HDU 5924 Mr. Frog’s Problem 【模拟】 (2016CCPC东北地区大学生程序设计竞赛)

Mr. Frog’s Problem

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

Total Submission(s): 312    Accepted Submission(s): 219

Problem Description

One day, you, a clever boy, feel bored in your math class, and then fall asleep without your control. In your dream, you meet Mr. Frog, an elder man. He has a problem for you.

He gives you two positive integers A and B, and your task is to find all pairs of integers (C, D), such that A≤C≤B,A≤D≤B and AB+BA≤CD+DC

 

Input

first line contains only one integer T (T≤125),
which indicates the number of test cases. Each test case contains two integers A and B (1≤A≤B≤1018).

 

Output

For each test case, first output one line "Case #x:", where x is the case number (starting from 1). 

Then in a new line, print an integer s indicating the number of pairs you find.

In each of the following s lines, print a pair of integers C and D. pairs should be sorted by C, and then by D in ascending order.

 

Sample Input

2
10 10
9 27

 

Sample Output

Case #1:
1
10 10
Case #2:
2
9 27
27 9

 

Source

2016CCPC东北地区大学生程序设计竞赛
- 重现赛

 

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Statistic | Submit | Discuss | Note

题目大意：

　　题目给定A和B(<=1018)，求满足

的C和D个个数，并全部输出。

题目思路：

　　【模拟】

　　+1s 这题一看样例就猜大概只有AB，BA两种情况。不妨假设C<=D

　　假设A/B+B/A>A/(B-1)+(B-1)/A，解得条件为B2-B>A2,所以如果要满足，则需要A2>=B2-B，而只有当A=B时满足(B>=A,B=A+1时，B2-B=A(A+1)>A2)

　　所以除了A=B的情况，其余都是减的，(C,D)可视为(A,B)->(A,D)->(C,D)，每次只改一维，递减，所以最终也是递减的。

　　所以最终答案就是AB,BA 注意A=B的情况。

//HDU 5924
//by coolxxx
//#include<bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<string>
#include<iomanip>
#include<map>
#include<stack>
#include<queue>
#include<set>
#include<bitset>
#include<memory.h>
#include<time.h>
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
//#include<stdbool.h>
#include<math.h>
#pragma comment(linker,"/STACK:1024000000,1024000000")
#define min(a,b) ((a)<(b)?(a):(b))
#define max(a,b) ((a)>(b)?(a):(b))
#define abs(a) ((a)>0?(a):(-(a)))
#define lowbit(a) (a&(-a))
#define sqr(a) ((a)*(a))
#define swap(a,b) ((a)^=(b),(b)^=(a),(a)^=(b))
#define mem(a,b) memset(a,b,sizeof(a))
#define eps (1e-10)
#define J 10000
#define mod 1000000007
#define MAX 0x7f7f7f7f
#define PI 3.14159265358979323
#define N 100004
using namespace std;
typedef long long LL;
double anss;
LL aans;
int cas,cass;
LL n,m,lll,ans;

int main()
{
#ifndef ONLINE_JUDGEW
//	freopen("1.txt","r",stdin);
//	freopen("2.txt","w",stdout);
#endif
int i,j,k;
int x,y,z;
//	init();
//	for(scanf("%d",&cass);cass;cass--)
for(scanf("%d",&cas),cass=1;cass<=cas;cass++)
//	while(~scanf("%s",s))
//	while(~scanf("%d%d",&n,&m))
{
printf("Case #%d:\n",cass);
scanf("%lld%lld",&n,&m);
if(n==m)printf("%d\n%lld %lld\n",1,n,m);
else printf("%d\n%lld %lld\n%lld %lld\n",2,n,m,m,n);
}
return 0;
}
/*
//

//
*/