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149. Max Points on a Line

Description

Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane, return the maximum number of points that lie on the same straight line.

 

Example 1:

Input: points = [[1,1],[2,2],[3,3]]
Output: 3

Example 2:

Input: points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
Output: 4

 

Constraints:

  • 1 <= points.length <= 300
  • points[i].length == 2
  • -104 <= xi, yi <= 104
  • All the points are unique.

Solutions

Solution 1

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class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        n = len(points)
        ans = 1
        for i in range(n):
            x1, y1 = points[i]
            for j in range(i + 1, n):
                x2, y2 = points[j]
                cnt = 2
                for k in range(j + 1, n):
                    x3, y3 = points[k]
                    a = (y2 - y1) * (x3 - x1)
                    b = (y3 - y1) * (x2 - x1)
                    cnt += a == b
                ans = max(ans, cnt)
        return ans

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class Solution {
    public int maxPoints(int[][] points) {
        int n = points.length;
        int ans = 1;
        for (int i = 0; i < n; ++i) {
            int x1 = points[i][0], y1 = points[i][1];
            for (int j = i + 1; j < n; ++j) {
                int x2 = points[j][0], y2 = points[j][1];
                int cnt = 2;
                for (int k = j + 1; k < n; ++k) {
                    int x3 = points[k][0], y3 = points[k][1];
                    int a = (y2 - y1) * (x3 - x1);
                    int b = (y3 - y1) * (x2 - x1);
                    if (a == b) {
                        ++cnt;
                    }
                }
                ans = Math.max(ans, cnt);
            }
        }
        return ans;
    }
}

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class Solution {
public:
    int maxPoints(vector<vector<int>>& points) {
        int n = points.size();
        int ans = 1;
        for (int i = 0; i < n; ++i) {
            int x1 = points[i][0], y1 = points[i][1];
            for (int j = i + 1; j < n; ++j) {
                int x2 = points[j][0], y2 = points[j][1];
                int cnt = 2;
                for (int k = j + 1; k < n; ++k) {
                    int x3 = points[k][0], y3 = points[k][1];
                    int a = (y2 - y1) * (x3 - x1);
                    int b = (y3 - y1) * (x2 - x1);
                    cnt += a == b;
                }
                ans = max(ans, cnt);
            }
        }
        return ans;
    }
};

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func maxPoints(points [][]int) int {
    n := len(points)
    ans := 1
    for i := 0; i < n; i++ {
        x1, y1 := points[i][0], points[i][1]
        for j := i + 1; j < n; j++ {
            x2, y2 := points[j][0], points[j][1]
            cnt := 2
            for k := j + 1; k < n; k++ {
                x3, y3 := points[k][0], points[k][1]
                a := (y2 - y1) * (x3 - x1)
                b := (y3 - y1) * (x2 - x1)
                if a == b {
                    cnt++
                }
            }
            if ans < cnt {
                ans = cnt
            }
        }
    }
    return ans
}

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public class Solution {
    public int MaxPoints(int[][] points) {
        int n = points.Length;
        int ans = 1;
        for (int i = 0; i < n; ++i) {
            int x1 = points[i][0], y1 = points[i][1];
            for (int j = i + 1; j < n; ++j) {
                int x2 = points[j][0], y2 = points[j][1];
                int cnt = 2;
                for (int k = j + 1; k < n; ++k) {
                    int x3 = points[k][0], y3 = points[k][1];
                    int a = (y2 - y1) * (x3 - x1);
                    int b = (y3 - y1) * (x2 - x1);
                    if (a == b) {
                        ++cnt;
                    }
                }
                if (ans < cnt) {
                    ans = cnt;
                }
            }
        }
        return ans;
    }
}

Solution 2

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class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        def gcd(a, b):
            return a if b == 0 else gcd(b, a % b)

        n = len(points)
        ans = 1
        for i in range(n):
            x1, y1 = points[i]
            cnt = Counter()
            for j in range(i + 1, n):
                x2, y2 = points[j]
                dx, dy = x2 - x1, y2 - y1
                g = gcd(dx, dy)
                k = (dx // g, dy // g)
                cnt[k] += 1
                ans = max(ans, cnt[k] + 1)
        return ans

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class Solution {
    public int maxPoints(int[][] points) {
        int n = points.length;
        int ans = 1;
        for (int i = 0; i < n; ++i) {
            int x1 = points[i][0], y1 = points[i][1];
            Map<String, Integer> cnt = new HashMap<>();
            for (int j = i + 1; j < n; ++j) {
                int x2 = points[j][0], y2 = points[j][1];
                int dx = x2 - x1, dy = y2 - y1;
                int g = gcd(dx, dy);
                String k = (dx / g) + "." + (dy / g);
                cnt.put(k, cnt.getOrDefault(k, 0) + 1);
                ans = Math.max(ans, cnt.get(k) + 1);
            }
        }
        return ans;
    }

    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
}

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class Solution {
public:
    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
    int maxPoints(vector<vector<int>>& points) {
        int n = points.size();
        int ans = 1;
        for (int i = 0; i < n; ++i) {
            int x1 = points[i][0], y1 = points[i][1];
            unordered_map<string, int> cnt;
            for (int j = i + 1; j < n; ++j) {
                int x2 = points[j][0], y2 = points[j][1];
                int dx = x2 - x1, dy = y2 - y1;
                int g = gcd(dx, dy);
                string k = to_string(dx / g) + "." + to_string(dy / g);
                cnt[k]++;
                ans = max(ans, cnt[k] + 1);
            }
        }
        return ans;
    }
};

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func maxPoints(points [][]int) int {
    n := len(points)
    ans := 1
    type pair struct{ x, y int }
    for i := 0; i < n; i++ {
        x1, y1 := points[i][0], points[i][1]
        cnt := map[pair]int{}
        for j := i + 1; j < n; j++ {
            x2, y2 := points[j][0], points[j][1]
            dx, dy := x2-x1, y2-y1
            g := gcd(dx, dy)
            k := pair{dx / g, dy / g}
            cnt[k]++
            if ans < cnt[k]+1 {
                ans = cnt[k] + 1
            }
        }
    }
    return ans
}

func gcd(a, b int) int {
    if b == 0 {
        return a
    }
    return gcd(b, a%b)
}

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