面试经典150题 P149 直线上最多的点数

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时间轴

时间轴

2025-11-26

init

数学

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题目：

P149 直线上最多的点数

https://leetcode.cn/problems/max-points-on-a-line/description/?envType=study-plan-v2&envId=top-interview-150

暴力枚举,注意比较两个浮点数a,b时用fabs(a-b)<= EPS来判断是否相等

#include <cfloat>
#include <cmath>
#include <vector>
using std::vector;

struct Line {
    double k;
    double b;
    bool is_vertical;
};

class Solution {
public:
    int maxPoints(vector<vector<int>>& points) {
        int n = points.size();
        if (n == 0) return 0;
        if (n == 1) return 1;

        const double EPS = 1e-9;
        vector<Line> lines;

        // 枚举两两点得到直线
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                double k, b;
                bool is_vertical;
                if (points[i][0] == points[j][0]) {
                    // 垂直线
                    is_vertical = true;
                    k = DBL_MAX;
                    b = points[i][0]; // x = b
                } else {
                    // 非垂直线
                    is_vertical = false;
                    k = (double)(points[j][1] - points[i][1]) / (points[j][0] - points[i][0]);
                    b = points[j][1] - k * points[j][0]; // y = kx + b
                }
                lines.push_back({k, b, is_vertical});
            }
        }

        int max_count = 0;

        // 遍历每条直线，统计点数
        for (const Line& line : lines) {
            int cnt = 0;
            for (const auto& point : points) {
                int x = point[0], y = point[1];
                if (line.is_vertical) {
                    if (fabs(x - line.b) < EPS) cnt++;
                } else {
                    if (fabs(y - (line.k * x + line.b)) < EPS) cnt++;
                }
            }
            if (cnt > max_count) max_count = cnt;
        }

        return max_count;
    }
};