Submission #755149

# Submission time Handle Problem Language Result Execution time Memory
755149 2023-06-09T12:48:57 Z boris_mihov Radio Towers (IOI22_towers) C++17
40 / 100
1252 ms 57116 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)
    {
        l = L - 1;
        r = R + 1;
        while (l < r - 1)
        {
            mid = (l + r) / 2;
            if (maxDiff.queryL(l, mid) >= D && maxDiff.queryR(mid, r) >= D)
            {
                return 2;
            }

            if (maxDiff.queryL(l, mid) < D) l = mid;
            else r = mid;
        }

        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)
      |                       ~~~~~~^~~
# Verdict Execution time Memory Grader output
1 Incorrect 672 ms 47588 KB 85th lines differ - on the 1st token, expected: '2', found: '1'
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Correct 17 ms 34896 KB Output is correct
2 Correct 18 ms 35152 KB Output is correct
3 Correct 19 ms 35152 KB Output is correct
4 Correct 21 ms 35120 KB Output is correct
5 Correct 22 ms 35128 KB Output is correct
6 Correct 22 ms 35088 KB Output is correct
7 Correct 19 ms 35152 KB Output is correct
8 Correct 19 ms 35152 KB Output is correct
9 Correct 19 ms 35076 KB Output is correct
10 Correct 20 ms 35116 KB Output is correct
11 Correct 19 ms 35152 KB Output is correct
12 Correct 19 ms 34768 KB Output is correct
13 Correct 20 ms 35060 KB Output is correct
14 Correct 21 ms 35152 KB Output is correct
15 Correct 24 ms 35148 KB Output is correct
16 Correct 19 ms 35152 KB Output is correct
17 Correct 20 ms 35116 KB Output is correct
18 Correct 19 ms 35096 KB Output is correct
19 Correct 21 ms 35152 KB Output is correct
20 Correct 22 ms 35064 KB Output is correct
21 Correct 19 ms 35152 KB Output is correct
22 Correct 21 ms 35152 KB Output is correct
23 Correct 19 ms 35152 KB Output is correct
24 Correct 19 ms 35060 KB Output is correct
25 Correct 19 ms 34944 KB Output is correct
26 Correct 18 ms 35096 KB Output is correct
27 Correct 19 ms 35176 KB Output is correct
28 Correct 21 ms 35152 KB Output is correct
29 Correct 19 ms 35152 KB Output is correct
30 Correct 19 ms 35152 KB Output is correct
31 Correct 19 ms 35152 KB Output is correct
32 Correct 20 ms 35108 KB Output is correct
33 Correct 19 ms 35072 KB Output is correct
34 Correct 19 ms 35152 KB Output is correct
35 Correct 19 ms 35124 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 17 ms 34896 KB Output is correct
2 Correct 18 ms 35152 KB Output is correct
3 Correct 19 ms 35152 KB Output is correct
4 Correct 21 ms 35120 KB Output is correct
5 Correct 22 ms 35128 KB Output is correct
6 Correct 22 ms 35088 KB Output is correct
7 Correct 19 ms 35152 KB Output is correct
8 Correct 19 ms 35152 KB Output is correct
9 Correct 19 ms 35076 KB Output is correct
10 Correct 20 ms 35116 KB Output is correct
11 Correct 19 ms 35152 KB Output is correct
12 Correct 19 ms 34768 KB Output is correct
13 Correct 20 ms 35060 KB Output is correct
14 Correct 21 ms 35152 KB Output is correct
15 Correct 24 ms 35148 KB Output is correct
16 Correct 19 ms 35152 KB Output is correct
17 Correct 20 ms 35116 KB Output is correct
18 Correct 19 ms 35096 KB Output is correct
19 Correct 21 ms 35152 KB Output is correct
20 Correct 22 ms 35064 KB Output is correct
21 Correct 19 ms 35152 KB Output is correct
22 Correct 21 ms 35152 KB Output is correct
23 Correct 19 ms 35152 KB Output is correct
24 Correct 19 ms 35060 KB Output is correct
25 Correct 19 ms 34944 KB Output is correct
26 Correct 18 ms 35096 KB Output is correct
