oj.uz

Submission #755122

# Submission time Handle Problem Language Result Execution time Memory
755122 2023-06-09T12:21:54 Z boris_mihov Radio Towers (IOI22_towers) C++17
17 / 100
 1475 ms 57096 KB 
#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>
#include <stack>

typedef long long llong;
const int MAXLOG = 20 + 5;
const int MAXN = 100000 + 10;
const int INF  = 1e9;

int n;
struct MST
{
    std::vector <int> tree[4*MAXN];
    void build(int l, int r, int node, int vals[])
    {
        if (l == r)
        {
            tree[node].push_back(vals[l]);
            return;
        }

        int mid = (l + r) / 2;
        build(l, mid, 2*node, vals);
        build(mid + 1, r, 2*node + 1, vals);
        tree[node].reserve(r - l + 1);

        int lPtr = 0, rPtr = 0;
        for (int i = l ; i <= r ; ++i)
        {
            if (lPtr == tree[2*node].size())
            {
                tree[node].push_back(tree[2*node + 1][rPtr++]);
                continue;
            }

            if (rPtr == tree[2*node + 1].size())
            {
                tree[node].push_back(tree[2*node][lPtr++]);
                continue;
            }

            if (tree[2*node][lPtr] < tree[2*node + 1][rPtr])
            {
                tree[node].push_back(tree[2*node][lPtr++]);
            } else
            {
                tree[node].push_back(tree[2*node + 1][rPtr++]);
            }
        }
    }

    int binaryCount(int node, int val)
    {
        int l = -1, r = tree[node].size(), mid;
        while (l < r - 1)
        {
            mid = (l + r) / 2;
            if (tree[node][mid] <= val) l = mid;
            else r = mid;
        }

        return r;
    }

    int binaryFirst(int node, int val)
    {
        int l = -1, r = tree[node].size(), mid;
        while (l < r - 1)
        {
            mid = (l + r) / 2;
            if (tree[node][mid] < val) l = mid;
            else r = mid;
        }

        return (r == tree[node].size() ? INF : tree[node][r]);
    }

    int binaryLast(int node, int val)
    {
        int l = -1, r = tree[node].size(), mid;
        while (l < r - 1)
        {
            mid = (l + r) / 2;
            if (tree[node][mid] <= val) l = mid;
            else r = mid;
        }

        return (l == -1 ? 0 : tree[node][l]);
    }

    int queryCount(int l, int r, int node, int queryL, int queryR, int queryValL, int queryValR)
    {
        if (queryL <= l && r <= queryR)
        {
            return binaryCount(node, queryValR) - binaryCount(node, queryValL - 1);
        }

        int res = 0;
        int mid = (l + r) / 2;
        if (queryL <= mid) res += queryCount(l, mid, 2*node, queryL, queryR, queryValL, queryValR);
        if (mid + 1 <= queryR) res += queryCount(mid + 1, r, 2*node + 1, queryL, queryR, queryValL, queryValR);
        return res;
    }

    int queryFirst(int l, int r, int node, int queryL, int queryR, int queryVal)
    {
        if (queryL <= l && r <= queryR)
        {
            return binaryFirst(node, queryVal);
        }

        int res = INF;
        int mid = (l + r) / 2;
        if (queryL <= mid) res = std::min(res, queryFirst(l, mid, 2*node, queryL, queryR, queryVal));
        if (mid + 1 <= queryR) res = std::min(res, queryFirst(mid + 1, r, 2*node + 1, queryL, queryR, queryVal));
        return res;
    }

    int queryLast(int l, int r, int node, int queryL, int queryR, int queryVal)
    {
        if (queryL <= l && r <= queryR)
        {
            return binaryLast(node, queryVal);
        }

        int res = 0;
        int mid = (l + r) / 2;
        if (queryL <= mid) res = std::max(res, queryLast(l, mid, 2*node, queryL, queryR, queryVal));
        if (mid + 1 <= queryR) res = std::max(res, queryLast(mid + 1, r, 2*node + 1, queryL, queryR, queryVal));
        return res;
    }

    void build(int vals[])
    {
        build(1, n, 1, vals);
    }

    int queryCount(int to, int l, int r)
    {
        return queryCount(1, n, 1, 1, to, l, r);
    }

    int queryFirst(int to, int l)
    {
        return queryFirst(1, n, 1, 1, to, l);
    }

    int queryLast(int to, int r)
    {
        return queryLast(1, n, 1, 1, to, r);
    }
};

