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Task/Closest-pair-problem/MATLAB/closest-pair-problem-1.m

@@ -0,0 +1,71 @@
+function [closest,closestpair] = closestPair(xP,yP)
+
+    N = numel(xP);
+
+    if(N <= 3)
+
+        %Brute force closestpair
+        if(N < 2)
+            closest = +Inf;
+            closestpair = {};
+        else
+            closest = norm(xP{1}-xP{2});
+            closestpair = {xP{1},xP{2}};
+
+            for i = ( 1:N-1 )
+                for j = ( (i+1):N )
+                    if ( norm(xP{i} - xP{j}) < closest )
+                        closest = norm(xP{i}-xP{j});
+                        closestpair = {xP{i},xP{j}};
+                    end %if
+                end %for
+            end %for
+        end %if (N < 2)
+    else
+
+        halfN = ceil(N/2);
+
+        xL = { xP{1:halfN} };
+        xR = { xP{halfN+1:N} };
+        xm = xP{halfN}(1);
+
+        %cellfun( @(p)le(p(1),xm),yP ) is the same as { p ∈ yP : px ≤ xm }
+        yLIndicies = cellfun( @(p)le(p(1),xm),yP );
+
+        yL = { yP{yLIndicies} };
+        yR = { yP{~yLIndicies} };
+
+        [dL,pairL] = closestPair(xL,yL);
+        [dR,pairR] = closestPair(xR,yR);
+
+        if dL < dR
+            dmin = dL;
+            pairMin = pairL;
+        else
+            dmin = dR;
+            pairMin = pairR;
+        end
+
+        %cellfun( @(p)lt(norm(xm-p(1)),dmin),yP ) is the same as
+        %{ p ∈ yP : |xm - px| < dmin }
+        yS = {yP{ cellfun( @(p)lt(norm(xm-p(1)),dmin),yP ) }};
+        nS = numel(yS);
+
+        closest = dmin;
+        closestpair = pairMin;
+
+        for i = (1:nS-1)
+            k = i+1;
+
+            while( (k<=nS) && (yS{k}(2)-yS{i}(2) < dmin) )
+
+                if norm(yS{k}-yS{i}) < closest
+                    closest = norm(yS{k}-yS{i});
+                    closestpair = {yS{k},yS{i}};
+                end
+
+                k = k+1;
+            end %while
+        end %for
+    end %if (N <= 3)
+end %closestPair

Task/Closest-pair-problem/MATLAB/closest-pair-problem-2.m

@@ -0,0 +1,10 @@
+[distance,pair]=closestPair({[0 -.3],[1 1],[1.5 2],[2 2],[3 3]},{[0 -.3],[1 1],[1.5 2],[2 2],[3 3]})
+
+distance =
+
+   0.500000000000000
+
+
+pair =
+
+    [1x2 double]    [1x2 double] %The pair is [1.5 2] and [2 2] which is correct