feat(cpp): add maximum_collinear_points.cpp

Author: ongshunping

cpp/Math and Geometry/maximum_collinear_points.cpp

@@ -0,0 +1,47 @@
+#include <vector>
+#include <map>
+#include <utility>
+#include <algorithm>
+#include <numeric> 
+
+int maximumCollinearPoints(std::vector<std::vector<int>>& points) {
+    int res = 0;
+    // Treat each point as a focal point, and determine the maximum
+    // number of points that are collinear with each focal point. The
+    // largest of these maximums is the answer.
+    for (int i = 0; i < points.size(); i++) {
+        res = std::max(res, maxPointsFromFocalPoint(i, points));
+    }
+    return res;
+}
+
+int maxPointsFromFocalPoint(int focalPointIndex, std::vector<std::vector<int>>& points) {
+    std::map<std::pair<int, int>, int> slopesMap;
+    int maxPoints = 0;
+    // For the current focal point, calculate the slope between it and
+    // every other point. This allows us to group points that share the
+    // same slope.
+    for (int j = 0; j < points.size(); j++) {
+        if (j != focalPointIndex) {
+            std::pair<int, int> currSlope = getSlope(points[focalPointIndex], points[j]);
+            slopesMap[currSlope]++;
+            // Update the maximum count of collinear points for the
+            // current focal point.
+            maxPoints = std::max(maxPoints, slopesMap[currSlope]);
+        }
+    }
+    // Add 1 to the maximum count to include the focal point itself.
+    return maxPoints + 1;
+}
+
+std::pair<int, int> getSlope(std::vector<int>& p1, std::vector<int>& p2) {
+    int rise = p2[1] - p1[1];
+    int run = p2[0] - p1[0];
+    // Handle vertical lines separately to avoid dividing by 0.
+    if (run == 0) {
+        return {1, 0};
+    }
+    // Simplify the slope to its reduced form.
+    int gcdVal = std::gcd(rise, run);
+    return {rise / gcdVal, run / gcdVal};
+}