct 84 ms 28720 KB Output is correct
10 Correct 22 ms 4436 KB Output is correct
11 Correct 29 ms 5556 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 300 KB Output is correct
15 Correct 1 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 41 ms 22604 KB Output is correct
19 Correct 53 ms 25488 KB Output is correct
20 Correct 47 ms 22604 KB Output is correct
21 Correct 45 ms 25176 KB Output is correct
22 Correct 40 ms 22620 KB Output is correct
23 Correct 48 ms 25104 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 35 ms 22904 KB Output is correct
26 Correct 43 ms 21852 KB Output is correct
27 Correct 41 ms 21992 KB Output is correct
28 Correct 58 ms 25420 KB Output is correct
29 Correct 60 ms 26292 KB Output is correct
30 Correct 59 ms 26900 KB Output is correct
31 Correct 61 ms 26804 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 0 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 340 KB Output is correct
41 Correct 1 ms 468 KB Output is correct
42 Correct 1 ms 340 KB Output is correct
43 Correct 1 ms 340 KB Output is correct
44 Correct 0 ms 212 KB Output is correct
45 Correct 1 ms 340 KB Output is correct
46 Correct 4 ms 3156 KB Output is correct
47 Correct 1 ms 468 KB Output is correct
48 Correct 16 ms 4272 KB Output is correct
49 Correct 17 ms 4164 KB Output is correct
50 Correct 16 ms 4148 KB Output is correct
51 Correct 15 ms 4164 KB Output is correct
52 Correct 17 ms 2740 KB Output is correct
53 Correct 26 ms 5300 KB Output is correct
54 Correct 6 ms 3412 KB Output is correct
55 Correct 11 ms 3828 KB Output is correct
56 Correct 1 ms 468 KB Output is correct
57 Correct 5 ms 3284 KB Output is correct
58 Correct 302 ms 282800 KB Output is correct
59 Correct 73 ms 23088 KB Output is correct
60 Correct 342 ms 245840 KB Output is correct
61 Correct 388 ms 289984 KB Output is correct
62 Correct 389 ms 289980 KB Output is correct
63 Correct 84 ms 16828 KB Output is correct
64 Correct 394 ms 289976 KB Output is correct
65 Correct 370 ms 289908 KB Output is correct
66 Correct 49 ms 18380 KB Output is correct
67 Correct 193 ms 115744 KB Output is correct
68 Runtime error 750 ms 2097152 KB Execution killed with signal 9
69 Halted 0 ms 0 KB -