UVA 11729 Commando War

Commando War
Input: Standard Input
Output: Standard Output


“Waiting for orders we held in the wood, word from the front never came
By evening the sound of the gunfire was miles away
Ah softly we moved through the shadows, slip away through the trees
Crossing their lines in the mists in the fields on our hands and our knees
And all that I ever, was able to see
The fire in the air, glowing red, silhouetting the smoke on the breeze”

There is a war and it doesn't look very promising for your country. Now it's time to act. You have a commando squad at your disposal and planning an ambush on an important enemy camp located nearby. You have N soldiers in your squad. In your master-plan, every single soldier has a unique responsibility and you don't want any of your soldier to know the plan for other soldiers so that everyone can focus on his task only. In order to enforce this, you brief every individual soldier about his tasks separately and just before sending him to the battlefield. You know that every single soldier needs a certain amount of time to execute his job. You also know very clearly how much time you need to brief every single soldier. Being anxious to finish the total operation as soon as possible, you need to find an order of briefing your soldiers that will minimize the time necessary for all the soldiers to complete their tasks. You may assume that, no soldier has a plan that depends on the tasks of his fellows. In other words, once a soldier begins a task, he can finish it without the necessity of pausing in between.

Input

There will be multiple test cases in the input file. Every test case starts with an integer N (1<=N<=1000), denoting the number of soldiers. Each of the following N lines describe a soldier with two integers B (1<=B<=10000) & J (1<=J<=10000). B seconds are needed to brief the soldier while completing his job needs J seconds. The end of input will be denoted by a case with N =0 . This case should not be processed.

Output

For each test case, print a line in the format, “Case X: Y”, where X is the case number & Y is the total number of seconds counted from the start of your first briefing till the completion of all jobs.

Sample Input Output for Sample Input
2 5
2
1
3 3
4
5
Case 1: 8
Case 2: 15

Problem Setter: Mohammad Mahmudur Rahman, Special Thanks: Manzurur Rahman Khan

分析：根据题意，交代任务不能并行，那么交代任务一定是一个接一个的。但是因为执行任务是可以并行的，那么为了缩短时间，我们应该让尽量多的任务并行执行。达到这个目标的做法就是执行时间长的任务先交待。

#include <iostream>
#include <map>

using namespace std;

int main(int argc, char const *argv[])
{
    int test, caseN = 0;
    while (cin >> test && test != 0) {
        multimap<int, int> soldierAndFinishTime;
        int B, J;
        int m = 0, sum = 0;
        for (int i = 0; i != test; ++i) {
            cin >> B >> J;
            soldierAndFinishTime.insert(pair<int, int>(1- J, B));  // map 的自动排序，按 job 从大到小排序
        }
        for (auto &i : soldierAndFinishTime) {
            /*
             *    mi: 分配第 i 个任务的时间，si: 第 i 个任务的执行时间
             *    那么第 i 个任务的执行完时间为 m1 + m2 + ... + mi + si，或者是
             *    前面的任务执行完的时间，这个情况就是前面任务的最长时间比现在这个任务执行完
             *    的时间还要长
             */
            m += i.second;    // 当前任务的开始时间
            sum = max(sum, m + (1 - i.first));    // sum表示到目前为止需要执行的最长时间
        }
        cout << "Case " << ++caseN << ": " << sum << endl;
    }
    return 0;
}