River Crossing

時間限制：1000?ms ?|? 內存限制：65535?KB 難度：4

描述

Afandi is herding?N?sheep?across the expanses of?grassland??when he finds himself blocked by a river. A single raft is available for transportation.

?

Afandi knows that he must ride on the raft for all crossings, but adding sheep to the raft makes it traverse the river more slowly.

?

When Afandi is on the raft alone, it can cross the river in M minutes When the i sheep are added, it takes Mi minutes longer to cross the river than with i-1 sheep (i.e., total M+M1 ??minutes with one sheep, M+M1+M2 with two, etc.).

?

Determine the minimum time it takes for Afandi to get all of the sheep across the river (including time returning to get more sheep).

輸入

On the first line of the input is a single positive integer k, telling the number of test cases to follow. 1 ≤ k ≤ 5 Each case contains:

* Line 1: one space-separated integers: N and M (1 ≤ N ≤ 1000 , 1≤ M ≤ 500).

* Lines 2..N+1: Line i+1 contains a single integer: Mi (1 ≤ Mi ≤ 1000)

輸出

For each test case, output a line with the minimum time it takes for Afandi to get all of the sheep across the river.

樣例輸入

2 2 10 3 5 5 10 3 4 6 100 1

樣例輸出

18 50

這是去年省賽的一道題，當時寫的代碼交上去一直WA，和隊友討論了好長時間也沒找到哪里錯了。后來才知道我們的思想就是錯的。因為這個題是dp，但是我們一直當成貪心做的。比賽完就放下沒做，沒想到今天比賽又拉出來了，雖然知道是dp，但是由于沒有找到狀態轉移方程，導致今天又沒有做出來。好傷心。。。。

題意：有1個人和N只羊要過河。一個人單獨過河花費的時間是M，每次帶一只羊過河花費時間M+M1，帶兩只羊過河花費時間M+M1+M2……給出N、M和Mi，問N只羊全部過河最少花費的時間是多少。

分析：用一個前綴和數組time，time[i]表示單獨運送i只羊所花費的時間。dp[i]表示一個人和i只羊過河所花費的最短時間，則開始時dp[i] = time[i] + M，以后更新時，dp[i] = min（dp[i]，dp[i-j] + m + dp[j]），j從1循環到i-1，即把i只羊分成兩個階段來運，只需求出這兩個階段的和，然后加上人從對岸回來所用的時間，與dp[i]進行比較，取最小值。

#include<stdio.h> #include<algorithm> using namespace std; int dp[1005], time[1005]; int main() {int T, n, m, i, j;scanf("%d",&T);while(T--){int a;scanf("%d%d",&n, &m);time[0] = 0;for(i = 1; i <= n; i++){scanf("%d",&a);time[i] = time[i-1] + a;}for(i = 1; i <= n; i++){dp[i] = time[i] + m;for(j = 1; j < i; j++)dp[i] = min(dp[i], dp[i-j] + dp[j] + m);}printf("%d\n",dp[n]);}return 0; } //time[i]表示一次運送i只羊所花費的時間 //dp[i]表示人和i只羊一起過河所花費的最短時間

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