二维线段树和二维树状数组

二维线段树，支持单点更新、元素求和、查询最大值和最小值。

代码：

struct Nodey {
    int ly, ry, val, Max, Min, sum;//元素 最大值 最小值 元素和
};
int nx, ny;//横长 竖长
int posx[MAXN], posy[MAXN];
struct Nodex {
    int lx, rx;
    Nodey treey[MAXN<<2];
    void Build_y(int o, int l, int r) {
        treey[o].ly = l; treey[o].ry = r;
        treey[o].Max = 0; treey[o].Min = INF;
        treey[o].sum = 0; treey[o].val = 0;
        if(l == r) {
            posy[l] = o;
            return ;
        }
        int mid = (l + r) >> 1;
        Build_y(ll, l, mid);
        Build_y(rr, mid+1, r);
    }
    int Query_y(int o, int y1, int y2, int op) {
        if(treey[o].ly == y1 && treey[o].ry == y2) {
            if(op == 0) return treey[o].Max;
            if(op == 1) return treey[o].Min;
            if(op == 2) return treey[o].sum;
        }
        int mid = (treey[o].ly + treey[o].ry) >> 1;
        if(y2 <= mid) return Query_y(ll, y1, y2, op);
        else if(y1 > mid) return Query_y(rr, y1, y2, op);
        else {
            if(op == 0) return max(Query_y(ll, y1, mid, op), Query_y(rr, mid+1, y2, op));
            if(op == 1) return min(Query_y(ll, y1, mid, op), Query_y(rr, mid+1, y2, op));
            if(op == 2) return Query_y(ll, y1, mid, op) + Query_y(rr, mid+1, y2, op);
        }
    }
};
Nodex treex[MAXN<<2];
void Build_x(int o, int l, int r) {
    treex[o].lx = l; treex[o].rx = r;
    treex[o].Build_y(1, 1, ny);
    if(l == r) {
        posx[l] = o;
        return ;
    }
    int mid = (l + r) >> 1;
    Build_x(ll, l, mid);
    Build_x(rr, mid+1, r);
}
int Query_x(int o, int x1, int x2, int y1, int y2, int op) {
    if(treex[o].lx == x1 && treex[o].rx == x2) {
        return treex[o].Query_y(1, y1, y2, op);
    }
    int mid = (treex[o].lx + treex[o].rx) >> 1;
    if(x2 <= mid) return Query_x(ll, x1, x2, y1, y2, op);
    else if(x1 > mid) return Query_x(rr, x1, x2, y1, y2, op);
    else {
        if(op == 0) return max(Query_x(ll, x1, mid, y1, y2, op), Query_x(rr, mid+1, x2, y1, y2, op));
        if(op == 1) return min(Query_x(ll, x1, mid, y1, y2, op), Query_x(rr, mid+1, x2, y1, y2, op));
        if(op == 2) return Query_x(ll, x1, mid, y1, y2, op) + Query_x(rr, mid+1, x2, y1, y2, op);
    }
}
void PushUpy(int x, int y) {
    treex[x].treey[y].Max = max(treex[x].treey[y<<1].Max, treex[x].treey[y<<1|1].Max);
    treex[x].treey[y].Min = min(treex[x].treey[y<<1].Min, treex[x].treey[y<<1|1].Min);
    treex[x].treey[y].sum = treex[x].treey[y<<1].sum + treex[x].treey[y<<1|1].sum;
}
void PushUpx(int x, int y) {
    treex[x].treey[y].Max = max(treex[x<<1].treey[y].Max, treex[x<<1|1].treey[y].Max);
    treex[x].treey[y].Min = min(treex[x<<1].treey[y].Min, treex[x<<1|1].treey[y].Min);
    treex[x].treey[y].sum = treex[x<<1].treey[y].sum + treex[x<<1|1].treey[y].sum;
}
void Change(int x, int y, int v) {
    treex[x].treey[y].Max = v;
    treex[x].treey[y].Min = v;
    treex[x].treey[y].sum = v;
    treex[x].treey[y].val = v;
}
void Update(int x, int y, int v) {//单点更新
    for(int i = posx[x]; i ; i >>= 1) {
        for(int j = posy[y]; j ; j >>= 1) {
            if(i == posx[x] && j == posy[y]) {
                Change(posx[x], posy[y], v);
                continue;
            }
            PushUpy(i, j);
        }
        if(i == posx[x]) continue;
        for(int j = posy[y]; j ; j >>= 1) {
            PushUpx(i, j);
        }
    }
}
int Sum(int x, int y) {//求 (x, y)对应节点到根路径的元素之和
    int sum = 0;
    for(int i = posx[x]; i ; i >>= 1) {
        for(int j = posy[y]; j ; j >>= 1) {
            sum += treex[i].treey[j].val;
        }
    }
    return sum;
}

二维树状数组，支持单点更新、求和。

代码：

int C[MAXN][MAXN];
int nx, ny;
int lowbit(int x) {
    return x & (-x);
}
void add(int x, int y, int d) {
    while(x <= nx) {
        int sy = y;
        while(sy <= ny) {
            C[x][sy] += d;
            sy += lowbit(sy);
        }
        x += lowbit(x);
    }
}
int Sum(int x, int y) {
    int s = 0;
    while(x > 0) {
        int sy = y;
        while(sy > 0) {
            s += C[x][sy];
            sy -= lowbit(sy);
        }
        x -= lowbit(x);
    }
    return s;
}