按点与参考点的距离对点数组进行排序

给定一个包含N个点和一个参考点P的数组 arr[] ，任务是根据它们与给定点P的距离对这些点进行排序。

例子：

Input: arr[] = {{5, 0}, {4, 0}, {3, 0}, {2, 0}, {1, 0}}, P = (0, 0) 
Output: (1, 0) (2, 0) (3, 0) (4, 0) (5, 0) 
Explanation: 
Distance between (0, 0) and (1, 0) = 1 
Distance between (0, 0) and (2, 0) = 2 
Distance between (0, 0) and (3, 0) = 3 
Distance between (0, 0) and (4, 0) = 4 
Distance between (0, 0) and (5, 0) = 5 

Hence, the sorted array of points will be: {(1, 0) (2, 0) (3, 0) (4, 0) (5, 0)}
Input: arr[] = {{5, 0}, {0, 4}, {0, 3}, {2, 0}, {1, 0}}, P = (0, 0) 
Output: (1, 0) (2, 0) (0, 3) (0, 4) (5, 0) 
Explanation: 
Distance between (0, 0) and (1, 0) = 1 
Distance between (0, 0) and (2, 0) = 2 
Distance between (0, 0) and (0, 3) = 3 
Distance between (0, 0) and (0, 4) = 4 
Distance between (0, 0) and (5, 0) = 5 
Hence, the sorted array of points will be: {(1, 0) (2, 0) (0, 3) (0, 4) (5, 0)}

方法：思想是将距离给定点P的每个元素成对存储，然后根据存储的距离对向量的所有元素进行排序。

• 对于每个给定的点：
  • 求该点到参考点 P 的距离公式如下：

距离 = $\sqrt{(p2-x1)^{2} + (p2-y1)^{2}}$

• 在数组中追加距离
• 对距离数组进行排序并根据排序后的距离打印点。
  • 时间复杂度：与上述方法一样，对长度为 N 的数组进行排序，在最坏的情况下需要 O(N*logN) 时间。因此，时间复杂度将为O(N*log N) 。
  • 辅助空间复杂度：与上述方法一样，有额外的空间用于将距离和点存储为成对。因此，辅助空间复杂度将为O(N) 。

Javascript

// Javascript program
 
function sortFunction(a, b) {
    if (a[0] === b[0]) {
        return 0;
    }
    else {
        return (a[0] < b[0]) ? -1 : 1;
    }
}
 
// Function to sort the array of
// points by its distance from P
function sortArr(arr, n, p)
{
    // Vector to store the distance
    // with respective elements
     
    var vp = new Array(n);
    // Storing the distance with its
    // distance in the vector array
    for (var i = 0; i < n; i++) {
   
        var dist = Math.pow((p[0] - arr[i][0]), 2)
              + Math.pow((p[1] - arr[i][1]), 2);
        vp[i] = [dist, [arr[i][0], arr[i][1]]];
    }
     
    // Sorting the array with
    // respect to its distance
    vp.sort(sortFunction);
   
    // Output
    for (var i = 0; i < n; i++) {
        document.write("(" + vp[i][1][0] + ", " + vp[i][1][1] + ") ");
    }
}
 
var arr = [[ 5, 5 ], [ 6, 6 ], [ 1, 0], [ 2, 0 ], [ 3, 1 ], [ 1, -2 ]];
var n = 6;
var p = [ 0, 0 ];
// Function to perform sorting
sortArr(arr, n, p);