Task Schedule

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 4003    Accepted Submission(s): 1347

Problem Description

Our geometry princess XMM has stoped her study in computational geometry to concentrate on her newly opened factory. Her factory has introduced M new machines in order to process the coming N tasks. For the i-th task, the factory
has to start processing it at or after day Si, process it for Pi days, and finish the task before or at day Ei. A machine can only work on one task at a time, and each task can be processed by at most one machine at a time. However, a task can be interrupted
and processed on different machines on different days.

Now she wonders whether he has a feasible schedule to finish all the tasks in time. She turns to you for help.

Input

On the first line comes an integer T(T<=20), indicating the number of test cases.

You are given two integer N(N<=500) and M(M<=200) on the first line of each test case. Then on each of next N lines are three integers Pi, Si and Ei (1<=Pi, Si, Ei<=500), which have the meaning described in the description. It is guaranteed that in a feasible
schedule every task that can be finished will be done before or at its end day.

Output

For each test case, print “Case x: ” first, where x is the case number. If there exists a feasible schedule to finish all the tasks, print “Yes”, otherwise print “No”.

Print a blank line after each test case.

Sample Input

2
4 3
1 3 5
1 1 4
2 3 7
3 5 9

2 2
2 1 3
1 2 2

Sample Output

Case 1: Yes

Case 2: Yes

Author

allenlowesy

Source

2010 ACM-ICPC Multi-University Training
Contest（13）——Host by UESTC

题意：有n个机器，m项任务，每个任务需要Pi天时间，开工日期到收工日期为Si到Ei，一次只能在一台机器上加工，可以挪到别的机器上，问能否按期完成所有任务。

题解：这题关键在构图，设置一个源点到每项任务有一条边，容量为该项任务所需要的天数，每项任务到合法加工日期内的每个天数加一条边，容量为1，即每天工作量为1，然后每个天数到汇点添加一条边，容量为机器数量n，表示一天最大加工量。可惜的是代码超时了-_-#

#include <stdio.h>
#include <string.h>

#define maxn 710
#define maxm 700000
#define inf 0x3f3f3f3f

int head[maxn], n, m, id; // n machines
struct Node {
    int u, v, c, next;
} E[maxm];
int source, sink, tar, maxDay, nv;
int que[maxn], Layer[maxn], pre[maxn];
bool vis[maxn];

void addEdge(int u, int v, int c) {
    E[id].u = u; E[id].v = v;
    E[id].c = c; E[id].next = head[u];
    head[u] = id++;

    E[id].u = v; E[id].v = u;
    E[id].c = 0; E[id].next = head[v];
    head[v] = id++;
}

void getMap() {
    int i, j, u, v, p, s, e;
    id = tar = maxDay = 0;
    scanf("%d%d", &m, &n);
    memset(head, -1, sizeof(head));
    source = 0; sink = 705;
    for(i = 1; i <= m; ++i) {
        scanf("%d%d%d", &p, &s, &e);
        tar += p;
        if(e > maxDay) maxDay = e;
        addEdge(source, i, p);
        for(j = s; j <= e; ++j)
            addEdge(i, m + j, 1);
    }
    sink = m + maxDay + 1; nv = sink + 1;
    for(i = 1; i <= maxDay; ++i)
        addEdge(m + i, sink, n);
}

bool countLayer() {
    memset(Layer, 0, sizeof(int) * nv);
    int id = 0, front = 0, u, v, i;
    Layer[source] = 1; que[id++] = source;
    while(front != id) {
        u = que[front++];
        for(i = head[u]; i != -1; i = E[i].next) {
            v = E[i].v;
            if(E[i].c && !Layer[v]) {
                Layer[v] = Layer[u] + 1;
                if(v == sink) return true;
                else que[id++] = v;
            }
        }
    }
    return false;
}

int Dinic() {
    int i, u, v, minCut, maxFlow = 0, pos, id = 0;
    while(countLayer()) {
        memset(vis, 0, sizeof(bool) * nv);
        memset(pre, -1, sizeof(int) * nv);
        que[id++] = source; vis[source] = 1;
        while(id) {
            u = que[id - 1];
            if(u == sink) {
                minCut = inf;
                for(i = pre[sink]; i != -1; i = pre[E[i].u])
                    if(minCut > E[i].c) {
                        minCut = E[i].c; pos = E[i].u;
                    }
                maxFlow += minCut;
                for(i = pre[sink]; i != -1; i = pre[E[i].u]) {
                    E[i].c -= minCut;
                    E[i^1].c += minCut;
                }
                while(que[id-1] != pos)
                    vis[que[--id]] = 0;
            } else {
                for(i = head[u]; i != -1; i = E[i].next)
                    if(E[i].c && Layer[u] + 1 == Layer[v = E[i].v] && !vis[v]) {
                        vis[v] = 1; que[id++] = v; pre[v] = i; break;
                    }
                if(i == -1) --id;
            }
        }
    }
    return maxFlow;
}

void solve(int cas) {
    printf("Case %d: %s\n\n", cas, tar == Dinic() ? "Yes" : "No");
}

int main() {
    // freopen("stdin.txt", "r", stdin);
    int t, cas;
    scanf("%d", &t);
    for(cas = 1; cas <= t; ++cas) {
        getMap();
        solve(cas);
    }
    return 0;
}