MST left, right;
struct SparseMAX
{
    int sparseMAX[MAXLOG][MAXN];
    int vals[MAXN];
    int lg[MAXN];

    int cmp(int x, int y)
    {
        if (vals[x] > vals[y]) return x;
        return y;
    }

    void build(int _vals[])
    {
        for (int i = 1 ; i <= n ; ++i)
        {
            sparseMAX[0][i] = i;
            vals[i] = _vals[i];
        }

        for (int log = 1 ; (1 << log) <= n ; ++log)
        {
            for (int i = 1 ; i + (1 << log) - 1 <= n ; ++i)
            {
                sparseMAX[log][i] = cmp(sparseMAX[log - 1][i], sparseMAX[log - 1][i + (1 << log - 1)]);
            }
        }
    
        for (int i = 1 ; i <= n ; ++i)
        {
            lg[i] = lg[i - 1];
            if ((1 << lg[i] + 1) < i)
            {
                lg[i]++;
            }
        }
    }

    int findMAX(int l, int r)
    {
        int log = lg[r - l + 1];
        return vals[cmp(sparseMAX[log][l], sparseMAX[log][r - (1 << log) + 1])];
    }

    int findIDX(int l, int r)
    {
        int log = lg[r - l + 1];
        return cmp(sparseMAX[log][l], sparseMAX[log][r - (1 << log) + 1]);
    }
};

struct SegmentTree
{
    struct Node
    {
        int max;
        int min;
        int maxDiffL;
        int maxDiffR;
        
        Node()
        {
            max = -1;
        }
    };

    Node combine(Node left, Node right)
    {
        if (left.max == -1)
        {
            return right;
        }

        Node res;
        res.min = std::min(left.min, right.min);
        res.max = std::max(left.max, right.max);
        res.maxDiffL = std::max(left.maxDiffL, right.maxDiffL);
        res.maxDiffR = std::max(left.maxDiffR, right.maxDiffR);
        res.maxDiffL = std::max(res.maxDiffL, right.max - left.min);
        res.maxDiffR = std::max(res.maxDiffR, left.max - right.min);
        return res;
    }

    Node tree[4*MAXN];
    void build(int l, int r, int node, int vals[])
    {
        if (l == r)
        {
            tree[node].min = vals[l];
            tree[node].max = vals[l];
            tree[node].maxDiffL = 0;
            tree[node].maxDiffR = 0;
            return;
        }

        int mid = (l + r) / 2;
        build(l, mid, 2*node, vals);
        build(mid + 1, r, 2*node + 1, vals);
        tree[node] = combine(tree[2*node], tree[2*node + 1]);
    }    

    Node query(int l, int r, int node, int queryL, int queryR)
    {
        if (queryL <= l && r <= queryR)
        {
            return tree[node];
        }

        Node res;
        int mid = (l + r) / 2;
        if (queryL <= mid) res = combine(res, query(l, mid, 2*node, queryL, queryR));
        if (mid + 1 <= queryR) res = combine(res, query(mid + 1, r, 2*node + 1, queryL, queryR));
        return res;
    }

    void build(int vals[])
    {
        build(1, n, 1, vals);
    }

    int queryL(int l, int r)
    {
        return query(1, n, 1, l, r).maxDiffL;
    }

    int queryR(int l, int r)
    {
        return query(1, n, 1, l, r).maxDiffR;
    }
};

int a[MAXN];
int b[MAXN];
int c[MAXN];
int d[MAXN];
int h[MAXN];
int perm[MAXN];
int cost[MAXN];
SparseMAX sparseMAX;
SegmentTree maxDiff;
std::stack <int> st;
std::vector <int> v;
MST tree;

void init(int N, std::vector <int> H) 
{
    n = N;
    for (int i = 1 ; i <= n ; ++i)
    {
        h[i] = H[i - 1];
    }

    sparseMAX.build(h);
    st.push(0);

    for (int i = 1 ; i <= n ; ++i)
    {
        while (h[st.top()] > h[i])
        {
            st.pop();
        }

        a[i] = st.top();
        st.push(i);
    }


    while (!st.empty())
    {
        st.pop();
    }

    st.push(n + 1);
    for (int i = n ; i >= 1 ; --i)
    {
        while (h[st.top()] > h[i])
        {
            st.pop();
        }

        c[i] = st.top();
        st.push(i);
    }

    for (int i = 1 ; i <= n ; ++i)
    {
        if (a[i] == i - 1)
        {
            b[i] = 0;
        } else
        {
            b[i] = sparseMAX.findMAX(a[i] + 1, i - 1) - h[i];
        }

