【HDU 4819】Mosaic

最新推荐文章于 2021-03-23 12:47:44 发布

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最新推荐文章于 2021-03-23 12:47:44 发布

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CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/evenbao/p/9196382.html

本文深入探讨了二维线段树（树套树）的实现原理与应用，通过具体代码示例，详细讲解了如何构建、修改及查询二维线段树，适用于解决复杂的空间范围查询问题。

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【题目链接】

点击打开链接

【算法】

二维线段树（树套树）

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN 800

int i,q,n,xa,xb,ya,yb,l,tmp,T,Max,Min,x,y;

struct info { int Max,Min; } Tree[MAXN*3][MAXN*3];

template <typename T> inline void read(T &x) {
    int f = 1; x = 0;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
    for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
        x *= f;    
}
template <typename T> inline void write(T x) {
    if (x < 0) { putchar('-'); x = -x; }
    if (x > 9) write(x/10);
    putchar(x%10+'0');    
}
template <typename T> inline void writeln(T x) {
    write(x);
    puts("");    
}

inline void push_up(int D,int index) {
    Tree[D][index].Max = max(Tree[D][index<<1].Max,Tree[D][index<<1|1].Max);
    Tree[D][index].Min = min(Tree[D][index<<1].Min,Tree[D][index<<1|1].Min);    
}

inline void build_y(int D,int index,int l,int r,int opt) {
    int mid,val;
    if (l == r) {
        if (opt == 1) {
            read(val);
            Tree[D][index].Max = Tree[D][index].Min = val;
        } else {
            Tree[D][index].Max = max(Tree[D<<1][index].Max,Tree[D<<1|1][index].Max);
            Tree[D][index].Min = min(Tree[D<<1][index].Min,Tree[D<<1|1][index].Min);
        }
        return;
    }    
    mid = (l + r) >> 1;
    build_y(D,index<<1,l,mid,opt);
    build_y(D,index<<1|1,mid+1,r,opt);
    push_up(D,index);
}

inline void build_x(int index,int l,int r) {
    int mid;
    if (l == r) {
        build_y(index,1,1,n,1);
        return;
    }
    mid = (l + r) >> 1;
    build_x(index<<1,l,mid);
    build_x(index<<1|1,mid+1,r);
    build_y(index,1,1,n,2);
}

inline void modify_y(int D,int index,int l,int r,int val,int opt) {
    int mid;
    if (l == r) {
        if (opt == 1) Tree[D][index].Max = Tree[D][index].Min = val;
        else {
            Tree[D][index].Max = max(Tree[D<<1][index].Max,Tree[D<<1|1][index].Max);
            Tree[D][index].Min = min(Tree[D<<1][index].Min,Tree[D<<1|1][index].Min);
        }
        return;
    }    
    mid = (l + r) >> 1;
    if (mid >= y) modify_y(D,index<<1,l,mid,val,opt);
    else modify_y(D,index<<1|1,mid+1,r,val,opt);
    push_up(D,index);
}

inline void modify_x(int index,int l,int r,int val) {
    int mid;
    if (l == r) {
        modify_y(index,1,1,n,val,1);
        return;
    }
    mid = (l + r) >> 1;
    if (mid >= x) modify_x(index<<1,l,mid,val);
    else modify_x(index<<1|1,mid+1,r,val);
    modify_y(index,1,1,n,val,2);
}

inline int query_min_y(int D,int index,int l,int r,int x,int y) {
    int mid;
    if (l == x && r == y) return Tree[D][index].Min;
    mid = (l + r) >> 1;
    if (mid >= y) return query_min_y(D,index<<1,l,mid,x,y);
    else if (mid + 1 <= x) return query_min_y(D,index<<1|1,mid+1,r,x,y);
    else return min(query_min_y(D,index<<1,l,mid,x,mid),query_min_y(D,index<<1|1,mid+1,r,mid+1,y));
}

inline int query_min_x(int index,int l,int r,int x,int y) {
    int mid;
    if (l == x && r == y) return query_min_y(index,1,1,n,ya,yb);
    mid = (l + r) >> 1;
    if (mid >= y) return query_min_x(index<<1,l,mid,x,y);
    else if (mid + 1 <= x) return query_min_x(index<<1|1,mid+1,r,x,y);
    else return min(query_min_x(index<<1,l,mid,x,mid),query_min_x(index<<1|1,mid+1,r,mid+1,y)); 
}

inline int query_max_y(int D,int index,int l,int r,int x,int y) {
    int mid;
    if (l == x && r == y) return Tree[D][index].Max;
    mid = (l + r) >> 1;
    if (mid >= y) return query_max_y(D,index<<1,l,mid,x,y);
    else if (mid + 1 <= x) return query_max_y(D,index<<1|1,mid+1,r,x,y);
    else return max(query_max_y(D,index<<1,l,mid,x,mid),query_max_y(D,index<<1|1,mid+1,r,mid+1,y));
}

inline int query_max_x(int index,int l,int r,int x,int y) {
    int mid;
    if (l == x && r == y) return query_max_y(index,1,1,n,ya,yb);
    mid = (l + r) >> 1;
    if (mid >= y) return query_max_x(index<<1,l,mid,x,y);
    else if (mid + 1 <= x) return query_max_x(index<<1|1,mid+1,r,x,y);
    else return max(query_max_x(index<<1,l,mid,x,mid),query_max_x(index<<1|1,mid+1,r,mid+1,y)); 
}

int main() {
    
    read(T);
    for (i = 1; i <= T; i++) {
        read(n);
        build_x(1,1,n);
        read(q);
        cout<<"Case #"<< i << ':' << endl;
        while (q--) {
            read(x); read(y); read(l);
            xa = max(1,x-l/2);
            xb = min(n,x+l/2);
            ya = max(1,y-l/2);
            yb = min(n,y+l/2);
            Max = query_max_x(1,1,n,xa,xb);
            Min = query_min_x(1,1,n,xa,xb);
            tmp = (Max + Min) / 2;
            writeln(tmp);
            modify_x(1,1,n,tmp);
        }        
    }
    return 0;
}