【bzoj3343】教主的魔法 (分块 + 二分)

传送门(权限题)

题目分析

题意为：给定一个数列，修改和查询两种操作，修改每次给定一个区间，区间的所有元素都加上一个给定值，查询询问一段区间的数权值大于等于给定值的数有多少个。 首先对原序列分块，然后将分块后的数组每个块内的数字进行排序，这样查询时就可以暴力枚举散块，并二分枚举每个整块。对于修改，对于整块部分只需修改tag，然后暴力修改散块的原序列值，然后对散块元素所在块进行重排序即可。

code

3048 ms

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
using namespace std;

const int N = 1e6 + 5;
int n, Q, h[N], H[N], tag[N], S, blo;
#define bug(x) cout<<#x<<":"<<x<<endl
inline int read(){
    int i = 0, f = 1; char ch = getchar();
    for(; (ch < '0' || ch > '9') && ch != '-'; ch = getchar());
    if(ch == '-') f = -1, ch = getchar();
    for(; ch >= '0' && ch <= '9'; ch = getchar())
        i = (i << 3) + (i << 1) + (ch - '0');
    return i * f;
}

inline void wr(int x){
    if(x < 0) putchar('-'),x = -x;
    if(x > 9) wr(x / 10);
    putchar(x % 10 + '0');
}

inline void add(int x, int y, int v){
    if(y - x + 1 <= 2 * S){
        for(int i = x; i <= y; i++)
            h[i] += v;
    }
    int Bx = x / S + (x % S ? 1 : 0), By = y / S + (y % S ? 1 : 0);
    int L = Bx + 1, R = By - 1;
    if(x == (Bx - 1) * S + 1) L--;
    if(y == min(n, By * S)) R++;
    int ans = 0;
    for(int i = x; i < (L - 1) * S; i++)
        h[i] += v;
    int l = (Bx - 1) * S + 1, r = min(n, Bx * S);
    for(int i = l; i <= r; i++)
        H[i] = h[i];
    sort(H + l, H + r + 1);
    for(int i = min(n, R * S) + 1; i <= y; i++)
        h[i] += v;
    l = (By - 1) * S + 1, r = min(n, By * S);
    for(int i = l; i <= r; i++)
        H[i] = h[i];
    sort(H + l, H + r + 1);
    for(int i = L; i <= R; i++)
        tag[i] += v;
}

inline int query(int x, int y, int v){
    int ans = 0;
    if(y - x + 1 <= 2 * S){
        for(int i = x; i <= y; i++)
            if(h[i] + tag[i / S + (i % S ? 1 : 0)] >= v) ans++;return ans;
    }
    int Bx = x / S + (x % S ? 1 : 0), By = y / S + (y % S ? 1 : 0);
//    bug(Bx), bug(By);
    int L = Bx + 1, R = By - 1;
    if(x == (Bx - 1) * S + 1) L--;
    if(y == min(n, By * S)) R++;    
//    bug(L), bug(R);
    for(int i = x; i <= (L - 1) * S; i++)
        if(h[i] + tag[Bx] >= v) ans++;
    for(int i = min(n, R * S) + 1; i <= y; i++)
        if(h[i] + tag[By] >= v) ans++;
    for(int i = L; i <= R; i++){
        int l = (i - 1) * S + 1, r = min(n, i * S), len = r - l + 1;
        int tmp = lower_bound(H + l, H + r + 1, v - tag[i]) - (H + l - 1);
        ans += len - (tmp - 1);
    }
    return ans;
}

int main(){
    n = read(), Q = read(), S = sqrt(n), blo = n / S + (n % S ? 1 : 0);
//    bug(S);
    for(int i = 1; i <= n; i++) h[i] = H[i] = read();
    for(int i = 1; i <= blo; i++){
        int l = (i - 1) * S + 1, r = min(i * S, n);
        sort(H + l, H + r + 1);
    }
    for(int i = 1; i <= Q; i++){
        char opt[5]; scanf("%s", opt + 1);
        if(opt[1] == 'M'){
            int l = read(), r = read(), w = read();
            add(l, r, w);
        }
        else if(opt[1] == 'A'){
            int l = read(), r = read(), c = read();
            wr(query(l, r, c)), putchar('\n');
        }
    }
    return 0;
}