codeforces 1207 C（水dp）
You are responsible for installing a gas pipeline along a road. Let's consider the road (for simplicity) as a segment [0,n][0,n] on OXOX axis. The road can have several crossroads, but for simplicity, we'll denote each crossroad as an interval (x,x+1)(x,x+1) with integer xx. So we can represent the road as a binary string consisting of nn characters, where character 0 means that current interval doesn't contain a crossroad, and 1 means that there is a crossroad.
Usually, we can install the pipeline along the road on height of 11 unit with supporting pillars in each integer point (so, if we are responsible for [0,n][0,n] road, we must install n+1n+1 pillars). But on crossroads we should lift the pipeline up to the height 22, so the pipeline won't obstruct the way for cars.
We can do so inserting several zig-zag-like lines. Each zig-zag can be represented as a segment [x,x+1][x,x+1] with integer xx consisting of three parts: 0.50.5 units of horizontal pipe + 11 unit of vertical pipe + 0.50.5 of horizontal. Note that if pipeline is currently on height 22, the pillars that support it should also have length equal to 22 units.
Each unit of gas pipeline costs us aa bourles, and each unit of pillar — bb bourles. So, it's not always optimal to make the whole pipeline on the height 22. Find the shape of the pipeline with minimum possible cost and calculate that cost.
Note that you must start and finish the pipeline on height 11 and, also, it's guaranteed that the first and last characters of the input string are equal to 0.
The fist line contains one integer TT (1≤T≤1001≤T≤100) — the number of queries. Next 2⋅T2⋅T lines contain independent queries — one query per two lines.
The first line contains three integers nn, aa, bb (2≤n≤2⋅1052≤n≤2⋅105, 1≤a≤1081≤a≤108, 1≤b≤1081≤b≤108) — the length of the road, the cost of one unit of the pipeline and the cost of one unit of the pillar, respectively.
The second line contains binary string ss (|s|=n|s|=n, si∈{0,1}si∈{0,1}, s1=sn=0s1=sn=0) — the description of the road.
It's guaranteed that the total length of all strings ss doesn't exceed 2⋅1052⋅105.
Print TT integers — one per query. For each query print the minimum possible cost of the constructed pipeline.
4 8 2 5 00110010 8 1 1 00110010 9 100000000 100000000 010101010 2 5 1 00
94 25 2900000000 13
主要没想到用dp写，不然随便写写就过了，
利用dp[i][0]表示到第i个路口右边的柱子为普通柱子时所需要的最低花费，dp[i][1]第i个路口右边的柱子为高柱子所需要的最低花费，
如果当前路口是1，那么此时路口右边的柱子只能是高柱子
dp[i][1] = dp[i-1][1] + a + 2*b;
如果当前路口是0，那么右边的柱子可能是普通柱子，也可能是高柱子
如果是普通柱子，
此时左边可能为普通柱子，也可能为高柱子，有：
dp[i][0] = min(dp[i-1][0] + a + b,dp[i-1][1] + 2*a + b);
如果是高柱子，
此时左边可能为普通柱子，也可能为高柱子，有：
dp[i][1] = min(dp[i-1][0] + 2*a + 2*b,dp[i-1][1] + a + 2*b);
#include <iostream> #include <cmath> #include <cstdio> #include <cstring> #include <string> #include <map> #include <iomanip> #include <algorithm> #include <queue> #include <stack> #include <set> #include <vector> //const int maxn = 1e5+5; #define ll long long ll gcd(ll a,ll b){return b?gcd(b,a%b):a;} ll lcm(ll a,ll b){return a/gcd(a,b)*b;} #define MAX INT_MAX #define FOR(i,a,b) for( int i = a;i <= b;++i) #define bug cout<<"--------------"<<endl using namespace std; ll inf = 0x3f3f3f3f3f3f3f3f; char s[210000]; int a,b,n,T; ll dp[210000][5]; int main() { cin>>T; while(T--) { scanf("%d%d%d",&n,&a,&b); scanf("%s",s+1); FOR(i,1,n) dp[i][1] = dp[i][0] = inf; dp[0][1] = inf; dp[0][0] = b; for(int i =1;i<=n;++i) { if(s[i] == '1') { dp[i][1] = dp[i-1][1] + a + 2*b; } else { dp[i][0] = min(dp[i-1][0] + a + b,dp[i-1][1] + 2*a + b); dp[i][1] = min(dp[i-1][0] + 2*a + 2*b,dp[i-1][1] + a + 2*b); } } printf("%lld\n",dp[n][0]); } }
