oj.uz

답안 #420202

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
420202 2021-06-08T07:35:25 Z rama_pang Financial Report (JOI21_financial) C++17
100 / 100
 2166 ms 49520 KB 
#include <bits/stdc++.h>
using namespace std;

struct Segment { // max 0-segment
  bool allZero = false;
  int lft = 0;
  int rgt = 0;
  int opt = 0;

  Segment(int c = 0) {
    if (c == 0) {
      allZero = 1;
      lft = 1;
      rgt = 1;
      opt = 1;
    } else {
      allZero = 0;
      lft = 0;
      rgt = 0;
      opt = 0;
    }
  }

  friend Segment operator+(const Segment &a, const Segment &b) {
    Segment c(0);
    c.allZero = a.allZero && b.allZero;
    c.lft = a.lft + (a.allZero ? b.lft : 0);
    c.rgt = b.rgt + (b.allZero ? a.rgt : 0);
    c.opt = max({a.opt, b.opt, a.rgt + b.lft});
    return c;
  }
};

class MaxSubsegment {
 public:
  int sz;
  vector<Segment> tree;

  MaxSubsegment(int sz) : sz(sz) {
    tree.resize(2 * sz);
    for (int i = sz - 1; i >= 0; i--) {
      tree[i] = tree[i * 2] + tree[i * 2 + 1];
    }
  }

  void Modify(int p, int x) {
    tree[p += sz] = Segment(x);
    for (p /= 2; p > 0; p /= 2) {
      tree[p] = tree[p * 2] + tree[p * 2 + 1];
    }
  }

  Segment Query(int l, int r) {
    Segment lft(1), rgt(1);
    for (l += sz, r += sz + 1; l < r; l /= 2, r /= 2) {
      if (l & 1) lft = lft + tree[l++];
      if (r & 1) rgt = tree[--r] + rgt;
    }
    return lft + rgt;
  }
};

class SegTree {
 public:
  int sz;
  vector<int> tree;

  SegTree(int sz) : sz(sz), tree(2 * sz, -1e9) {}

  int Query(int l, int r) {
    int z = 0;
    for (l += sz, r += sz + 1; l < r; l /= 2, r /= 2) {
      if (l & 1) z = max(z, tree[l++]);
      if (r & 1) z = max(z, tree[--r]);
    }
    return z;
  }

  void Modify(int p, int x) {
    tree[p += sz] = x;
    for (p /= 2; p > 0; p /= 2) {
      tree[p] = max(tree[p * 2], tree[p * 2 + 1]);
    }
  }
};

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N, D;
  cin >> N >> D;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }
  { // Coordinate Compression
    vector<int> coords = A;
    sort(begin(coords), end(coords));
    coords.resize(unique(begin(coords), end(coords)) - begin(coords));
    for (auto &a : A) {
      a = lower_bound(begin(coords), end(coords), a) - begin(coords);
    }
  }

  // dp[pos][max_element]
  // find maximum value on dp[pos-D...pos][0...A[pos] - 1] -> dp[pos][A[pos]] = 1 + best
  // for x >= A[pos]: dp[pos-D...pos][x] -> dp[pos][x]
  //
  // If we group all occurrences of value val which has distance <= D, then
  // dp[i][val] <= dp[j][val] for i < j (since we can retake "val").
  // We can transform the sequence such that this condition is fullfilled without
  // the distance <= D condition.
  //
  // How? We scan from least valued element, then when we arrive at "val", group them
  // which has distance <= D. Afterwards, we reassign values s.t. the ones in the back
  // has lower value than the ones in the front.
  //
  // After this transformation, dp[i][val] <= dp[j][val] for i < j. So, we only need
  // to store last occurrence of dp[i][val]. This yields O(N^2).
  //
  // For a value "val", since all adjacent occurrence has distance <= D, then the value
  // "val" is valid only for some subsegment of the array. We can precompute this, then
  // we only need to consider "active" values when transitioning. Afterwards, we don't
  // need the array last[], and it's basically a simple DP optimized with segment tree.
  //
  // Time complexity: O(N log N).

