分块思想

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线性分块， 国外通常把块大小为 sqrt(n) 的分块方式叫做 “SQRT Decomposition”。

资料：

《入门经典：训练指南》P395

http://sysmagazine.com/posts/138946/

http://algoacm.com/Algorithms/sqrt_decomposition/sqrt_decomposition.html

题目：

Uva 12003 Array Transformer

#include
using namespace std;

#define SPEED_UP iostream::sync_with_stdio(false);
#define FIXED_FLOAT cout.setf(ios::fixed, ios::floatfield);
#define rep(i, s, t) for(int (i)=(s);(i)<=(t);++(i))
#define urep(i, s, t) for(int (i)=(s);(i)>=(t);--(i))

typedef long long LL;

struct Edge{
    int u, v, c;
    Edge(){}
    Edge(int u, int v, int c):u(u), v(v), c(c){}
    int getAdj(int x) {
        return x == u ? v : u;
    }
};

const int Maxn = 300000;
const int SIZE = 4096;
int n, m, u, a[Maxn+5], block[Maxn/SIZE+5][SIZE], numBlock, numLastBlock;
//#define DEBUG
void init() {
    cin >> n >> m >> u;
    int b = 0, j = 0;
    rep(i, 0, n-1) {
        cin >> a[i];
        block[b][j] = a[i];
        ++j;
        if (j == SIZE) {++b;j=0;}
    }
    rep(i, 0, b-1) sort(block[i], block[i]+SIZE);
    if (j) sort(block[b], block[b]+j);
    numBlock = b;
    numLastBlock = j ? j : SIZE;
}

int countOrderedRange(const int * l, const int * r, int v) {
    int ret = 0;
    for (const int *p=l;p<=r;++p) {
        if (*p < v) ++ret;
    }
    return ret;
}

int Query(int L, int R, int v) {
    int lb = L/SIZE, rb = R/SIZE, ret = 0;
    rep(i, lb+1, rb-1) {
        ret += lower_bound(block[i], block[i]+SIZE, v) - block[i];
    }
    if (lb == rb) {
        ret += countOrderedRange(a+L, a+R, v);
    }
    else {
        ret += countOrderedRange(a+L, a+(lb+1)*SIZE-1, v);
        ret += countOrderedRange(a+rb*SIZE, a+R, v);
    }
    return ret;
}

void Update(int p, int x) {
    int * B = block[p/SIZE];
    int old = a[p];
    a[p] = x;

    const int bSize = p/SIZE == numBlock ? numLastBlock : SIZE;
    int pos = lower_bound(B, B+bSize, old) - B;
#ifdef DEBUG
    cout << "in update: old->" << old  << " pos->" << pos << endl;
    cout << "Elements in this block: ";
    rep(i, 0, bSize-2) cout << B[i] << ' ';cout << B[bSize-1] << endl;
#endif
    while (pos > 0 && x < B[pos-1]) {
            B[pos] = B[pos-1];
            --pos;
    }
    while (pos < bSize-1 && x > B[pos+1]) {
        B[pos] = B[pos+1];
        ++pos;
    }
    B[pos] = x;
}

void printBlocks() {
    cout << "-------Show Blocks-------" << endl;
    rep(i, 0, numBlock-1) {
        cout << "Block " << i << ": ";
        rep(j, 0, SIZE-2) cout << block[i][j] << ' ';cout << block[i][SIZE-1] << endl;
    }
    cout << "Block " << numBlock << ": ";
    rep(j, 0, numLastBlock-2) cout << block[numBlock][j] << ' ';cout << block[numBlock][numLastBlock-1] << endl;
}


int main() {
#ifndef ONLINE_JUDGE
    freopen("input.in", "r", stdin);
#endif
    SPEED_UP
    init();

    //printBlocks();

    while (m--) {
        int L, R, v, p;
        cin >> L >> R >> v >> p;
        --L;--R;--p;

        int k = Query(L, R, v);
        Update(p, u*1ll*k/(R-L+1));
#ifdef DEBUG
        cout << "Q: " << L << ' ' << R << ' ' << v << ' ' << p << " k: " << k << endl;
        printBlocks();
#endif
    }

    rep(i, 0, n-1) cout << a[i] << endl;

    return 0;
}

hdu 5057 Argestes and Sequence

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codeforces 13E - Holes

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