UVA 11992 - Fast Matrix Operations

题目链接：

https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=501&page=show_problem&problem=3143

解题思路：

题目大意：给你一个矩阵，然后有3种操作：

1 x1 y1 x2 y2 val是将矩阵x1 y1 x2 y2的区间内的值全部增加val

2 x1 y1 x2 y2 val是将矩阵x1 y1 x2 y2的区间内的值全部设置为val

3 x1 y1 x2 y2 求出x1 y1 x2 y2的区间内的和，最大值，最小值。

矩阵不超过20行，矩阵元素却可能达到1000000个，可以想到每行建一颗线段树，则本题转为一维问题。

本题有两个操作，add和set，因此需要两个标记add和setv，含义同前。规定同时有两个标记时，表示先执行set再执行add，传递代码如下：

void pushdown(int id){    if(tree[id].l >= tree[id].r)        return;    if(tree[id].setv){        tree[id<<1].setv = tree[id<<1|1].setv = tree[id].setv;        tree[id<<1].minn = tree[id<<1|1].minn = tree[id].setv;        tree[id<<1].maxn = tree[id<<1|1].maxn = tree[id].setv;        tree[id<<1].add = tree[id<<1|1].add = 0;        tree[id<<1].sum = (tree[id<<1].r-tree[id<<1].l+1)*tree[id].setv;        tree[id<<1|1].sum = (tree[id<<1|1].r-tree[id<<1|1].l+1)*tree[id].setv;        tree[id].setv = 0;    }    if(tree[id].add){        int tmp = tree[id].add;        tree[id<<1].add += tmp;tree[id<<1|1].add += tmp;        tree[id<<1].minn += tmp;tree[id<<1|1].minn += tmp;        tree[id<<1].maxn +=tmp;tree[id<<1|1].maxn += tmp;        tree[id<<1].sum += (tree[id<<1].r-tree[id<<1].l+1)*tmp;        tree[id<<1|1].sum += (tree[id<<1|1].r - tree[id<<1|1].l+1)*tmp;        tree[id].add = 0;    }}

AC代码：

#include <iostream>#include <cstdio>#include <algorithm>#define INF 0xfffffffusing namespace std;const int N = 1000010;struct node{    int l,r;    int minn,maxn,sum;    int add,setv;}tree[N<<2];int anssum,ansmin,ansmax;void maintain(int id){    if(tree[id].l >= tree[id].r)        return ;    tree[id].maxn = max(tree[id<<1].maxn,tree[id<<1|1].maxn);    tree[id].minn = min(tree[id<<1].minn,tree[id<<1|1].minn);    tree[id].sum  = tree[id<<1].sum + tree[id<<1|1].sum;}void build(int id,int l,int r){//id:index    tree[id].l = l;    tree[id].r = r;    tree[id].add = 0;    tree[id].setv = 0;    if(l == r){        tree[id].sum = tree[id].minn = tree[id].maxn = 0;        return;    }    int mid = (l+r)>>1;    build(id<<1,l,mid);    build(id<<1|1,mid+1,r);    maintain(id);}void pushdown(int id){    if(tree[id].l >= tree[id].r)        return;    if(tree[id].setv){        tree[id<<1].setv = tree[id<<1|1].setv = tree[id].setv;        tree[id<<1].minn = tree[id<<1|1].minn = tree[id].setv;        tree[id<<1].maxn = tree[id<<1|1].maxn = tree[id].setv;        tree[id<<1].add = tree[id<<1|1].add = 0;        tree[id<<1].sum = (tree[id<<1].r-tree[id<<1].l+1)*tree[id].setv;        tree[id<<1|1].sum = (tree[id<<1|1].r-tree[id<<1|1].l+1)*tree[id].setv;        tree[id].setv = 0;    }    if(tree[id].add){        int tmp = tree[id].add;        tree[id<<1].add += tmp;tree[id<<1|1].add += tmp;        tree[id<<1].minn += tmp;tree[id<<1|1].minn += tmp;        tree[id<<1].maxn +=tmp;tree[id<<1|1].maxn += tmp;        tree[id<<1].sum += (tree[id<<1].r-tree[id<<1].l+1)*tmp;        tree[id<<1|1].sum += (tree[id<<1|1].r - tree[id<<1|1].l+1)*tmp;        tree[id].add = 0;    }}void updateSet(int id,int l,int r,int val){    if(tree[id].l >= l && tree[id].r <= r){        tree[id].setv = val;        tree[id].minn = val;        tree[id].maxn = val;        tree[id].add = 0;        tree[id].sum = (tree[id].r-tree[id].l+1)*val;        return;    }    pushdown(id);    int mid = (tree[id].l+tree[id].r)>>1;    if(l <= mid)        updateSet(id<<1,l,r,val);    if(mid < r)        updateSet((id<<1)+1,l,r,val);    maintain(id);}void updateAdd(int id,int l,int r,int val){    if(tree[id].l >= l && tree[id].r <= r){        tree[id].add += val;        tree[id].minn += val;        tree[id].maxn += val;        tree[id].sum += (tree[id].r-tree[id].l+1)*val;        return;    }    pushdown(id);    int mid = (tree[id].l+tree[id].r)>>1;    if(l <= mid)        updateAdd(id<<1,l,r,val);    if(mid < r)        updateAdd((id<<1)+1,l,r,val);    maintain(id);}void query(int id,int l,int r){     if(tree[id].l >= l && tree[id].r <= r){        anssum += tree[id].sum;        ansmin = min(ansmin,tree[id].minn);        ansmax = max(ansmax,tree[id].maxn);        return;    }    pushdown(id);    int mid = (tree[id].l+tree[id].r)>>1;    if(l <= mid)        query(id<<1,l,r);    if(mid < r)        query(id<<1|1,l,r);    maintain(id);}int main(){    int r,c,m;    while(~scanf("%d%d%d",&r,&c,&m)){        build(1,1,r*c);        int op,x1,x2,y1,y2,val;        while(m--){            scanf("%d",&op);            if(op == 1){                scanf("%d%d%d%d%d",&x1,&y1,&x2,&y2,&val);                for(int i = x1; i <= x2; i++)                    updateAdd(1,(i-1)*c+y1,(i-1)*c+y2,val);            }            else if(op == 2){                scanf("%d%d%d%d%d",&x1,&y1,&x2,&y2,&val);                for(int i = x1; i <= x2; i++)                    updateSet(1,(i-1)*c+y1,(i-1)*c+y2,val);            }            else{                scanf("%d%d%d%d",&x1,&y1,&x2,&y2);                anssum = 0;ansmin = INF;ansmax = -INF;                for(int i = x1; i <= x2; i++)                    query(1,(i-1)*c+y1,(i-1)*c+y2);                printf("%d %d %d\n",anssum,ansmin,ansmax);            }        }    }    return 0;}/*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*/