2024.9.26

今日总结：
完成了作业中的三道题
1：GCD vs XOR

点击查看代码

#include<bits/stdc++.h>

using namespace std;

const int M = 1e6 + 10;
typedef long long LL;

int cnt[M];
vector<int> vec[M];

void init()
{
	int cnt = 0;
	for(int i = 1;i < M;i ++)
    {
		for(int j = 1;j * j <= i;j ++)
        {
			if(i % j) continue;
			cnt ++;
			int a = i;
			int d = j;
			int b = a ^ d;
			if(b > 0 && a > b)
            {
				int g = __gcd(a,b);
				if(g == d) vec[i].push_back(b);
			}
			if(j * j != i)
            {
				d = i / j;
				b = a ^ d;
				if(b > 0 && a > b)
                {
					int g = __gcd(a,b);
					if(g == d) vec[i].push_back(b);
				}
			}
		}
	}
}

int main(){
    init();
	int T;
	scanf("%d",&T);
	while(T --)
    {
		int n;
		scanf("%d",&n);
		int tot = 0;
		for(int i = 1;i <= n;i ++)
        {
			int x;
			scanf("%d",&x);
			cnt[x] ++;
			tot = max(tot,x);
		}
		LL ans = 0;
		for(int x = tot;x >= 1;x --)
        {
			for(auto y : vec[x])
				ans += 1ll * cnt[x] * cnt[y];
			cnt[x] = 0;
		}
		printf("%lld\n",ans);
	}
	return 0;
}

2：Emojis

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#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 5;
const int INF = 10000000000;

int T,n,cnt,ans;
int a[N],dp[N],pos[N];

int main() 
{
	scanf("%d",&T);
	while(T --) 
    {
		cnt = 0; 
        ans = INF;
		scanf("%d",&n);
		fill(dp,dp + n + 1,INF);
		for(int i = 1;i <= n;i ++) 
            scanf("%d",&a[i]);
		for(int i = 1;i <= n;i ++) 
        { 
			int tmp = upper_bound(dp + 1, dp + n + 1, a[i]) - dp;
			dp[tmp] = a[i];
			pos[i] = tmp;
		}
		cnt = lower_bound(dp + 1,dp + n + 1,INF) - dp - 1;
		for(int i = n;i;i --) 
        {
			int j,k;
			if(pos[i] == cnt) 
            {
				j = i - 1,k = cnt - 1;
				while(k) 
                {
					if(pos[j] == k) k --;
					j --;
				}
				ans = min(ans,i - j - cnt);
			}
		}
		printf("%d %d\n",cnt,ans);
	}
	return 0;
}

3：Fenwick Tree

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#include <bits/stdc++.h>

using namespace std;

#define int long long

int lowbit(int x)
{
    return x & (-x);
}

signed main()
{
	int T;
	scanf("%lld",&T);
	while(T --)
	{
		int n;
		string s;
		scanf("%lld",&n);
		cin >> s;
		vector<int> cnt(n + 1);
		for(int i = 1;i <= n;i ++)
			if(s[i - 1] == '1')
				if(i + lowbit(i) <= n) cnt[i + lowbit(i)] ++;
		int sum = 0;
		for(int i = 1;i <= n;i ++)
		{
			if(s[i - 1] == '0' && cnt[i] == 1) sum ++;
			else if(s[i - 1] == '1' && cnt[i] == 0) sum ++;
		}
		printf("%lld\n",sum);
    }
    return 0;
}