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답안 #629808

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
629808 2022-08-15T08:09:58 Z spacewalker 메기 농장 (IOI22_fish) C++17
55 / 100
 773 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)) + 1), H = *max_element(begin(Y), end(Y)) + 2;
    int W = N, H = N;

    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:58:25: 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]
   58 |     for (int xc = 0; xc < columnSum.size(); ++xc) {
      |                      ~~~^~~~~~~~~~~~~~~~~~

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 22 ms 3048 KB Output is correct
2 Correct 29 ms 3784 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 86 ms 10732 KB Output is correct
6 Correct 89 ms 10736 KB Output is correct

Subtask #2
0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Runtime error 773 ms 2097152 KB Execution killed with signal 9
3 Halted 0 ms 0 KB -

Subtask #3
0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Runtime error 726 ms 2097152 KB Execution killed with signal 9
3 Halted 0 ms 0 KB -

Subtask #4
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 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 1 ms 212 KB Output is correct
9 Correct 2 ms 980 KB Output is correct
10 Correct 5 ms 3284 KB Output is correct
11 Correct 1 ms 980 KB Output is correct
12 Correct 4 ms 3228 KB Output is correct
13 Correct 1 ms 428 KB Output is correct
14 Correct 4 ms 3124 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 1 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 1 ms 212 KB Output is correct
9 Correct 2 ms 980 KB Output is correct
10 Correct 5 ms 3284 KB Output is correct
11 Correct 1 ms 980 KB Output is correct
12 Correct 4 ms 3228 KB Output is correct
13 Correct 1 ms 428 KB Output is correct
14 Correct 4 ms 3124 KB Output is correct
15 Correct 4 ms 3116 KB Output is correct
16 Correct 1 ms 568 KB Output is correct
17 Correct 16 ms 5028 KB Output is correct
18 Correct 16 ms 4932 KB Output is correct
19 Correct 16 ms 4908 KB Output is correct
20 Correct 15 ms 4892 KB Output is correct
21 Correct 16 ms 4904 KB Output is correct
22 Correct 27 ms 6700 KB Output is correct
23 Correct 6 ms 3496 KB Output is correct
24 Correct 11 ms 4340 KB Output is correct
25 Correct 4 ms 3156 KB Output is correct
26 Correct 7 ms 3412 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 1 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 1 ms 212 KB Output is correct
9 Correct 2 ms 980 KB Output is correct
10 Correct 5 ms 3284 KB Output is correct
11 Correct 1 ms 980 KB Output is correct
12 Correct 4 ms 3228 KB Output is correct
13 Correct 1 ms 428 KB Output is correct
14 Correct 4 ms 3124 KB Output is correct
15 Correct 4 ms 3116 KB Output is correct
16 Correct 1 ms 568 KB Output is correct
17 Correct 16 ms 5028 KB Output is correct
18 Correct 16 ms 4932 KB Output is correct
19 Correct 16 ms 4908 KB Output is correct
20 Correct 15 ms 4892 KB Output is correct
21 Correct 16 ms 4904 KB Output is correct
22 Correct 27 ms 6700 KB Output is correct
23 Correct 6 ms 3496 KB Output is correct
24 Correct 11 ms 4340 KB Output is correct
25 Correct 4 ms 3156 KB Output is correct
26 Correct 7 ms 3412 KB Output is correct
27 Correct 316 ms 282972 KB Output is correct
28 Correct 75 ms 23144 KB Output is correct
29 Correct 404 ms 289980 KB Output is correct
30 Correct 398 ms 289964 KB Output is correct
31 Correct 394 ms 289984 KB Output is correct
32 Correct 95 ms 16804 KB Output is correct
33 Correct 383 ms 289968 KB Output is correct
34 Correct 373 ms 289988 KB Output is correct
35 Correct 336 ms 285680 KB Output is correct
36 Correct 378 ms 289980 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 Runtime error 726 ms 2097152 KB Execution killed with signal 9
3 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 22 ms 3048 KB Output is correct
2 Correct 29 ms 3784 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 86 ms 10732 KB Output is correct
6 Correct 89 ms 10736 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Runtime error 773 ms 2097152 KB Execution killed with signal 9
9 Halted 0 ms 0 KB -