CF704B Ant Man 题解

合集 - 题解(97)

1.BZOJ3364 Distance Queries 距离咨询 题解2023-08-082.UVA12390 Distributing Ballot Boxes 题解2023-08-243.UVA1108 Mining Your Own Business 题解2023-08-244.CF1425F Flamingoes of Mystery 题解2023-09-295.SP16113 SUBTLEBA - Trucks Transportation 题解2023-10-016.UVA12655 Trucks 题解2023-10-017.P5943 [POI2002] 最大的园地 题解2023-10-018.SP9494 ZSUM - Just Add It 题解2023-10-029.CF1878C Vasilije in Cacak 题解2023-10-0210.CF1010C Border 题解2023-10-0611.CF131D Subway 题解2023-10-0612.B3610 [图论与代数结构 801] 无向图的块 题解2023-11-0413.P9801 [NERC2018] King Kog’s Reception2023-11-0514.CF1089K King Kog's Reception 题解2023-11-0515.SP28304 ADATEAMS - Ada and Teams 题解2023-11-1916.CF327C Magic Five 题解2023-12-1617.P1405 苦恼的小明 题解2023-12-1618.SP10050 POWTOW - Power Tower City 题解2023-12-1619.SP21690 POWERUP - Power the Power Up 题解2023-12-1620.P2898 [USACO08JAN] Haybale Guessing G 题解2023-12-3121.AT_arc125_c [ARC125C] LIS to Original Sequence 题解2024-01-1322.CF1433E Two Round Dances 题解2024-01-2723.CF739A Alyona and mex 题解2024-01-2724.AT_abc270_g [ABC270G] Sequence in mod P 题解2024-02-0725.SP277 CTGAME - City Game 题解2024-02-0726.P8670 [蓝桥杯 2018 国 B] 矩阵求和 题解2024-02-1027.UVA12467 Secret Word 题解2024-02-1328.SP34020 ADAPET - Ada and Pet 题解2024-02-1329.AT_joig2021_d 展覧会 2 (Exhibition 2) 题解2024-03-0330.AT_abc184_f [ABC184F] Programming Contest 题解2024-03-0331.AT_abc343_g [ABC343G] Compress Strings 题解2024-03-1332.CF494C Helping People 题解2024-03-2333.CF922E Birds 题解2024-03-2334.CF1628D1 Game on Sum (Easy Version) 题解2024-03-2335.P7137 [THUPC2021 初赛] 切切糕 题解2024-03-2736.CF1392H ZS Shuffles Cards 题解2024-03-2837.luogu P1543 [POI2004] SZP 题解2024-03-3038.SP64 PERMUT1 - Permutations 题解2024-04-0739.AT_s8pc_2_e 部分文字列 题解2024-04-0740.UVA1223 Editor 题解2024-04-0741.UVA10870 Recurrences 题解2024-05-0242.UVA1362 Exploring Pyramids 题解2024-05-0243.CF1141E Superhero Battle 题解2024-05-2644.SP14943 DRTREE - Dynamically-Rooted Tree 题解2024-05-2645.UVA11922 Permutation Transformer 题解2024-05-2646.UVA1674 闪电的能量 Lightning Energy Report 题解2024-05-2647.P10499 开关问题 题解2024-06-0848.P10466 邻值查找 题解2024-06-0849.P10596 BZOJ2839 集合计数 题解2024-06-2450.UVA12369 Cards 题解2024-06-2851.CF696B Puzzles 题解2024-06-2852.P10672 【MX-S1-T1】壁垒 题解2024-06-2953.P10673 【MX-S1-T2】催化剂 题解2024-06-2954.UVA11181 条件概率 Probability|Given 题解2024-06-2955.SP8177 JZPEXT - Beautiful numbers EXTREME 题解2024-07-0256.AT_tdpc_number 数 题解2024-07-0257.AT_dp_y Grid 2 题解2024-07-0358.P7690 [CEOI2002] A decorative fence 题解2024-07-0459.SP15620 POSTERIN - Postering 题解2024-07-0460.SP14887 GOODA - Good Travels 题解2024-07-1461.P2188 小Z的 k 紧凑数 题解2024-07-1462.SP8099 TABLE - Crash´s number table 题解2024-07-3063.AT_abl_e Replace Digits 题解2024-08-0564.AT_past202010_m 筆塗り 题解2024-08-0965.P8575 「DTOI-2」星之河 题解2024-08-0966.CF641E Little Artem and Time Machine 题解2024-08-0967.P10633 BZOJ2989 数列/BZOJ4170 极光 题解2024-08-1568.P10238 [yLCPC2024] F. PANDORA PARADOXXX 题解2024-08-1669.P4271 [USACO18FEB] New Barns P 题解2024-08-1670.P8512 [Ynoi Easy Round 2021] TEST_152 题解2024-08-1871.CF1514D Cut and Stick 题解2024-08-2372.P10933 创世纪 题解2024-08-2473.P10957 环路运输 题解2024-08-2474.SP10502 VIDEO - Video game combos 题解2024-08-2575.P10956 金字塔 题解2024-08-26

