E. Money Buys Happiness

合集 - 动态规划dp(55)

1.P8784 [蓝桥杯 2022 省 B] 积木画2024-02-172.P9847 [ICPC2021 Nanjing R] Crystalfly2024-02-183.G. Vlad and Trouble at MIT2024-02-204.P2899 [USACO08JAN] Cell Phone Network G2024-02-205.P5322 [BJOI2019] 排兵布阵2024-03-036.P2946 [USACO09MAR] Cow Frisbee Team S2024-03-037.P1156 垃圾陷阱2024-03-038.P1064 [NOIP2006 提高组] 金明的预算方案2024-03-049.P2466 [SDOI2008] Sue 的小球2024-03-0410.P5020 [NOIP2018 提高组] 货币系统2024-03-0411.P1757 通天之分组背包2024-03-0412.P2135 方块消除2024-03-0613.D - String Bags2024-03-1014.P4395 [BOI2003] Gem 气垫车2024-03-1015.A - A Multiply2024-03-2416.P2642 双子序列最大和2024-03-2517.P1121 环状最大两段子段和2024-03-2518.P2422 良好的感觉2024-03-2519.P2854 [USACO06DEC] Cow Roller Coaster S2024-03-2620.C. Theofanis' Nightmare2024-03-2721.D. Birthday Gift2024-03-2722.P1284 三角形牧场2024-03-2823.P1353 [USACO08JAN] Running S2024-03-2824.P8736 [蓝桥杯 2020 国 B] 游园安排2024-03-3025.P1470 [USACO2.3] 最长前缀 Longest Prefix2024-04-0126.P7859 [COCI2015-2016#2] GEPPETTO2024-04-0527.P1435 [IOI2000] 回文字串2024-05-0828.P2340 [USACO03FALL] Cow Exhibition G2024-05-1329.P1854 花店橱窗布置2024-05-1330.P3147 [USACO16OPEN] 262144 P2024-05-1331.Game on Tree2024-05-1432.P2938 [USACO09FEB] Stock Market G2024-05-1833.P9691 [GDCPC2023] Base Station Construction2024-05-1834.P8624 [蓝桥杯 2015 省 AB] 垒骰子2024-05-20

35.E. Money Buys Happiness2024-05-22

36.P8675 [蓝桥杯 2018 国 B] 搭积木2024-05-2237.P8774 [蓝桥杯 2022 省 A] 爬树的甲壳虫2024-05-2238.P8806 [蓝桥杯 2022 国 B] 搬砖2024-05-2339.P5662 [CSP-J2019] 纪念品2024-05-2440.B. Mashmokh and ACM2024-06-0841.C. Minimizing the Sum2024-06-1242.H. Don't Blame Me2024-06-1343.D. Bicolorings2024-06-1444.D. Armchairs2024-06-1845.C. Chef Monocarp2024-06-1846.D. Invertible Bracket Sequences2024-06-2047.P1351 [NOIP2014 提高组] 联合权值2024-06-2648.D. World is Mine2024-07-0249.F. Feed Cats2024-07-0750.P3522 [POI2011] TEM-Temperature2024-07-2151.P3572 [POI2014] PTA-Little Bird2024-07-2252.P3089 [USACO13NOV] Pogo-Cow S2024-07-2253.E - Maximum Glutton2024-07-2854.Projects2024-07-2855.Elevator Rides2024-07-28

收起

原题链接

题解

观察到h不大于1e5，于是拿h做文章
如果想要在第 $i$ 个月的幸福值达到 $j$ 那么第 $i-1$ 个月的幸福值一定能达到 $j-h_i$ 而且 $cos{t}_{[i-1][j-h_i]}+c_i\le x·(i-1)$
记得用滚动数组优化，因为这里 $i$ 只和 $i-1$ 的小幸福值有关

code

#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll c[55]={0},h[55]={0};
ll dp[100005]={0};
int main()
{
    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    ll t;
    cin>>t;
    while(t--)
    {
        ll m,x;
        cin>>m>>x;

        ll happy=0;

        for(ll i=1;i<=m;i++)
        {
            cin>>c[i]>>h[i];
            happy+=h[i];
        }


        for(ll j=0;j<=happy;j++) dp[j]=5e9+2;
        dp[0]=0;
        ll ans=0;
        for(ll i=1;i<=m;i++)
        {
            for(ll j=happy;j>=h[i];j--)
            {
                if(x*(i-1)-dp[j-h[i]]>=c[i])
                {
                    dp[j]=min(dp[j],dp[j-h[i]]+c[i]);
                    ans=max(ans,j);
                }
            }
        }

        cout<<ans<<"\n";
    }
    return 0;
}