2018 Multi-University Training Contest 4 L(Graph Theory Homework)

Problem Description
There is a complete graph containing n vertices, the weight of the i-th vertex is wi.
The length of edge between vertex i and j (i≠j) is ⌊√|wi−wj|⌋.
Calculate the length of the shortest path from 1 to n.

Input
The first line of the input contains an integer T (1≤T≤10) denoting the number of test cases.
Each test case starts with an integer n (1≤n≤105) denoting the number of vertices in the graph.
The second line contains n integers, the i-th integer denotes wi (1≤wi≤105).
 

Output
For each test case, print an integer denoting the length of the shortest path from 1 to n.
 

Sample Input
1
3
1 3 5
 

Sample Output
2
 

题意:给出n个点的完全图,边的权值为两点绝对值之差的开根号,问从1走到n的最短路花费。

思路:容易证明 ⌊√​a​​​⌋+⌊√​b​​​⌋≥⌊√​a+b​​​⌋,进而可以证明边权满足三角不等式,故直接从 1走到 n就是最优的。

const int maxn=100010;
int n,m,k,a[maxn];
int main()
{
    int T;
    scanf("%d",&T);
    while(T--){
        scanf("%d",&n);
        for(int i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
        }
        int k=abs(a[n-1]-a[0]);
        k=sqrt(k);
        printf("%d\n",k);
    }
    return 0;
}

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转载自blog.csdn.net/snayf/article/details/81394184