简单又复杂的算法--分块

对于区间操作的问题，部分可以用分块来做

事实上分块还是蛮简单的，主要是看分块之后怎么样进行处理，它很灵活，没有固定的模式

还是拿题目来举例吧

Bzoj 2002 Bzoj 3065

Bzoj 2002 分块版
#include"cstdio"
#include"cmath"
#define Maxn 200005
int st[Maxn],pt[Maxn],belong[Maxn],k[Maxn];
int l[1000],r[1000];
inline int read() {
    int x = 0,f = 1;char ch;
    ch = getchar();
    while (ch>'9' || ch<'0') {if (ch == '-') f = -1;ch = getchar();}
    while (ch<='9' && ch>='0') {x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void init(int n,int block) {
    for (int i = 1;i <= n;i ++) {
        k[i] = read();
        belong[i] = (i-1)/block + 1;
    }
    int cnt;
    if (n%block) cnt = n/block + 1; else
        cnt = n/block;
    for (int i = 1;i <= cnt;i ++) {
        l[i] = (i-1)*block + 1;
        r[i] = i*block;
    }
    r[cnt] = n;
    for (int i = n;i > 0;i --)
        if (i+k[i] > n) st[i] = 1; else
            if (belong[i] == belong[i+k[i]])
                st[i] = st[i+k[i]]+1,pt[i] = pt[i+k[i]]; else
                    st[i] = 1,pt[i] = i+k[i];
}
int cal(int x) {
    int ans = 0;
    while (1) {
        ans += st[x];
        if (!pt[x]) break;
        x = pt[x];
    }
    return ans;
}
int main() {
    int n = read(),block = sqrt(n);
    init(n,block);
    int m = read();
    while (m--) {
        int f = read(),x = read()+1,y;
        if (f == 1) printf("%d\n",cal(x)); else {
            k[x] = y = read();
            for(int i = x;i >= l[belong[x]];i --)
                if (i+k[i] > n) st[i] = 1,pt[i] = 0; else
                    if (belong[i] == belong[i+k[i]])
                        st[i] = st[i+k[i]]+1,pt[i] = pt[i+k[i]]; else
                            st[i] = 1,pt[i] = i+k[i];
        }
    }
    return 0;
}

Bzoj 3065 自己模大佬的分块版
#include"cstdio"
#include"algorithm"
#include"cmath"
using namespace std;
int a[1005][1005],b[1005][1005],inum[100002];
int idx,ipos,tot[1005],nxt[1005];
int cnt,N,B,lastans;
typedef pair<int,int> abcd;
abcd lp,rp;
inline void shuchu() {
    for (int i = 1;i <= cnt;i ++) {
        for (int j = 1;j <= tot[i];j ++)
            printf("%d ",b[i][j]);
        printf("\n");
    }
    printf("\n");
}
inline char read() {
    char ch = getchar();
    while(ch > 'Z' || ch < 'A') ch = getchar();
    return ch;
}
inline abcd kth(int k) {
    for (int i = 1;i;i = nxt[i]) {
        if (!nxt[i] && k>tot[i])
            return abcd(i,k);
        if (k>tot[i])
            k -= tot[i];else
            return abcd(i,k);
    }
}
bool check(int mid,int K) {
    int ret = 0;
    if (lp.first == rp.first) {
        for(int i = lp.second;i <= rp.second;i ++)
            if(a[lp.first][i] <= mid) ret++;
        return ret>=K;
    }
    for(int i = lp.second;i <= tot[lp.first];i ++)
        if (a[lp.first][i] <= mid) ret++;
    for(int i= 1;i <= rp.second;i ++)
        if (a[rp.first][i] <= mid) ret++;
    for (int i = nxt[lp.first];i != rp.first;i = nxt[i])
        ret+=upper_bound(b[i]+1,b[i]+tot[i]+1,mid) - b[i] - 1;
    return ret>=K;
}
void Query() {
    int l,r,K;
    //abcd lp,rp;
    scanf("%d%d%d",&l,&r,&K);
    l^=lastans,r^=lastans,K^=lastans;
    lp = kth(l),rp = kth(r);
    int L=-1,R=70000,MID;
    while (L+1<R)
        if(check(MID = (L+R)>>1,K))
            R = MID; else L = MID;
    //printf("Q %d %d %d\n",l,r,K);
    //shuchu();
    printf("%d\n",lastans = R);

}
void Modify() {
    int x,val,t;
    scanf("%d%d",&x,&val);
    x^=lastans,val^=lastans;
    abcd p = kth(x);
    idx = p.first;
    t = a[idx][p.second];
    ipos = lower_bound(b[idx]+1,b[idx]+tot[idx]+1,t) - b[idx];
    a[idx][p.second] = val;
    b[idx][ipos] = val;
    while (ipos-1>=1 && b[idx][ipos]<b[idx][ipos-1])
        swap(b[idx][ipos],b[idx][ipos-1]),ipos--;
    while (ipos+1<=tot[idx] && b[idx][ipos]>b[idx][ipos+1])
        swap(b[idx][ipos],b[idx][ipos+1]),ipos++;
    //printf("M %d %d\n",x,val);
    //shuchu();
}
void Depth(int idx) {
    cnt ++;
    for (int i = B+1;i <= tot[idx];i ++)
        b[cnt][++tot[cnt]]=a[idx][i],a[cnt][tot[cnt]] = a[idx][i],a[idx][i]=0;
    sort(b[cnt]+1,b[cnt]+tot[cnt]+1);
    tot[idx] -= B;
    for (int i = 1;i <= tot[idx];i ++)
        b[idx][i] = a[idx][i];
    sort(b[idx]+1,b[idx]+tot[idx]+1);
    nxt[cnt] = nxt[idx];nxt[idx] = cnt;
}
void Insert() {
    int x,val;
    scanf("%d%d",&x,&val);
    x^=lastans,val^=lastans;
    abcd p = kth(x);
    idx = p.first;
    for (int i = tot[idx]+1;i>p.second;i --)
        a[idx][i] = a[idx][i-1];
    a[idx][p.second] = val;
    b[idx][++tot[idx]] = val;
    ipos = tot[idx];
    while (ipos-1>=1 && b[idx][ipos]<b[idx][ipos-1])
        swap(b[idx][ipos],b[idx][ipos-1]),ipos--;
    while (ipos+1<=tot[idx] && b[idx][ipos]>b[idx][ipos+1])
        swap(b[idx][ipos],b[idx][ipos+1]),ipos++;
    if (tot[idx]>=2*B) Depth(idx);
    //printf("I %d %d\n",x,val);
    //shuchu();
}
int main() {
    //freopen("t.in","r",stdin);
    int p;
    scanf("%d",&N);
    for (int i = 1;i <= N;i ++) scanf("%d",&inum[i]);
    B = sqrt(N),cnt = (N-1)/B + 1;
    for (int i = 1;i <= N;i ++) {
        idx = (i-1)/B + 1;
        a[idx][++tot[idx]] = inum[i];
        b[idx][tot[idx]] = inum[i];
    }
    for (int i = 1;i <= cnt;i ++)
        sort(b[i]+1,b[i]+tot[i]+1),nxt[i] = i+1;
    nxt[cnt] = 0;
    scanf("%d",&p);
    while (p--) {
        char ch;
        //getchar();
        ch = read();
        if (ch == 'Q')
            Query(); else if (ch == 'M')
                Modify(); else
                    Insert();
    }
    return 0;
}