http://codeforces.com/problemset/problem/1249/E

E. By Elevator or Stairs?
time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are planning to buy an apartment in a n

-floor building. The floors are numbered from 1 to n

from the bottom to the top. At first for each floor you want to know the minimum total time to reach it from the first (the bottom) floor.

Let:

  • ai

for all i from 1 to n−1 be the time required to go from the i-th floor to the (i+1)-th one (and from the (i+1)-th to the i

  • -th as well) using the stairs;
  • bi

for all i from 1 to n−1 be the time required to go from the i-th floor to the (i+1)-th one (and from the (i+1)-th to the i-th as well) using the elevator, also there is a value c

  • — time overhead for elevator usage (you need to wait for it, the elevator doors are too slow!).

In one move, you can go from the floor you are staying at x

to any floor y (x≠y

) in two different ways:

  • If you are using the stairs, just sum up the corresponding values of ai

. Formally, it will take ∑i=min(x,y)max(x,y)−1ai

  • time units.
  • If you are using the elevator, just sum up c

and the corresponding values of bi. Formally, it will take c+∑i=min(x,y)max(x,y)−1bi

  • time units.

You can perform as many moves as you want (possibly zero).

So your task is for each i

to determine the minimum total time it takes to reach the i-th floor from the 1

-st (bottom) floor.

Input

The first line of the input contains two integers n

and c (2≤n≤2⋅105,1≤c≤1000

) — the number of floors in the building and the time overhead for the elevator rides.

The second line of the input contains n−1

integers a1,a2,…,an−1 (1≤ai≤1000), where ai is the time required to go from the i-th floor to the (i+1)-th one (and from the (i+1)-th to the i

-th as well) using the stairs.

The third line of the input contains n−1

integers b1,b2,…,bn−1 (1≤bi≤1000), where bi is the time required to go from the i-th floor to the (i+1)-th one (and from the (i+1)-th to the i

-th as well) using the elevator.

Output

Print n

integers t1,t2,…,tn, where ti is the minimum total time to reach the i

-th floor from the first floor if you can perform as many moves as you want.

Examples
Input

Copy
10 2
7 6 18 6 16 18 1 17 17
6 9 3 10 9 1 10 1 5
Output

Copy
0 7 13 18 24 35 36 37 40 45
Input

Copy
10 1
3 2 3 1 3 3 1 4 1
1 2 3 4 4 1 2 1 3
Output

Copy
0 2 4 7 8 11 13 14 16 17

题意:有n楼,给你1到2,2到3....n-1到n楼的爬楼梯时间和坐电梯时间。从楼梯去坐电梯需要等电梯开门的时间c。问每一楼到一楼的最短时间。

解法:考虑四个转移状态:从楼梯到楼梯,从楼梯到电梯,从电梯到楼梯,从电梯到电梯。

//#include <bits/stdc++.h>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <stdio.h>
#include <queue>
#include <stack>;
#include <map>
#include <set>
#include <string.h>
#include <vector>
#define ME(x , y) memset(x , y , sizeof(x))
#define SF(n) scanf("%d" , &n)
#define rep(i , n) for(int i = 0 ; i < n ; i ++)
#define INF 0x3f3f3f3f
#define mod 998244353
#define PI acos(-1)
using namespace std;
typedef long long ll ;
ll a[] , b[];
ll dp[][]; int main()
{
ll n , c ;
while(~scanf("%lld%lld" , &n , &c))
{
for(int i = ; i <= n ; i++)
{
scanf("%lld" , &a[i]);
}
for(int i = ; i <= n ; i++)
{
scanf("%lld" , &b[i]);
}
memset(dp , INF , sizeof(dp));
dp[][] = c ;
dp[][] = ;
for(int i = ; i <= n ; i++)
{
dp[i][] = min(dp[i][] , dp[i-][]+a[i]);//电梯到楼梯
dp[i][] = min(dp[i][] , dp[i-][]+a[i]);//楼梯到楼梯
dp[i][] = min(dp[i][] , dp[i-][]+b[i]);//电梯到电梯
dp[i][] = min(dp[i][] , dp[i-][]+b[i]+c);//楼梯到电梯
} for(int i = ; i < n ; i++)
cout << min(dp[i][] , dp[i][]) << " " ;
cout << min(dp[n][] , dp[n][]) << endl ;
} return ;
}

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