链接：https://www.nowcoder.com/acm/contest/140/J
来源：牛客网
题目描述
White Rabbit has a rectangular farmland of n*m. In each of the grid there is a kind of plant. The plant in the j-th column of the i-th row belongs the a[i][j]-th type.
White Cloud wants to help White Rabbit fertilize plants, but the i-th plant can only adapt to the i-th fertilizer. If the j-th fertilizer is applied to the i-th plant (i!=j), the plant will immediately die.
Now White Cloud plans to apply fertilizers T times. In the i-th plan, White Cloud will use k[i]-th fertilizer to fertilize all the plants in a rectangle [x1[i]...x2[i]][y1[i]...y2[i]].
White rabbits wants to know how many plants would eventually die if they were to be fertilized according to the expected schedule of White Cloud.
输入描述:
The first line of input contains 3 integers n,m,T(n*m<=1000000,T<=1000000) For the next n lines, each line contains m integers in range[1,n*m] denoting the type of plant in each grid. For the next T lines, the i-th line contains 5 integers x1,y1,x2,y2,k(1<=x1<=x2<=n,1<=y1<=y2<=m,1<=k<=n*m)
输出描述:
Print an integer, denoting the number of plants which would die.
示例1
输入
2 2 2 1 2 2 3 1 1 2 2 2 2 1 2 1 1
输出
3
给出一个n*m的田地矩阵，每个格子上种着一种植物。给格子施肥t次，每一次给出五个数字，x1，y1，x2，y2，k，要施肥的区域坐标和要施的肥料种类。如果植物和施肥种类不匹配，植物会死亡。问最终会死多少个植物。
思路：
用二维树状数组维护每个格子施肥种类总和和施肥次数，最后判断植物种类*施肥次数==施肥种类总和，如果相等，这个格子植物就没有死。但如果一个格子植物种类是3，施的肥料分别是1、2、4、5，满足上面判断条件，但这个植物还是死了。
用随机数处理这个问题，因为随机数分布离散，上面这种情况几乎不可能发生。
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=1e6+10;
int a[maxn],cnt[maxn],ran[maxn];
ll sum[maxn];
int n,m,t,x,y,z,w,k;
int lowbit(int x){
return x&-x;
}
void update(int x,int y,int add,int d)
{
int tempy=y;
while(x<=n)
{
y=tempy;
while(y<=m)
{
sum[(x-1)*m+y-1]+=add;
cnt[(x-1)*m+y-1]+=d;
y+=lowbit(y);
}
x+=lowbit(x);
}
}
bool query(int x,int y)
{
ll rets=0,retc=0;
int tmp=ran[a[(x-1)*m+y-1]];
int tempy=y;
while(x>0){
y=tempy;
while(y>0){
rets+=sum[(x-1)*m+y-1];
retc+=cnt[(x-1)*m+y-1];
y-=lowbit(y);
}
x-=lowbit(x);
}
if(rets==retc*tmp) return true;
else return false;
}
void init(){
for(int i=0;i<maxn;i++){
ran[i]=rand();
}
}
int main(){
init();
while(scanf("%d%d%d",&n,&m,&t)==3){
memset(cnt,0,sizeof(cnt));
memset(sum,0,sizeof(sum));
for(int i=0;i<n;i++){
for(int j=0;j<m;j++){
scanf("%d",&a[i*m+j]);
}
}
for(int i=0;i<t;i++){
scanf("%d%d%d%d%d",&x,&y,&z,&w,&k);
update(z+1,w+1,ran[k],1);
update(x,y,ran[k],1);
update(x,w+1,-ran[k],-1);
update(z+1,y,-ran[k],-1);
}
int ans=n*m;
for(int i=1;i<=n;i++){
for(int j=1;j<=m;j++)
if(query(i,j)) ans--;
}
printf("%d\n",ans);
}
return 0;
}