E. Increasing Subsequences

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 Problems2023-12-188.C. Game with Multiset2023-12-199.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 Monsters2024-01-22

33.E. Increasing Subsequences2024-01-23

34.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

题解 太巧妙了

1.对于一个递增子序列个数为 $sum$ ，元素值域为 $[l,r]$ 的序列而言
在最右端插入一个

• $l-1$ ,对 $sum$ 的影响是 $+1$
• $r+1$ ,对 $sum$ 的影响是 $\ast 2$

由于乘二加一可以在两百次操作内使 $sum$ 能达到任意 $X$ ,(gan jue)
然后空序列的 $sum$ 是1，因此我们依靠倒推得出序列(我们从1e9开始，这样确保r/l是递减/递增，且数量足够)

code

#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll x;
void solve()
{
    stack<ll> ans;
    ll l=-1e9,r=1e9;
    while(x>1)
    {
        if(x%2)
        {
            ans.push(l++);
            x--;
        }
        else
        {
            ans.push(r--);
            x>>=1;
        }
    }

    cout<<ans.size()<<endl;
    while(ans.size())
    {
        cout<<ans.top()<<" ";
        ans.pop();
    }
    cout<<endl;
}
int main()
{
    ios::sync_with_stdio(false);
    ll t;
    cin>>t;
    while(t--)
    {
        cin>>x;
        solve();
    }
    return 0;
}