27 Correct 19 ms 35176 KB Output is correct
28 Correct 21 ms 35152 KB Output is correct
29 Correct 19 ms 35152 KB Output is correct
30 Correct 19 ms 35152 KB Output is correct
31 Correct 19 ms 35152 KB Output is correct
32 Correct 20 ms 35108 KB Output is correct
33 Correct 19 ms 35072 KB Output is correct
34 Correct 19 ms 35152 KB Output is correct
35 Correct 19 ms 35124 KB Output is correct
36 Correct 54 ms 48744 KB Output is correct
37 Correct 74 ms 56616 KB Output is correct
38 Correct 71 ms 56632 KB Output is correct
39 Correct 74 ms 56644 KB Output is correct
40 Correct 76 ms 56676 KB Output is correct
41 Correct 72 ms 56632 KB Output is correct
42 Correct 74 ms 56644 KB Output is correct
43 Correct 72 ms 56708 KB Output is correct
44 Correct 65 ms 57116 KB Output is correct
45 Correct 72 ms 56668 KB Output is correct
46 Correct 66 ms 56888 KB Output is correct
47 Correct 73 ms 56680 KB Output is correct
48 Correct 83 ms 56612 KB Output is correct
49 Correct 74 ms 56604 KB Output is correct
50 Correct 76 ms 57032 KB Output is correct
51 Correct 71 ms 56608 KB Output is correct
52 Correct 77 ms 56604 KB Output is correct
53 Correct 75 ms 56756 KB Output is correct
54 Correct 73 ms 56616 KB Output is correct
55 Correct 74 ms 57024 KB Output is correct
56 Correct 66 ms 56696 KB Output is correct
57 Correct 72 ms 55988 KB Output is correct
58 Correct 79 ms 56600 KB Output is correct
59 Correct 73 ms 56700 KB Output is correct
60 Correct 75 ms 56796 KB Output is correct
61 Correct 78 ms 56696 KB Output is correct
62 Correct 73 ms 56648 KB Output is correct
63 Correct 73 ms 56648 KB Output is correct
64 Correct 74 ms 56652 KB Output is correct
65 Correct 62 ms 57116 KB Output is correct
66 Correct 75 ms 56636 KB Output is correct
67 Correct 74 ms 57028 KB Output is correct
# Verdict Execution time Memory Grader output
1 Incorrect 858 ms 56600 KB 74909th lines differ - on the 1st token, expected: '1', found: '2'
2 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Correct 323 ms 39696 KB Output is correct
2 Correct 1116 ms 56716 KB Output is correct
3 Correct 851 ms 56608 KB Output is correct
4 Correct 1208 ms 56644 KB Output is correct
5 Correct 1199 ms 56636 KB Output is correct
6 Correct 1077 ms 56608 KB Output is correct
7 Correct 1252 ms 56660 KB Output is correct
8 Correct 1038 ms 56620 KB Output is correct
9 Correct 1100 ms 57028 KB Output is correct
10 Correct 1027 ms 56612 KB Output is correct
11 Correct 1085 ms 56680 KB Output is correct
12 Correct 79 ms 56672 KB Output is correct
13 Correct 76 ms 56648 KB Output is correct
14 Correct 77 ms 56704 KB Output is correct
15 Correct 90 ms 57068 KB Output is correct
16 Correct 80 ms 56680 KB Output is correct
17 Correct 86 ms 55976 KB Output is correct
18 Correct 77 ms 56704 KB Output is correct
19 Correct 80 ms 56648 KB Output is correct
20 Correct 78 ms 56644 KB Output is correct
21 Correct 83 ms 56716 KB Output is correct
22 Correct 92 ms 56640 KB Output is correct
23 Correct 86 ms 56644 KB Output is correct
24 Correct 92 ms 56792 KB Output is correct
25 Correct 89 ms 57024 KB Output is correct
26 Correct 68 ms 56724 KB Output is correct
27 Correct 79 ms 57044 KB Output is correct
28 Correct 22 ms 35064 KB Output is correct
29 Correct 19 ms 35120 KB Output is correct
30 Correct 25 ms 35072 KB Output is correct
31 Correct 19 ms 35148 KB Output is correct
32 Correct 24 ms 35168 KB Output is correct
33 Correct 20 ms 34896 KB Output is correct
34 Correct 28 ms 35156 KB Output is correct
35 Correct 20 ms 35152 KB Output is correct
36 Correct 24 ms 35152 KB Output is correct