76.CF704B Ant Man 题解2024-09-05

77.P6638 「JYLOI Round 1」常规 题解2024-09-0678.SP1825 FTOUR2 - Free tour II 题解2024-09-2379.P10603 BZOJ4372 烁烁的游戏 题解2024-09-2780.P3364 Cool loves touli 题解2024-09-3081.CF946G Almost Increasing Array 题解2024-10-0582.AT_abc283_g [ABC283G] Partial Xor Enumeration 题解2024-10-1083.CF959F Mahmoud and Ehab and yet another xor task 题解2024-10-1084.P3794 签到题IV 题解2024-10-1685.P7984 [USACO21DEC] Tickets P 题解2024-11-0886.P5479 [BJOI2015] 隐身术 题解2024-11-0887.CF2030D QED's Favorite Permutation 题解2024-11-1088.CF633H Fibonacci-ish II 题解2024-11-1489.AT_abc129_f [ABC129F] Takahashi's Basics in Education and Learning 题解2024-12-1890.P8060 [POI2003] Sums 题解2024-12-2191.AT_keyence2019_e Connecting Cities 题解2024-12-2392.CF1534G A New Beginning 题解2024-12-2693.AT_abc237_g [ABC237G] Range Sort Query 题解2024-12-3094.CF601E A Museum Robbery 题解01-0195.P5680 [GZOI2017] 共享单车 题解01-0496.P3081 [USACO13MAR] Hill Walk G 题解01-0697.AT_abc248_h [ABC248Ex] Beautiful Subsequences 题解01-10

收起

题目传送门

前置知识

预设性 DP

解法

考虑统计每个数单独的贡献，然后进行预设性 DP。

设 $f_{i,j}$ 表示当前填了 $[1,i]$ 时有 $j$ 个连续段的最小权值，边界为 $f_{0,0}=0$。

对 $i(i\ne s,i\ne e)$ 填入的位置进行分讨。

• 新开一段
  • 后面填入的数都比 $i$ 大（如果存在后面填入的数的话，即 $j>[i>s]+[i>t]$），故 $f_{i,j}=min(f_{i,j},f_{i-1,j-1}-2x_i+b_i+d_i)$。
• 连接到某个连续段的前后
  • 连接到某个连续段的前面（如果可以在前面的话，即 $j>[i>s]$）时，后面填入的数（在 $i$ 左面）比 $i$ 大，而 $i$ 右面的数比 $i$ 小，故 $f_{i,j}=min(f_{i,j},f_{i-1,j}+b_i+c_i)$。
  • 连接到某个连续段的后面（如果可以在后面的话，即 $j>[i>t]$）时，后面填入的数（在 $i$ 右面）比 $i$ 大，而 $i$ 左面的数比 $i$ 小，故 $f_{i,j}=min(f_{i,j},f_{i-1,j}+a_i+d_i)$。
• 连接两个连续段
  • $i$ 比旁边的两个数都要大，故 $f_{i,j}=min(f_{i,j},f_{i-1,j+1}+2x_i+a_i+c_i)$。

当 $i=s$ 时只可能放到首端，可行的转移操作只有新开一段和连接到某个连续段的前面且前面不会再有数填，故 $f_{i,j}=min(f_{i-1,j-1}-x_i+d_i,f_{i-1,j}+x_i+c_i)$；当 $i=e$ 时只可能放到末端，可行的转移操作只有新开一段和连接到某个连续段的后面且后面不会再有数填，故 $f_{i,j}=min(f_{i-1,j-1}-x_i+b_i,f_{i-1,j}+x_i+a_i)$。

最终有 $f_{n,1}$ 即为所求。

代码

#include<bits/stdc++.h>
using namespace std;
#define ll long long 
#define ull unsigned long long
#define sort stable_sort 
#define endl '\n'
ll f[5010][5010],x[5010],a[5010],b[5010],c[5010],d[5010];
int main()
{
	ll n,s,e,i,j;
	cin>>n>>s>>e;
	for(i=1;i<=n;i++)
	{
		cin>>x[i];
	}
	for(i=1;i<=n;i++)
	{
		cin>>a[i];
	}
	for(i=1;i<=n;i++)
	{
		cin>>b[i];
	}
	for(i=1;i<=n;i++)
	{
		cin>>c[i];
	}
	for(i=1;i<=n;i++)
	{
		cin>>d[i];
	}
	memset(f,0x3f,sizeof(f));
	f[0][0]=0;
	for(i=1;i<=n;i++)
	{
		for(j=1;j<=i;j++)
		{
			if(i==s)
			{
				f[i][j]=min(f[i][j],f[i-1][j-1]-x[i]+d[i]);
				f[i][j]=min(f[i][j],f[i-1][j]+x[i]+c[i]);
			}
			else
			{
				if(i==e)
				{
					f[i][j]=min(f[i][j],f[i-1][j-1]-x[i]+b[i]);
					f[i][j]=min(f[i][j],f[i-1][j]+x[i]+a[i]);
				}
				else
				{
					if(j>(i>s)+(i>e))
					{
						f[i][j]=min(f[i][j],f[i-1][j-1]-2*x[i]+b[i]+d[i]);
					}
					if(j>(i>s))
					{
						f[i][j]=min(f[i][j],f[i-1][j]+b[i]+c[i]);
					}
					if(j>(i>e))
					{
						f[i][j]=min(f[i][j],f[i-1][j]+a[i]+d[i]);
					}
					f[i][j]=min(f[i][j],f[i-1][j+1]+2*x[i]+a[i]+c[i]);
				}
			}
		}
	}
	cout<<f[n][1]<<endl;
	return 0;
}