  { // Transformation s.t. dp[i][val] <= dp[j][val] for i < j
    int value = 0;
    vector<vector<int>> occ(N);
    for (int i = 0; i < N; i++) {
      occ[A[i]].emplace_back(i);
    }
    for (int v = 0; v < N; v++) {
      int cnt = 0;
      for (int i = 0; i < int(occ[v].size()); i++) {
        int j = i;
        while (j + 1 < int(occ[v].size()) && occ[v][j + 1] - occ[v][j] <= D) {
          j += 1;
        }
        cnt += 1;
        i = j;
      }
      value += cnt;
      cnt = 0;
      for (int i = 0; i < int(occ[v].size()); i++) {
        int j = i;
        while (j + 1 < int(occ[v].size()) && occ[v][j + 1] - occ[v][j] <= D) {
          j += 1;
        }
        cnt += 1;
        for (int k = i; k <= j; k++) {
          A[occ[v][k]] = value - cnt;
        }
        i = j;
      }
    }
    assert(*max_element(begin(A), end(A)) < N);
  }

  const auto DP_N2_Old = [&](int N, int D, vector<int> A) {
    vector<int> dp(N, -1e9);
    vector<int> last(N, -1e9);
    for (int pos = 0; pos < N; pos++) {
      for (int i = A[pos]; i < N; i++) {
        if (pos - last[i] <= D) {
          last[i] = pos;
        }
      }
      last[A[pos]] = pos;
      dp[A[pos]] = max(dp[A[pos]], 1);
      for (int i = 0; i < A[pos]; i++) {
        if (pos - last[i] <= D) {
          dp[A[pos]] = max(dp[A[pos]], dp[i] + 1);
        }
      }
    }

    int ans = 0;
    for (int i = A[N - 1]; i < N; i++) {
      if (N - 1 - last[i] <= D) {
        ans = max(ans, dp[i]);
      }
    }
    return ans;
  };

  const auto Solve = [&](int N, int D, vector<int> A) {
    vector<int> startValid(N, -1);
    vector<int> endValid(N, -1);
    for (int i = 0; i < N; i++) {
      if (startValid[A[i]] == -1) {
        startValid[A[i]] = i;
      }
      endValid[A[i]] = i;
    }

    vector<vector<int>> occ(N);
    for (int i = 0; i < N; i++) {
      occ[A[i]].emplace_back(i);
    }

    MaxSubsegment maxSeg(N);
    for (int i = 0; i < N; i++) if (endValid[i] != -1) {
      for (auto j : occ[i]) {
        maxSeg.Modify(j, 1);
      }

      int lo = endValid[i];
      int hi = N - 1;
      while (lo < hi) {
        int md = (lo + hi) / 2;
        if (maxSeg.Query(endValid[i], md).opt >= D) {
          hi = md;
        } else {
          lo = md + 1;
        }
      }
      endValid[i] = lo;
    }

    SegTree dpSeg(N);
    vector<vector<int>> endEvent(N + 1);
    for (int i = 0; i < N; i++) {
      endEvent[endValid[i] + 1].emplace_back(i);
    }
    for (int pos = 0; pos < N; pos++) {
      for (auto j : endEvent[pos]) {
        dpSeg.Modify(j, -1e9);
      }
      int val = max({dpSeg.Query(A[pos], A[pos]), 1, 1 + dpSeg.Query(0, A[pos] - 1)});
      dpSeg.Modify(A[pos], val);
    }

    return dpSeg.Query(0, N - 1);
  };

  cout << Solve(N, D, A) << '\n';
  return 0;
}

Compilation message

Main.cpp: In function 'int main()':
Main.cpp:162:14: warning: variable 'DP_N2_Old' set but not used [-Wunused-but-set-variable]
  162 |   const auto DP_N2_Old = [&](int N, int D, vector<int> A) {
      |              ^~~~~~~~~

Subtask #1
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 224 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 0 ms 204 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 0 ms 204 KB Output is correct
25 Correct 0 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct

Subtask #2
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 224 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 0 ms 204 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 0 ms 204 KB Output is correct
25 Correct 0 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 332 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 2 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 2 ms 332 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 1 ms 332 KB Output is correct
39 Correct 2 ms 332 KB Output is correct
40 Correct 1 ms 332 KB Output is correct

Subtask #3
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 224 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 0 ms 204 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 0 ms 204 KB Output is correct
25 Correct 0 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 332 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 2 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 2 ms 332 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 1 ms 332 KB Output is correct
39 Correct 2 ms 332 KB Output is correct
40 Correct 1 ms 332 KB Output is correct
41 Correct 16 ms 1316 KB Output is correct
42 Correct 16 ms 1336 KB Output is correct
43 Correct 10 ms 1064 KB Output is correct
44 Correct 18 ms 1152 KB Output is correct
45 Correct 17 ms 1200 KB Output is correct
46 Correct 19 ms 1296 KB Output is correct
47 Correct 15 ms 1276 KB Output is correct
48 Correct 17 ms 1196 KB Output is correct
49 Correct 22 ms 1296 KB Output is correct
50 Correct 27 ms 1308 KB Output is correct
51 Correct 20 ms 1304 KB Output is correct
52 Correct 17 ms 1316 KB Output is correct
53 Correct 13 ms 1308 KB Output is correct
54 Correct 16 ms 1188 KB Output is correct
55 Correct 20 ms 1308 KB Output is correct
56 Correct 19 ms 1288 KB Output is correct
57 Correct 19 ms 1296 KB Output is correct
58 Correct 19 ms 1316 KB Output is correct
59 Correct 18 ms 1348 KB Output is correct
60 Correct 23 ms 1292 KB Output is correct
61 Correct 18 ms 1268 KB Output is correct

Subtask #4
12.0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 201 ms 36236 KB Output is correct
2 Correct 971 ms 43580 KB Output is correct
3 Correct 1553 ms 44972 KB Output is correct
4 Correct 1984 ms 45168 KB Output is correct
5 Correct 1508 ms 46296 KB Output is correct
6 Correct 2023 ms 45168 KB Output is correct
7 Correct 893 ms 49296 KB Output is correct
8 Correct 1462 ms 43276 KB Output is correct
9 Correct 1014 ms 46916 KB Output is correct
10 Correct 1173 ms 44264 KB Output is correct
11 Correct 1273 ms 45036 KB Output is correct
12 Correct 1392 ms 45092 KB Output is correct
13 Correct 1512 ms 49520 KB Output is correct
14 Correct 1893 ms 41836 KB Output is correct

Subtask #5
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 200 ms 36188 KB Output is correct
2 Correct 296 ms 35556 KB Output is correct
3 Correct 361 ms 36108 KB Output is correct
4 Correct 2166 ms 43380 KB Output is correct
5 Correct 1788 ms 43376 KB Output is correct
6 Correct 2115 ms 43456 KB Output is correct
7 Correct 1354 ms 43376 KB Output is correct
8 Correct 1283 ms 43372 KB Output is correct
9 Correct 1294 ms 43180 KB Output is correct
10 Correct 1703 ms 43320 KB Output is correct
11 Correct 2059 ms 43376 KB Output is correct
12 Correct 1880 ms 43380 KB Output is correct

