[C++知识库]算法基础课（三）＜双指针算法，位运算，lowbit，离散化，区间合并＞

1. 双指针算法

作用：优化

时间复杂度为O(N)

eg1:单词识别：

#include <iostream>
#include <string.h>

using namespace std;

int main()
{
	char str[1000];
	gets(str);
	int n = strlen(str);
	
	for(int i = 0;i<n;i++)
	{
		int j = i;
		while(j<n&&str[j]!=' ') j++;
		
		for(int k = i;k<j;k++) cout<<str[k];
		cout<<endl;
		
		i=j;
	}
	return 0;
 } 

eg2:判断数字不重复连续个数

#include <iostream>
#include <string.h>
using namespace std;

const int N = 100010;
int n;
int s[N],a[N];

int main()
{
	cin >> n;
	for(int i = 0;i<n;i++) cin>>a[i];
	int res = 0;
	for(int i = 0,j = 0;i<n;i++){
		s[a[i]]++;
		while(s[a[i]] > 1){
			s[a[j]]--;
			j++;
		}
		res = max(res,i-j+1);
	}
	cout << res <<endl;
	return 0;
}

2.位运算

n的二进制第k位是多少？
常用操作：n >> k & 1

#include <iostream>
#include <string.h>

using namespace std;

int main()
{
	int n = 10;
	for(int k = 3;k>=0;k --) cout << (n >> k & 1);
	return 0;
}

3.lowbit

lowbit(x)返回x的最后一位1，包括后面的0

C++里 -x为x的补码，-x为取反x+1，
作用:求x的二进制表示里面1的个数

4.整数离散化

模板

eg:

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

typedef pair<int,int> PII;

const int N = 300010;
int n,m;
int a[N],s[N];

vector<int> alls;
vector<PII> add,query;

vector<int>::iterator unique(vector<int> &a)
{
	int j = 0;
	for(int i = 0;i < a.size();i++)
		if(!i || a[i]!=a[i-1])
			a[j++] = a[i];
			
	return a.begin() + j;
}

int find(int x)
{
	int l = 0,r=alls.size()-1;
	while(l<r)
	{
		int mid = l+r>>1;
		if(alls[mid] >= x) r = mid;
		else l = mid + 1;
	}
	return r+1;
}

int main()
{
	cin >> n >> m;
	for(int i = 0;i<n;i++)
	{
		int x,c;
		cin>> x>> c;
		add.push_back({x,c});
		alls.push_back(x);
	}
	for(int i = 0;i < m;i++){
		int l,r;
		cin >> l >> r;
		query.push_back({l,r});
		
		alls.push_back(l);
		alls.push_back(r);
	}
	//去重
	sort(alls.begin(),alls.end());
	alls.erase(unique(alls.begin(),alls.end()),alls.end());
	
	for(auto item : add){
		int x = find(item.first);
		a[x]+=item.second;
	}
	
	//预处理前缀和
	for(int i = 1;i<=alls.size();i++) s[i] = s[i-1]+a[i];
	
	//处理询问
	for(auto item : query)
	{
		int l = find(item.first),r = find(item.second);
		cout << s[r] - s[l-1] <<endl;
	} 
	
	return 0;
	
}

4.区间合并

#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;
typedef pair<int,int> PII;

const int N = 100010;

int n;
vector<PII> segs;

void merge(vector<PII> &segs)
{
	vector<PII> res;
	
	sort(segs.begin(),segs.end());
	
	int st = -2e9,ed = -2e9;
	for(auto seg : segs)
		if(ed < seg.first)
		{
			if (st != -2e9) res.push_back({st,ed});
			st = seg.first,ed = seg.second;
		}
		else ed = max(ed,seg.second);
	if(st != -2e9) res.push_back({st,ed});
	
	segs = res;
}

int main()
{
	cin >> n;
	for(int i = 0;i<n;i++)
	{
		int l,r;
		cin >> l >> r;
		segs.push_back({l,r});
	}
	
	merge(segs);
	
	cout << segs.size() <<endl;
	return 0;
}