One, the most recent problem: the two-dimensional or multi-bit space to find the closest point in the distance
1. Steps
A, calculate the distance between each pair of points separately
B. Find the closest pair
(to avoid repeated calculations, consider only those pairs of i<j)
2. JavaScript implementation
1<! DOCTYPE html>234<meta charset= "UTF-8" >5<title> Recent Issues </title>67<body>8 9</body>Ten<script type= "Text/javascript" > One varPoint =function(x, y) { A var_arr =NewArray (); -_arr =[x, y]; -_arr.x =x; the_ARR.Y =y; - return_arr; - } - + varCaculate =function(P1, p2) { - return(p1.x-p2.x) * (p1.x-p2.x) + (P1.Y-P2.Y) * (P1.Y-p2.y); + } A at functionSearch (arr) { - vardis =number.positive_infinity; - varIndexx =NULL; - varIndexy =NULL; - for(vari = 0; i < arr.length-1; i++){ - for(varj = i+1; J < Arr.length; J + +){ in varD =caculate (Arr[i], arr[j]); - if(D <dis) { todis =D; +Indexx =i; -Indexy =J; the } * } $ }Panax Notoginseng return"The distance between the" +indexx+ "point and the" +indexy+ "point is Nearest"; - } the + //Experimental Phase A //Four point coordinates were created (0,0), (2,0), (0,3), (2,1) the varP1 =NewPoint (0,0); + varP2 =NewPoint (2,0); - varP3 =NewPoint (0,3); $ varP4 =NewPoint (2,1); $ Console.log (Search ([P1, P2, p3, P4] ) -</script> -3. Algorithm Analysis
can be used (XI-XJ) 2 + (YI-YJ) 2 instead of sqrt ((XI-XJ) 2 + (YI-YJ) 2), as far as possible to avoid the root; so the basic operation of this algorithm is to calculate the square, the number of executions C (n) =σ[i=1 to N-1]σ[j=i+1 to n] 2 = n ( n-1), belonging to θ (N2)
One, convex hull problem
1, Convex set concept: For a set of points on a plane, if the set of any two points P and Q are not power cut line segments, the collection is convex
2. Convex hull: Convex hull is the smallest convex set containing all points
3. General Judgment method: Judge whether all other points are in the same side of the line connecting P1 and P2
4. General time Efficiency: it belongs to θ (n3); for each n (n-1)/2 of different points, compare the symbols of the other n-2 points
On the algorithm--brute force method--recent pair and convex hull problems
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