Subtask #6
35.0 / 35.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 224 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 0 ms 204 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 0 ms 204 KB Output is correct
25 Correct 0 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 332 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 2 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 2 ms 332 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 1 ms 332 KB Output is correct
39 Correct 2 ms 332 KB Output is correct
40 Correct 1 ms 332 KB Output is correct
41 Correct 16 ms 1316 KB Output is correct
42 Correct 16 ms 1336 KB Output is correct
43 Correct 10 ms 1064 KB Output is correct
44 Correct 18 ms 1152 KB Output is correct
45 Correct 17 ms 1200 KB Output is correct
46 Correct 19 ms 1296 KB Output is correct
47 Correct 15 ms 1276 KB Output is correct
48 Correct 17 ms 1196 KB Output is correct
49 Correct 22 ms 1296 KB Output is correct
50 Correct 27 ms 1308 KB Output is correct
51 Correct 20 ms 1304 KB Output is correct
52 Correct 17 ms 1316 KB Output is correct
53 Correct 13 ms 1308 KB Output is correct
54 Correct 16 ms 1188 KB Output is correct
55 Correct 20 ms 1308 KB Output is correct
56 Correct 19 ms 1288 KB Output is correct
57 Correct 19 ms 1296 KB Output is correct
58 Correct 19 ms 1316 KB Output is correct
59 Correct 18 ms 1348 KB Output is correct
60 Correct 23 ms 1292 KB Output is correct
61 Correct 18 ms 1268 KB Output is correct
62 Correct 201 ms 36236 KB Output is correct
63 Correct 971 ms 43580 KB Output is correct
64 Correct 1553 ms 44972 KB Output is correct
65 Correct 1984 ms 45168 KB Output is correct
66 Correct 1508 ms 46296 KB Output is correct
67 Correct 2023 ms 45168 KB Output is correct
68 Correct 893 ms 49296 KB Output is correct
69 Correct 1462 ms 43276 KB Output is correct
70 Correct 1014 ms 46916 KB Output is correct
71 Correct 1173 ms 44264 KB Output is correct
72 Correct 1273 ms 45036 KB Output is correct
73 Correct 1392 ms 45092 KB Output is correct
74 Correct 1512 ms 49520 KB Output is correct
75 Correct 1893 ms 41836 KB Output is correct
76 Correct 200 ms 36188 KB Output is correct
77 Correct 296 ms 35556 KB Output is correct
78 Correct 361 ms 36108 KB Output is correct
79 Correct 2166 ms 43380 KB Output is correct
80 Correct 1788 ms 43376 KB Output is correct
81 Correct 2115 ms 43456 KB Output is correct
82 Correct 1354 ms 43376 KB Output is correct
83 Correct 1283 ms 43372 KB Output is correct
84 Correct 1294 ms 43180 KB Output is correct
85 Correct 1703 ms 43320 KB Output is correct
86 Correct 2059 ms 43376 KB Output is correct
87 Correct 1880 ms 43380 KB Output is correct
88 Correct 1737 ms 44028 KB Output is correct
89 Correct 1888 ms 43608 KB Output is correct
90 Correct 2005 ms 42864 KB Output is correct
91 Correct 2102 ms 43504 KB Output is correct
92 Correct 234 ms 35900 KB Output is correct
93 Correct 507 ms 36332 KB Output is correct
94 Correct 1549 ms 39496 KB Output is correct
95 Correct 1589 ms 44652 KB Output is correct
96 Correct 1769 ms 42976 KB Output is correct
97 Correct 1978 ms 42100 KB Output is correct
98 Correct 1925 ms 43636 KB Output is correct
99 Correct 1862 ms 43480 KB Output is correct
100 Correct 1826 ms 43460 KB Output is correct
101 Correct 824 ms 44916 KB Output is correct
102 Correct 939 ms 42228 KB Output is correct
103 Correct 1196 ms 41868 KB Output is correct
104 Correct 1329 ms 41844 KB Output is correct
105 Correct 1590 ms 42204 KB Output is correct
106 Correct 1417 ms 43372 KB Output is correct
107 Correct 1492 ms 43428 KB Output is correct
108 Correct 1715 ms 43456 KB Output is correct
109 Correct 1227 ms 49516 KB Output is correct
110 Correct 1725 ms 43756 KB Output is correct
111 Correct 1818 ms 42608 KB Output is correct
112 Correct 1478 ms 43812 KB Output is correct
113 Correct 1804 ms 43380 KB Output is correct
114 Correct 1812 ms 43372 KB Output is correct
115 Correct 1214 ms 43376 KB Output is correct
116 Correct 1194 ms 43376 KB Output is correct
117 Correct 1287 ms 43372 KB Output is correct
118 Correct 1262 ms 43376 KB Output is correct
119 Correct 1584 ms 43332 KB Output is correct
120 Correct 1616 ms 43336 KB Output is correct