C. Game with Multiset

合集 - codeforces(57)

1.C. Insert and Equalize2023-12-062.C. Removal of Unattractive Pairs2023-12-063.D. Jumping Through Segments2023-12-084.E. Good Triples2023-12-085.F. Shift and Reverse2023-12-086.D. Yet Another Monster Fight2023-12-117.A. Constructive Problems2023-12-18

8.C. Game with Multiset2023-12-19

9.A. Rating Increase2023-12-1910.B. Swap and Delete2023-12-1911.A. Problemsolving Log2023-12-2012.B. Preparing for the Contest2023-12-2013.C. Quests2023-12-2014.D. Three Activities2023-12-2015.E2. Game with Marbles (Hard Version)2023-12-2016.cf刷题有感2023-12-2017.A. Anonymous Informant2023-12-2118.A. Forked!2023-12-2319.B. Make Almost Equal With Mod2023-12-2720.C. Heavy Intervals2023-12-2721.D. Split Plus K2023-12-2822.A. 20232023-12-3123.B. Two Divisors2023-12-3124.C. Training Before the Olympiad2023-12-3125.D. Mathematical Problem2024-01-0226.F. Greetings2024-01-0227.C. Partitioning the Array2024-01-1528.G. Bicycles2024-01-1629.E. Eat the Chip2024-01-1730.G. Lights2024-01-1731.D. Array Repetition2024-01-1732.D. Berserk Monsters2024-01-2233.E. Increasing Subsequences2024-01-2334.D. Very Different Array2024-01-2435.G. Mischievous Shooter2024-01-2536.B. Plus-Minus Split2024-01-2737.B. A Balanced Problemset2024-01-2838.C. Did We Get Everything Covered2024-01-2839.D. Find the Different Ones!2024-02-0840.C. Grouping Increases2024-02-1041.D. Good Trip2024-02-1242.C. Physical Education Lesson2024-02-1243.E. Final Countdown2024-02-1844.D. Divisible Pairs2024-02-1945.G. Vlad and Trouble at MIT2024-02-2046.A. Brick Wall2024-02-2847.B. Minimize Inversions2024-02-2848.C. XOR-distance2024-02-2849.A. Moving Chips2024-02-2850.B. Monsters Attack!2024-02-2851.C. Find B2024-02-2852.D. Slimes2024-02-2853.C. Turtle Fingers: Count the Values of k2024-02-2854.D. Turtle Tenacity: Continual Mods2024-02-2855.D. Vlad and Division2024-02-2856.C. LR-remainders2024-02-2857.D. Lonely Mountain Dungeons2024-03-12

收起

原题链接

反思：要把各种可能的情况都判断一遍再提交！不要急着提交

简介

仓库里有若干个二次方数，请问是否能取出若干数使得刚好等于给定数？

情况讨论

情况1.仓库里只有一个4，但是我要求2，求不得
情况2.仓库里有三个1，我要求3，能求

大概思路

从$i\in [log2(v),0]$遍历（从大到小），如果对于i，仓库里有，就一直减$2^i$直到无法再减（再减就小于零或库里的i次数用光了）

细节注意

1.for循环减法可以用一次性减法（除法找出减的次数）代替，速度会快很多
2.$v$不会超过${10}^9$，所以$2^i$也不会超过long long 范围
3.pow函数比较耗时，可以用(1<<n)或者log2代替

代码1

#include<bits/stdc++.h>
using namespace std;
#define ll long long
int main()
{
    ll n;
    cin>>n;
    ll a[35]={0};
    while(n--)
    {
        ll q,v;
        cin>>q>>v;
        if(q==1) a[v]++;
        else
        {
            int i=log2(v);;//1.判断是否正常退出
            //2.代表最外面的1的位置
            for(i;i>=0;i--)//不从29开始，一定程度的优化
            {
                ll b=a[i];//仓库里i的数量
                ll d=pow(2,i);//当前i代表的实际值
                if(log2(v)>=i) v-=min(b,v/d)*d;//最多能减多少乘上减去的值，核心优化
                if(v==0)break;
            }
            if(i!=-1)puts("YES");
            else puts("NO");
        }
    }
    return 0;
}

dalao的代码2

#include<bits/stdc++.h>
using namespace std;
int c[60];
int main(){
	ios::sync_with_stdio(false),cin.tie(0);
	int q,op,v,i,j;
	for(cin>>q;q>0;q--)
	{
		cin>>op;
		if(op==1)
		{
			cin>>v;
			c[v]++;
			for(i=0;i<59;i++)
			{
				if(c[i]==3)//4可以由一个4组成，也可以由两个2组成，任意一个数可以由1 or 0个二次方数组成，多出来的部分就可以去进位Orz
				{
					c[i]-=2;
					c[i+1]++;
				}
			}
		}
		if(op==2)
		{
			cin>>v;
			for(i=30;i>-1;i--)
			{
				for(j=0;j<c[i];j++)
				{
					if(v>=(1<<i))v-=(1<<i);
				}
			}
			if(v==0)cout<<"YES\n";
			else cout<<"NO\n";
		}
	}
	return 0;
}