二分贪心 D
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题目:
The SUM problem can be formulated as follows: given four lists A, B, C, D of integer values, compute how many quadruplet (a, b, c, d ) ∈ A x B x C x D are such that a + b + c + d = 0 . In the following, we assume that all lists have the same size n .
Input
The first line of the input file contains the size of the lists n (this value can be as large as 4000). We then have n lines containing four integer values (with absolute value as large as 228 ) that belong respectively to A, B, C and D .
Output
For each input file, your program has to write the number quadruplets whose sum is zero.
Sample Input
6-45 22 42 -16-41 -27 56 30-36 53 -37 77-36 30 -75 -4626 -38 -10 62-32 -54 -6 45
Sample Output
5
Hint
Sample Explanation: Indeed, the sum of the five following quadruplets is zero: (-45, -27, 42, 30), (26, 30, -10, -46), (-32, 22, 56, -46),(-32, 30, -75, 77), (-32, -54, 56, 30).
分析:
在a,b,c,d四组中分别找出四个数相加,找出相加为0的个数简单的用回溯会超时,可以先把这四组变成两组,再用二分
代码:
#include<iostream>
#include<iomanip>
#include<algorithm>
#include<stdio.h>
using namespace std;
long long int a[4005],b[4005],c[4005],d[4005],h[16000005],f[16000005];
int sum=0,n;
void vp(int k)
{
int l,mid,r,x1,x2;
long long int x;
l=0;
r=n*n-1;
x=-1*h[k];
while(l<=r)
{
mid=(l+r)/2;
if(f[mid]<x)
l=mid+1;
else
if(f[mid]>x)
r=mid-1;
else
{ x1=x2=mid;
while(f[x1]==x&&x1>=0)
{
sum++;
x1--;
}
while(f[x2+1]==x&&x2+1<n*n)
{
sum++;
x2++;
}
r=l-1;
}
}
}
int main()
{
int i,k,j;
scanf("%d",&n);
for(i=0;i<n;i++)
scanf("%lld%lld%lld%lld",&a[i],&b[i],&c[i],&d[i]);
for(i=0;i<n;i++)
for(j=0;j<n;j++)
h[i*n+j]=a[i]+b[j];
for(i=0;i<n;i++)
for(j=0;j<n;j++)
f[i*n+j]=c[i]+d[j];
sort(h,h+n*n);
sort(f,f+n*n);
for(i=0;i<n*n;i++)
vp(i);
printf("%d\n",sum);
}
#include<iomanip>
#include<algorithm>
#include<stdio.h>
using namespace std;
long long int a[4005],b[4005],c[4005],d[4005],h[16000005],f[16000005];
int sum=0,n;
void vp(int k)
{
int l,mid,r,x1,x2;
long long int x;
l=0;
r=n*n-1;
x=-1*h[k];
while(l<=r)
{
mid=(l+r)/2;
if(f[mid]<x)
l=mid+1;
else
if(f[mid]>x)
r=mid-1;
else
{ x1=x2=mid;
while(f[x1]==x&&x1>=0)
{
sum++;
x1--;
}
while(f[x2+1]==x&&x2+1<n*n)
{
sum++;
x2++;
}
r=l-1;
}
}
}
int main()
{
int i,k,j;
scanf("%d",&n);
for(i=0;i<n;i++)
scanf("%lld%lld%lld%lld",&a[i],&b[i],&c[i],&d[i]);
for(i=0;i<n;i++)
for(j=0;j<n;j++)
h[i*n+j]=a[i]+b[j];
for(i=0;i<n;i++)
for(j=0;j<n;j++)
f[i*n+j]=c[i]+d[j];
sort(h,h+n*n);
sort(f,f+n*n);
for(i=0;i<n*n;i++)
vp(i);
printf("%d\n",sum);
}
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