UVA 11992- Fast Matrix Operations（线段树区间各种操作）

Description

Problem F

Fast Matrix Operations

There is a matrix containing at most 10⁶ elements divided into r rows and c columns. Each element has a location (x,y) where 1<=x<=r,1<=y<=c. Initially, all the elements are zero. You need to handle four kinds of operations:

1 x1 y1 x2 y2 v

Increment each element (x,y) in submatrix (x1,y1,x2,y2) by v (v>0)

2 x1 y1 x2 y2 v

Set each element (x,y) in submatrix (x1,y1,x2,y2) to v

3 x1 y1 x2 y2

Output the summation, min value and max value of submatrix (x1,y1,x2,y2)

In the above descriptions, submatrix (x1,y1,x2,y2) means all the elements (x,y) satisfying x1<=x<=x2 and y1<=x<=y2. It is guaranteed that 1<=x1<=x2<=r, 1<=y1<=y2<=c. After any operation, the sum of all the elements in the matrix does not exceed 10⁹.

Input

There are several test cases. The first line of each case contains three positive integers r, c, m, where m (1<=m<=20,000) is the number of operations. Each of the next m lines contains a query. There will be at most twenty rows in the matrix. The input is terminated by end-of-file (EOF). The size of input file does not exceed 500KB.

Output

For each type-3 query, print the summation, min and max.

Sample Input

4 4 81 1 2 4 4 53 2 1 4 41 1 1 3 4 23 1 2 4 43 1 1 3 42 2 1 4 4 23 1 2 4 41 1 1 4 3 3

Output for the Sample Input

45 0 578 5 769 2 739 2 7

                                                                                   

思路：线段树的区间的值add 和 set ，区间求最大值，最小值，总和。

注意：当add 和set 混合使用的时候应该注意在存在set 之后应该将之前的add 清空，但是注意不要将后面的add 清零~在代码中已有注释。

CODE：

#include <iostream>#include <cstdio>#include <algorithm>#include <cmath>#include <string>#include <cstring>#include <queue>#include <stack>#include <vector>#include <set>#include <map>const int inf=1000000009;typedef long long ll;using namespace std;const int Max=60005;int R,C,M,q;int sum,minn,maxn;struct SegmentTree{    int sumv[Max<<2];    int addv[Max<<2];    int setv[Max<<2];    int maxv[Max<<2];    int minv[Max<<2];    void maintain(int pos){        sumv[pos]=sumv[pos*2]+sumv[pos*2+1];        maxv[pos]=max(maxv[pos*2],maxv[pos*2+1]);        minv[pos]=min(minv[pos*2],minv[pos*2+1]);    }    void build(int pos,int l,int r){        setv[pos]=addv[pos]=0;        if(l==r){            sumv[pos]=maxv[pos]=minv[pos]            =setv[pos]=addv[pos]=0;        }        else{            int mid=(l+r)/2;            build(pos*2,l,mid);            build(pos*2+1,mid+1,r);            maintain(pos);        }    }    void pushdown(int pos,int l,int r){        int mid=(l+r)/2;        if(setv[pos]!=0){            setv[pos*2]=setv[pos*2+1]=setv[pos];            sumv[pos*2]=(mid-l+1)*setv[pos];            sumv[pos*2+1]=(r-mid)*setv[pos];            minv[pos*2]=minv[pos*2+1]=setv[pos];            maxv[pos*2]=maxv[pos*2+1]=setv[pos];            setv[pos]=0;            addv[pos*2]=addv[pos*2+1]=0;//记得清0~        }        if(addv[pos]!=0){            addv[pos*2]+=addv[pos];            addv[pos*2+1]+=addv[pos];            sumv[pos*2]+=(mid-l+1)*addv[pos];            sumv[pos*2+1]+=(r-mid)*addv[pos];            minv[pos*2]+=addv[pos];            minv[pos*2+1]+=addv[pos];            maxv[pos*2]+=addv[pos];            maxv[pos*2+1]+=addv[pos];            addv[pos]=0;        }    }    void update(int pos,int l,int r,int x,int y,int v){        if(x<=l && y>=r){            if(q==1){                addv[pos]+=v;                sumv[pos]+=(r-l+1)*v;                minv[pos]+=v;                maxv[pos]+=v;            }            else{                setv[pos]=v;                sumv[pos]=(r-l+1)*v;                minv[pos]=v;                maxv[pos]=v;                addv[pos]=0;//同样要记得清零！            }        }        else{            pushdown(pos,l,r);            int mid=(l+r)/2;            if(x<=mid) update(pos*2,l,mid,x,y,v);            if(y>mid) update(pos*2+1,mid+1,r,x,y,v);            maintain(pos);        }    }    void query(int pos,int l,int r,int x,int y){        if(x<=l && y>=r){            sum+=sumv[pos];            minn=min(minn,minv[pos]);            maxn=max(maxn,maxv[pos]);        }        else{            pushdown(pos,l,r);            int mid=(l+r)/2;            if(x<=mid) query(pos*2,l,mid,x,y);            if(y>mid) query(pos*2+1,mid+1,r,x,y);        }    }}Tree[25];int main(){    //freopen("in.in","r",stdin);    while(~scanf("%d%d%d",&R,&C,&M)){        for(int i=1;i<=R;i++){            Tree[i].build(1,1,C);        }        while(M--){            int x1,y1,x2,y2,vv;            scanf("%d %d%d%d%d",                  &q,&x1,&y1,&x2,&y2);            if(q==3){                sum=0;minn=inf;maxn=-inf;                for(int i=x1;i<=x2;i++){                    Tree[i].query(1,1,C,y1,y2);                }                printf("%d %d %d\n",sum,minn,maxn);            }            else{                scanf("%d",&vv);                for(int i=x1;i<=x2;i++){                    Tree[i].update(1,1,C,y1,y2,vv);                }            }        }    }    return 0;}