1046 Shortest Distance (20 分)
The task is really simple: given N exits on a highway which forms a simple cycle, you are supposed to tell the shortest distance between any pair of exits.
Input Specification:
Each input file contains one test case. For each case, the first line contains an integer N (in [3,105]), followed by N integer distances D1 D2 ⋯ DN, where Di is the distance between the i-th and the (i+1)-st exits, and DN is between the N-th and the 1st exits. All the numbers in a line are separated by a space. The second line gives a positive integer M (≤104), with M lines follow, each contains a pair of exit numbers, provided that the exits are numbered from 1 to N. It is guaranteed that the total round trip distance is no more than 107.
Output Specification:
For each test case, print your results in M lines, each contains the shortest distance between the corresponding given pair of exits.
Sample Input:
5 1 2 4 14 9
3
1 3
2 5
4 1
Sample Output:
3
10
7
Analysis:
use the prefix sum to calculate the distance (d1) between a and b(a<b).the answer is the minimum between d1 and sum-d1(sum is the circular distance).
C++:
#include<stdio.h>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<queue>
#include<set>
#include<math.h>
#include<string.h>
#include<algorithm>
using namespace std;
int main()
{
int n,sum=0;
cin>>n;
int d[n+1];
d[n]=0;
for(int i=0;i<n;i++){
cin>>d[i];
sum+=d[i];// circular distance
}
for(int i=1;i<n;i++){
d[i]=d[i]+d[i-1];//prefix sum
}
int m;
cin>>m;
for(int j=0;j<m;j++){
int a,b,dis1=0,dis2=0;
cin>>a>>b;
a--;b--;
if(a>b){//ensure a<b
int temp=b;
b=a;
a=temp;
}
dis1=d[b-1]-d[a-1>=0?a-1:n];//if a-1<0,dis=d[b-1]-0;
int num=min(dis1,sum-dis1);
cout<<num<<endl;
}
return 0;
}