woj1074 數學 技巧 雜題

題意：

在每組輸入數據給出的最多1萬個整數裏面找出三個數A, B, C滿足 C = A + B。
如果能夠找出，輸出滿足次條件的最大的C
否則輸出-1。

解答：

思路很巧妙，特寫題解

暴力n^3必然超時  (3<=n<=10000)

先從小到大排序，然後枚舉C（這裏用a[i]表示），兩個指針j,k分別在開始和結束位置。

如果a[j]+a[k]<a[i]，則表示A + B<C,和需要更大一點，所以j++,往後移動；

同理，如果a[j]+a[k]>a[i]，則表示A + B>C,和需要更小一點，所以k--,往前移動；

否則，找到C = A + B，並繼續尋找最大的C

時間複雜度n^2

參考：felix021的題解

/*
 * Author: NICK WONG
 * Created Time:  2/22/2016 00:21:31
 * File Name: woj1074.cpp
 */
#include<iostream>
#include<sstream>
#include<fstream>
#include<vector>
#include<list>
#include<deque>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cctype>
#include<cmath>
#include<ctime>
#include<iomanip>
using namespace std;
#define out(x) cout<<#x<<": "<<x<<endl
const double eps(1e-8);
const int maxn=10100;
const long long maxint=-1u>>1;
const long long maxlong=maxint*maxint;
typedef long long lint;
int n,a[maxn];

void init()
{
    cin>>n;
    for (int i=1; i<=n; i++)
        cin>>a[i];
}

void work()
{
    int ans=-1;
    sort(a+1,a+n+1);
    bool flag=true;
    for (int i=n; i>=1 && flag; i--)
        for (int j=1,k=n; j<k; )
        {
            if (a[j]+a[k]==a[i])
            {
                ans=max(ans,a[i]);
                flag=false;
                break;
            } else
            if (a[j]+a[k]<a[i])
            {
                j++;
            } else
            {
                k--;   
            }
        }
    cout<<ans<<endl;
}

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        init();
        work();
    }
    return 0;
}

 Problem 1074 - ABC
Time Limit: 1000MS   Memory Limit: 65536KB   Difficulty: 3
Total Submit: 1530  Accepted: 613  Special Judge: No
Description
Given an array consists of n positive integers,your task is to find the largest C which makes C=A+B. A,B,C are all in the given array.
Input
   Standard input will contain multiple test cases. The first line of the input is an integer T (1 <= T <= 20) which is the number of test cases.
   For each test case,there is an integer n (3<=n<=10000) in the first line,indicating the number of elements in the array.The next line contains
n positive integers.You can assume all the integers will be less then 10^9.
Output
   For each test case,if you can find the largest integer C=A+B, output C. Notice, A and B should be different elements in the array.If there isn't
such integer C,output -1 instead.
Sample Input
3
10
1 1 1 4 5 5 6 6 10 9
3
5 5 10
3
1 3 6
Sample Output
10
10
-1
Hint
Optimize your algorithm,make it as fast as possible!
Source
cowork@whu