GCJ Bribe the Prisoners 解题报告


In a kingdom there are prison cells (numbered 1 to P) built to form a straight line segment. Cells number i and i+1 are adjacent, and prisoners in adjacent cells are called "neighbours." A wall with a window separates adjacent cells, and neighbours can communicate through that window.

All prisoners live in peace until a prisoner is released. When that happens, the released prisoner's neighbours find out, and each communicates this to his other neighbour. That prisoner passes it on to his other neighbour, and so on until they reach a prisoner with no other neighbour (because he is in cell 1, or in cell P, or the other adjacent cell is empty). A prisoner who discovers that another prisoner has been released will angrily break everything in his cell, unless he is bribed with a gold coin. So, after releasing a prisoner in cell A, all prisoners housed on either side of cell A - until cell 1, cell P or an empty cell - need to be bribed.

Assume that each prison cell is initially occupied by exactly one prisoner, and that only one prisoner can be released per day. Given the list of Q prisoners to be released in Q days, find the minimum total number of gold coins needed as bribes if the prisoners may be released in any order.

Note that each bribe only has an effect for one day. If a prisoner who was bribed yesterday hears about another released prisoner today, then he needs to be bribed again.


The first line of input gives the number of cases, N. N test cases follow. Each case consists of 2 lines. The first line is formatted as

where P is the number of prison cells and Q is the number of prisoners to be released. This will be followed by a line with Q distinct cell numbers (of the prisoners to be released), space separated, sorted in ascending order. Output For each test case, output one line in the format
Case #X: C

where X is the case number, starting from 1, and C is the minimum number of gold coins needed as bribes.


1 ≤ N ≤ 100
Q ≤ P
Each cell number is between 1 and P, inclusive.

Small dataset

1 ≤ P ≤ 100
1 ≤ Q ≤ 5

Large dataset

1 ≤ P ≤ 10000
1 ≤ Q ≤ 100


Input         Output

2             Case #1: 7
8 1           Case #2: 35
20 3
3 6 14

In the second sample case, you first release the person in cell 14, then cell 6, then cell 3. The number of gold coins needed is 19 + 12 + 4 = 35. If you instead release the person in cell 6 first, the cost will be 19 + 4 + 13 = 36.

Code :

*题目出处:http://code.google.com/codejam/contest/189252/dashboard#s=p2   Bribe the Prisoners
*date:  2013.12.8
#include <iostream>
#include <cstdio>

using namespace std;

const int INT_MAX=1e9;
const int MAX_Q=100;
int P,Q,A[MAX_Q+1],dp[MAX_Q+1][MAX_Q+1];  //A[MAX_Q+2]:存储要释放囚犯的牢房号,下标从1开始
void initial()     //初始化dp[]数组
	for(int i=0;i<=Q+1;i++)
		for(int j=0;j<=Q+1;j++)

int get_min(int a,int b)
	return a<b?a:b;

int solve(int i,int j)  //计算释放牢房号在A[i]~A[j]之间的囚犯所需要的最小金币数
{						//d[i][j]表示释放牢房号在A[i]~A[j]之间的囚犯(不包含两端的囚犯)所需的最小金币数
	if(dp[i][j]!=INT_MAX) return dp[i][j];
	if(i+1>=j) return 0;  //说明A[i]~A[j]之间没有要释放的囚犯
	for(int k=i+1;k<=j-1;k++)
	return dp[i][j];

int main()
	int N;
	for(int i=1;i<=N;i++)
		initial();     //初始化dp数组
		A[0]=0;        //牢房两端即墙壁赋值给A[0]和A[Q+1]
		for(int j=1;j<=Q;j++)   //输入A[]
		printf("Case #%d: %d\n",i,solve(0,Q+1));
	return 0;


void solve()
	for(int q=0;q<=Q;q++){

	for(int w=2;w<=Q+1;w++){
		for(int i=0;i+w<=Q+1;i++){
			int j=i+w,t=INT_MAX;
			for(int k=i+1;k<j;k++){



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