HDU5813 Elegant Construction

时间：2023-03-08 19:51:36

Elegant Construction

                                                                        Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
                                                                                             Total Submission(s): 1021    Accepted Submission(s): 534
                                                                                                                                Special Judge

Problem Description
Being an ACMer requires knowledge in many fields, because problems in this contest may use physics, biology, and even musicology as background. And now in this problem, you are being a city architect!
A city with N towns (numbered 1 through N) is under construction. You, the architect, are being responsible for designing how these towns are connected by one-way roads. Each road connects two towns, and passengers can travel through in one direction.

For business purpose, the connectivity between towns has some requirements. You are given N non-negative integers a1 .. aN. For 1 <= i <= N, passenger start from town i, should be able to reach exactly ai towns (directly or indirectly, not include i itself).
To prevent confusion on the trip, every road should be different, and cycles (one can travel through several roads and back to the starting point) should not exist.

Your task is constructing such a city. Now it's your showtime!

Input
The first line is an integer T (T <= 10), indicating the number of test case. Each test case begins with an integer N (1 <= N <= 1000), indicating the number of towns. Then N numbers in a line, the ith number ai (0 <= ai < N) has been described above.
Output
For each test case, output "Case #X: Y" in a line (without quotes), where X is the case number starting from 1, and Y is "Yes" if you can construct successfully or "No" if it's impossible to reach the requirements.

If Y is "Yes", output an integer M in a line, indicating the number of roads. Then M lines follow, each line contains two integers u and v (1 <= u, v <= N), separated with one single space, indicating a road direct from town u to town v. If there are multiple
possible solutions, print any of them.

Sample Input
3
3
2 1 0
2
1 1
4
3 1 1 0
Sample Output
Case #1: Yes
2
1 2
2 3
Case #2: No
Case #3: Yes
4
1 2
1 3
2 4
3 4
Author
SYSU
Source
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————————————————————————————————
题目：构造一张有向图。保证每个点能到达的点得数量恰好等于a[i]。

思路：按照a[i]排序，针对每个点i，对于每个小于i的点j，看是否有a[i]个数满足a[j]<a[i]。然后依次连边即可。由于每次都贪心选择小的所以不会重复

#include <iostream>

#include <cstdio>

#include <cstring>

#include <string>

#include <algorithm>

#include <cmath>

#include <map>

#include <cmath>

#include <set>

#include <stack>

#include <queue>

#include <vector>

#include <bitset>

#include <functional>

using namespace std;

#define LL long long

const int INF = 0x3f3f3f3f;

int n,u[10005*1005],v[1005*1005];

struct node

{

    int id,x;

    friend bool operator<(node a,node b)

    {

        return a.x<b.x;

    }

}a[1005];

int main()

{

    int t,cas=0;

    scanf("%d",&t);

    while(t--)

    {

        int flag=1,cnt=0;

        printf("Case #%d: ",++cas);

        scanf("%d",&n);

        for(int i=1;i<=n;i++) scanf("%d",&a[i].x),a[i].id=i;

        sort(a+1,a+1+n);

        if(a[1].x!=0) {printf("No\n");continue;}

        int k=2;

        while(a[k].x==0) k++;

        for(int i=k;i<=n;i++)

        {

            if(a[i].x>i-1) {flag=0;break;}

            for(int j=1;j<=a[i].x;j++)

                u[cnt]=a[i].id,v[cnt++]=a[j].id;

        }

        if(!flag) {printf("No\n");continue;}

        printf("Yes\n%d\n",cnt);

        for(int i=0;i<cnt;i++)

            printf("%d %d\n",u[i],v[i]);

    }

    return 0;

}

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