37 Correct 24 ms 35076 KB Output is correct
38 Correct 24 ms 35052 KB Output is correct
39 Correct 21 ms 35096 KB Output is correct
40 Correct 22 ms 35152 KB Output is correct
41 Correct 25 ms 35192 KB Output is correct
42 Correct 25 ms 35100 KB Output is correct
43 Correct 21 ms 35120 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 17 ms 34896 KB Output is correct
2 Correct 18 ms 35152 KB Output is correct
3 Correct 19 ms 35152 KB Output is correct
4 Correct 21 ms 35120 KB Output is correct
5 Correct 22 ms 35128 KB Output is correct
6 Correct 22 ms 35088 KB Output is correct
7 Correct 19 ms 35152 KB Output is correct
8 Correct 19 ms 35152 KB Output is correct
9 Correct 19 ms 35076 KB Output is correct
10 Correct 20 ms 35116 KB Output is correct
11 Correct 19 ms 35152 KB Output is correct
12 Correct 19 ms 34768 KB Output is correct
13 Correct 20 ms 35060 KB Output is correct
14 Correct 21 ms 35152 KB Output is correct
15 Correct 24 ms 35148 KB Output is correct
16 Correct 19 ms 35152 KB Output is correct
17 Correct 20 ms 35116 KB Output is correct
18 Correct 19 ms 35096 KB Output is correct
19 Correct 21 ms 35152 KB Output is correct
20 Correct 22 ms 35064 KB Output is correct
21 Correct 19 ms 35152 KB Output is correct
22 Correct 21 ms 35152 KB Output is correct
23 Correct 19 ms 35152 KB Output is correct
24 Correct 19 ms 35060 KB Output is correct
25 Correct 19 ms 34944 KB Output is correct
26 Correct 18 ms 35096 KB Output is correct
27 Correct 19 ms 35176 KB Output is correct
28 Correct 21 ms 35152 KB Output is correct
29 Correct 19 ms 35152 KB Output is correct
30 Correct 19 ms 35152 KB Output is correct
31 Correct 19 ms 35152 KB Output is correct
32 Correct 20 ms 35108 KB Output is correct
33 Correct 19 ms 35072 KB Output is correct
34 Correct 19 ms 35152 KB Output is correct
35 Correct 19 ms 35124 KB Output is correct
36 Correct 54 ms 48744 KB Output is correct
37 Correct 74 ms 56616 KB Output is correct
38 Correct 71 ms 56632 KB Output is correct
39 Correct 74 ms 56644 KB Output is correct
40 Correct 76 ms 56676 KB Output is correct
41 Correct 72 ms 56632 KB Output is correct
42 Correct 74 ms 56644 KB Output is correct
43 Correct 72 ms 56708 KB Output is correct
44 Correct 65 ms 57116 KB Output is correct
45 Correct 72 ms 56668 KB Output is correct
46 Correct 66 ms 56888 KB Output is correct
47 Correct 73 ms 56680 KB Output is correct
48 Correct 83 ms 56612 KB Output is correct
49 Correct 74 ms 56604 KB Output is correct
50 Correct 76 ms 57032 KB Output is correct
51 Correct 71 ms 56608 KB Output is correct
52 Correct 77 ms 56604 KB Output is correct
53 Correct 75 ms 56756 KB Output is correct
54 Correct 73 ms 56616 KB Output is correct
55 Correct 74 ms 57024 KB Output is correct
56 Correct 66 ms 56696 KB Output is correct
57 Correct 72 ms 55988 KB Output is correct
58 Correct 79 ms 56600 KB Output is correct
59 Correct 73 ms 56700 KB Output is correct
60 Correct 75 ms 56796 KB Output is correct
61 Correct 78 ms 56696 KB Output is correct
62 Correct 73 ms 56648 KB Output is correct
63 Correct 73 ms 56648 KB Output is correct
64 Correct 74 ms 56652 KB Output is correct
65 Correct 62 ms 57116 KB Output is correct
66 Correct 75 ms 56636 KB Output is correct
67 Correct 74 ms 57028 KB Output is correct
68 Incorrect 858 ms 56600 KB 74909th lines differ - on the 1st token, expected: '1', found: '2'
69 Halted 0 ms 0 KB -
# Verdict Execution time Memory Grader output
1 Incorrect 672 ms 47588 KB 85th lines differ - on the 1st token, expected: '2', found: '1'
2 Halted 0 ms 0 KB -