POJ 2777 Count Color（线段树染色，二进制优化）

Count Color

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 42940		Accepted: 13011

Description

Chosen Problem Solving and Program design as an optional course, you are required to solve all kinds of problems. Here, we get a new problem.

There is a very long board with length L centimeter, L is a positive integer, so we can evenly divide the board into L segments, and they are labeled by 1, 2, ... L from left to right, each is 1 centimeter long. Now we have to color the board - one segment
with only one color. We can do following two operations on the board:

1. "C A B C" Color the board from segment A to segment B with color C. 
2. "P A B" Output the number of different colors painted between segment A and segment B (including).

In our daily life, we have very few words to describe a color (red, green, blue, yellow…), so you may assume that the total number of different colors T is very small. To make it simple, we express the names of colors as color 1, color 2, ... color T. At the
beginning, the board was painted in color 1. Now the rest of problem is left to your. 

Input

First line of input contains L (1 <= L <= 100000), T (1 <= T <= 30) and O (1 <= O <= 100000). Here O denotes the number of operations. Following O lines, each contains "C A B C" or "P A B" (here A, B, C are integers, and A may be larger than B) as an operation
defined previously.

Output

Ouput results of the output operation in order, each line contains a number.

Sample Input

2 2 4
C 1 1 2
P 1 2
C 2 2 2
P 1 2

Sample Output

2
1

Source

POJ Monthly--2006.03.26,dodo

题目链接：POJ 2777

大致题意就是区间染色覆盖，区间查询出现的颜色种类。跟以往的普通线段树倒是有点不一样，就是如何进行颜色的记录问题，看了一下别人的做法，就是用2的幂数来代表颜色，由于题目中颜色小于等于30种，小于log2（INT_MAX），可以存的下，那怎么表示呢？看下面的表格

1	1
2	10
3	100
4	1000
5	10000
6	100000
..	.....
..	.....
..	.....
30	100000..（29个0）

由以上表格可以看出，某种颜色用2的幂来表示相当于二进制的1和(颜色标号-1)个0，比如6用2的幂表示就是1和5个0。

那为什么要用这个表示呢？因为后面还要用到按位或“|”运算，即重复的二进制中的1也只算一个，只要出现过，就能算计去，出现两次，也只会按位或得到一个1，比如一棵树有5（表示为10000）和2（表示为10），按位或后就得到10010，其中的1的个数就是颜色个数，不信再试试，再和颜色2按位或（表示为10），还是10010，这显然是符合同色只算一次的情况的，然后就稍微改写一下向上更新、向下更新函数，就差不多了，计算出最后的query结果中1的个数也就是答案了。用了bitset的简化求二进制1个数的写法挺方便

代码：

#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<sstream>
#include<cstring>
#include<cstdio>
#include<bitset>
#include<string>
#include<deque>
#include<stack>
#include<cmath>
#include<queue>
#include<set>
#include<map>
using namespace std;
#define INF 0x3f3f3f3f
#define CLR(x,y) memset(x,y,sizeof(x))
#define LC(x) (x<<1)
#define RC(x) ((x<<1)+1)
#define MID(x,y) ((x+y)>>1)
typedef pair<int,int> pii;
typedef long long LL;
const double PI=acos(-1.0);
const int N=100010;
struct seg
{
	int l,mid,r;
	int color;
	int add;
}T[N<<2];
void pushup(int k)
{
	T[k].color=T[LC(k)].color|T[RC(k)].color;
}
void pushdown(int k)
{
	if(T[k].add)
	{
		T[LC(k)].color=T[k].add;
		T[RC(k)].color=T[k].add;
		T[LC(k)].add=T[k].add;
		T[RC(k)].add=T[k].add;
		T[k].add=0;
	}
}
void build(int k,int l,int r)
{
	T[k].l=l;
	T[k].r=r;
	T[k].mid=MID(l,r);
	T[k].add=0;
	T[k].color=0;
	if(l==r)
	{
		T[k].color=1;
		return ;
	}
	build(LC(k),l,T[k].mid);
	build(RC(k),T[k].mid+1,r);
	pushup(k);
}
void update(int k,int l,int r,int color)
{
	if(r<T[k].l||l>T[k].r)
		return ;
	if(l<=T[k].l&&r>=T[k].r)
	{
		int bina_val=1<<(color-1);
		T[k].color=T[k].add=bina_val;
		return ;
	}
	pushdown(k);
	if(l<=T[k].mid)
		update(LC(k),l,r,color);
	if(r>T[k].mid)
		update(RC(k),l,r,color);
	pushup(k);
}
int query(int k,int l,int r)
{
	if(l<=T[k].l&&T[k].r<=r)
		return T[k].color;
	else
	{
		pushdown(k);
		if(r<=T[k].mid)
			return query(LC(k),l,r);
		else if(l>T[k].mid)
			return query(RC(k),l,r);
		else
			return query(LC(k),l,T[k].mid)|query(RC(k),T[k].mid+1,r);
	}
}
int main(void)
{
	int L,t,O;
	int i,j,l,r,c;
	char ops[3];
	while (~scanf("%d%d%d",&L,&t,&O))
	{
		build(1,1,L);
		for (i=0; i<O; ++i)
		{
			scanf("%s",ops);
			if(ops[0]=='C')
			{
				scanf("%d%d%d",&l,&r,&c);
				if(l>r)
					swap(l,r);
				update(1,l,r,c);
			}
			else
			{
				scanf("%d%d",&l,&r);
				if(l>r)
					swap(l,r);
				printf("%d\n",bitset<32>(query(1,l,r)).count());
			}
		}
	}
	return 0;
}