        if (c[i] == i + 1)
        {
            d[i] = 0;
        } else
        {
            d[i] = sparseMAX.findMAX(i + 1, c[i] - 1) - h[i];
        }
    }

    for (int i = 1 ; i <= n ; ++i)
    {
        cost[i] = INF; 
        if (a[i] > 0) cost[i] = std::min(cost[i], b[i]);
        if (c[i] < n + 1) cost[i] = std::min(cost[i], d[i]);
    }

    std::iota(perm + 1, perm + 1 + n, 1);
    std::sort(perm + 1, perm + 1 + n, [&](const int &x, const int &y)
    {
        return cost[x] > cost[y];
    });

    tree.build(perm);
    maxDiff.build(h);
}

int max_towers(int L, int R, int D) 
{
    L++; R++;
    int l = 0, r = n + 1, mid;
    while (l < r - 1)
    {
        mid = (l + r) / 2;
        if (cost[perm[mid]] >= D) l = mid;
        else r = mid;
    }

    if (l == 0)
    {
        return 1;
    }

    int cnt = tree.queryCount(l, L, R);
    if (cnt == 0)
    {
        return 1;
    }

    int first = tree.queryFirst(l, L);
    int last = tree.queryLast(l, R);

    l = L, r = first;
    while (l < r - 1)
    {
        mid = (l + r) / 2;
        if (sparseMAX.findMAX(mid, first - 1) < h[first] + D) r = mid;
        else l = mid;
    }

    if (maxDiff.queryL(L, l) >= D)
    {
        cnt++;
    }

    l = last, r = R;
    while (l < r - 1)
    {
        mid = (l + r) / 2;
        if (sparseMAX.findMAX(last + 1, mid) < h[last] + D) l = mid;
        else r = mid;
    }

    if (maxDiff.queryR(r, R) >= D)
    {
        cnt++;
    }

    return cnt;
}

Compilation message

towers.cpp: In member function 'void MST::build(int, int, int, int*)':
towers.cpp:33:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   33 |             if (lPtr == tree[2*node].size())
      |                 ~~~~~^~~~~~~~~~~~~~~~~~~~~~
towers.cpp:39:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   39 |             if (rPtr == tree[2*node + 1].size())
      |                 ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
towers.cpp: In member function 'int MST::binaryFirst(int, int)':
towers.cpp:78:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   78 |         return (r == tree[node].size() ? INF : tree[node][r]);
      |                 ~~^~~~~~~~~~~~~~~~~~~~
towers.cpp: In member function 'void SparseMAX::build(int*)':
towers.cpp:182:97: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
  182 |                 sparseMAX[log][i] = cmp(sparseMAX[log - 1][i], sparseMAX[log - 1][i + (1 << log - 1)]);
      |                                                                                             ~~~~^~~
towers.cpp:189:29: warning: suggest parentheses around '+' inside '<<' [-Wparentheses]
  189 |             if ((1 << lg[i] + 1) < i)
      |                       ~~~~~~^~~

Subtask #1
0 / 4.0

# Verdict Execution time Memory Grader output
1 Incorrect 544 ms 47568 KB 12th lines differ - on the 1st token, expected: '2', found: '1'
2 Halted 0 ms 0 KB -

Subtask #2
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 34896 KB Output is correct
2 Correct 18 ms 35104 KB Output is correct
3 Correct 18 ms 35152 KB Output is correct
4 Correct 19 ms 35160 KB Output is correct
5 Correct 19 ms 35076 KB Output is correct
6 Correct 18 ms 35152 KB Output is correct
7 Correct 19 ms 35152 KB Output is correct
8 Correct 18 ms 35088 KB Output is correct
9 Correct 20 ms 35152 KB Output is correct
10 Correct 19 ms 35152 KB Output is correct
11 Correct 21 ms 35156 KB Output is correct
12 Incorrect 18 ms 34696 KB 1st lines differ - on the 1st token, expected: '2', found: '1'
13 Halted 0 ms 0 KB -

Subtask #3
0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 34896 KB Output is correct
2 Correct 18 ms 35104 KB Output is correct
3 Correct 18 ms 35152 KB Output is correct
4 Correct 19 ms 35160 KB Output is correct
5 Correct 19 ms 35076 KB Output is correct
6 Correct 18 ms 35152 KB Output is correct
7 Correct 19 ms 35152 KB Output is correct
8 Correct 18 ms 35088 KB Output is correct
9 Correct 20 ms 35152 KB Output is correct
10 Correct 19 ms 35152 KB Output is correct
11 Correct 21 ms 35156 KB Output is correct
12 Incorrect 18 ms 34696 KB 1st lines differ - on the 1st token, expected: '2', found: '1'
13 Halted 0 ms 0 KB -

