【模板】分块

今天写分块的时候模板忘光了，故写以记之。

Code

Init

void init()
{
    sz = sqrt(n), block = n / sz + (n % sz != 0);
    for (int i = 1; i <= block; i ++)
        st[i] = (i - 1) * sz + 1, ed[i] = i * sz;
    ed[block] = n;

    for (int i = 1; i <= block; i ++)
        for (int j = st[i]; j <= ed[i]; j ++)
            belong[j] = i;
}

其中块长视题目情况而改变，一般为 \(\sqrt n\)。

Modify / Query

void/int function(int x, int y)
{
	int bx = belong[x], by = belong[y];
    // pushdown(bx), pushdown(by);	根据题目情况而改变
    
    if (by <= bx + 1)	// 特判没有完整块的情况
    {
		for (int i = x; i <= y; i ++)
            ...;
        return ...;
    }
    for (int i = x; i <= st[bx]; i ++) ...;
    for (int i = st[by]; i <= y; i ++) ...;
    for (int i = bx + 1; i <= by - 1; i ++) ...;
}

区间和

void modify(int x, int y, int k)
{
    int bx = belong[x], by = belong[y];
    if (by - bx <= 1)
    {
        for (int i = x; i <= y; i ++)
            a[i] += k, sum[belong[i]] += k;
        return;
    }
    for (int i = x; i <= ed[bx]; i ++) a[i] += k, sum[bx] += k;
    for (int i = bx + 1; i <= by - 1; i ++) tag[i] += k;
    for (int i = st[by]; i <= y; i ++) a[i] += k, sum[by] += k;
}

int query(int x, int y)
{
    int bx = belong[x], by = belong[y];
    if (by - bx <= 1)
    {
        int res = 0;
        for (int i = x; i <= y; i ++) res += a[i] + tag[belong[i]];
        return res;
    }
    int res = 0;
    for (int i = x; i <= ed[bx]; i ++) res += a[i] + tag[bx];
    for (int i = bx + 1; i <= by - 1; i ++)
        res += sum[i] + tag[i] * (ed[i] - st[i] + 1);
    for (int i = st[by]; i <= y; i ++) res += a[i] + tag[by];
    return res;
}