Subtask #4
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 901 ms 56508 KB Output is correct
2 Correct 1254 ms 56624 KB Output is correct
3 Correct 1453 ms 56692 KB Output is correct
4 Correct 831 ms 56648 KB Output is correct
5 Correct 1094 ms 56596 KB Output is correct
6 Correct 1073 ms 56640 KB Output is correct
7 Correct 1475 ms 56652 KB Output is correct
8 Correct 879 ms 56652 KB Output is correct
9 Correct 888 ms 57032 KB Output is correct
10 Correct 1217 ms 56636 KB Output is correct
11 Correct 1083 ms 56784 KB Output is correct
12 Incorrect 1020 ms 56600 KB 170th lines differ - on the 1st token, expected: '2', found: '1'
13 Halted 0 ms 0 KB -

Subtask #5
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 371 ms 39704 KB Output is correct
2 Correct 1282 ms 56676 KB Output is correct
3 Correct 1224 ms 56604 KB Output is correct
4 Correct 1200 ms 56704 KB Output is correct
5 Correct 1272 ms 56644 KB Output is correct
6 Correct 1326 ms 56644 KB Output is correct
7 Correct 1365 ms 56672 KB Output is correct
8 Correct 1081 ms 56664 KB Output is correct
9 Correct 987 ms 57032 KB Output is correct
10 Correct 1075 ms 56784 KB Output is correct
11 Correct 1030 ms 56696 KB Output is correct
12 Correct 72 ms 56620 KB Output is correct
13 Correct 75 ms 56644 KB Output is correct
14 Correct 74 ms 56628 KB Output is correct
15 Correct 65 ms 57032 KB Output is correct
16 Correct 73 ms 56656 KB Output is correct
17 Correct 72 ms 55984 KB Output is correct
18 Correct 81 ms 56644 KB Output is correct
19 Correct 80 ms 56612 KB Output is correct
20 Correct 71 ms 56632 KB Output is correct
21 Correct 74 ms 56612 KB Output is correct
22 Correct 81 ms 56704 KB Output is correct
23 Correct 70 ms 56648 KB Output is correct
24 Correct 74 ms 56636 KB Output is correct
25 Correct 64 ms 57096 KB Output is correct
26 Correct 67 ms 56628 KB Output is correct
27 Correct 65 ms 57040 KB Output is correct
28 Correct 19 ms 35144 KB Output is correct
29 Correct 19 ms 35064 KB Output is correct
30 Correct 20 ms 35156 KB Output is correct
31 Correct 20 ms 35064 KB Output is correct
32 Correct 20 ms 35172 KB Output is correct
33 Correct 21 ms 34948 KB Output is correct
34 Correct 22 ms 35132 KB Output is correct
35 Correct 19 ms 35124 KB Output is correct
36 Correct 19 ms 35152 KB Output is correct
37 Correct 19 ms 35152 KB Output is correct
38 Correct 19 ms 35152 KB Output is correct
39 Correct 18 ms 35152 KB Output is correct
40 Correct 19 ms 35152 KB Output is correct
41 Correct 19 ms 35152 KB Output is correct
42 Correct 21 ms 35140 KB Output is correct
43 Correct 22 ms 35152 KB Output is correct

Subtask #6
0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 34896 KB Output is correct
2 Correct 18 ms 35104 KB Output is correct
3 Correct 18 ms 35152 KB Output is correct
4 Correct 19 ms 35160 KB Output is correct
5 Correct 19 ms 35076 KB Output is correct
6 Correct 18 ms 35152 KB Output is correct
7 Correct 19 ms 35152 KB Output is correct
8 Correct 18 ms 35088 KB Output is correct
9 Correct 20 ms 35152 KB Output is correct
10 Correct 19 ms 35152 KB Output is correct
11 Correct 21 ms 35156 KB Output is correct
12 Incorrect 18 ms 34696 KB 1st lines differ - on the 1st token, expected: '2', found: '1'
13 Halted 0 ms 0 KB -

Subtask #7
0 / 23.0

# Verdict Execution time Memory Grader output
1 Incorrect 544 ms 47568 KB 12th lines differ - on the 1st token, expected: '2', found: '1'
2 Halted 0 ms 0 KB -