**Points on a Line- Amazon Top Interview Questions**

### Problem Statement :

You are given a two-dimensional list of integers coordinates. Each list contains two integers [x, y] representing a point on the Cartesian plane. Return the maximum number of points that lie on some line. Constraints n ≤ 1,000 where n is the length of coordinates Example 1 Input coordinates = [ [5, 1], [7, 2], [9, 3], [0, 0], [1, 1], [5, 5], [6, 6] ] Output 4 Explanation The points [[0, 0], [1, 1], [5, 5], [6, 6]] all fall in a line.

### Solution :

` ````
Solution in C++ :
int solve(vector<vector<int>>& p) {
int global_max = 0, n = p.size();
unordered_map<double, int> slope_map;
for (int i = 0; i < n; i++) {
slope_map.clear();
int x1 = p[i][0], y1 = p[i][1];
int isSamePoint = 0, local_max = 0;
for (int j = 0; j < n; j++) {
int x2 = p[j][0], y2 = p[j][1];
if (x1 == x2 and y1 == y2)
isSamePoint++;
else {
double slope = (1.0 * (y1 - y2)) / (x2 - x1);
slope_map[slope]++;
}
}
for (auto& [x, y] : slope_map) local_max = max(local_max, y);
global_max = max(global_max, local_max + isSamePoint);
}
return global_max;
}
```

` ````
Solution in Java :
import java.util.*;
class Solution {
public int solve(int[][] points) {
int n = points.length;
if (n == 0)
return 0;
int ans = 1;
for (int i = 0; i < n; i++) {
var map = new HashMap<Double, Integer>();
for (int j = 0; j < n; j++) {
if (j == i)
continue;
double slope =
((double) points[j][1] - points[i][1]) / (points[j][0] - points[i][0]);
int count = map.getOrDefault(slope, 0);
map.put(slope, count + 1);
ans = Math.max(ans, count + 2);
}
}
return ans;
}
}
```

` ````
Solution in Python :
class Solution:
def solve(self, coordinates):
if not coordinates:
return 0
if len(coordinates) <= 2:
return len(coordinates)
max_line = 0
seen = set()
for i, p1 in enumerate(coordinates):
max_count = float("-inf")
slope_counter = collections.Counter()
for j, p2 in enumerate(coordinates):
if i == j:
continue
x1, y1 = p1
x2, y2 = p2
try:
slope = (y2 - y1) / (x2 - x1)
except:
slope = float("inf")
slope_counter[slope] += 1
if slope_counter[slope] > max_count:
max_count = slope_counter[slope]
max_line = max(max_line, max_count + 1)
return max_line
```

## View More Similar Problems

## No Prefix Set

There is a given list of strings where each string contains only lowercase letters from a - j, inclusive. The set of strings is said to be a GOOD SET if no string is a prefix of another string. In this case, print GOOD SET. Otherwise, print BAD SET on the first line followed by the string being checked. Note If two strings are identical, they are prefixes of each other. Function Descriptio

View Solution →## Cube Summation

You are given a 3-D Matrix in which each block contains 0 initially. The first block is defined by the coordinate (1,1,1) and the last block is defined by the coordinate (N,N,N). There are two types of queries. UPDATE x y z W updates the value of block (x,y,z) to W. QUERY x1 y1 z1 x2 y2 z2 calculates the sum of the value of blocks whose x coordinate is between x1 and x2 (inclusive), y coor

View Solution →## Direct Connections

Enter-View ( EV ) is a linear, street-like country. By linear, we mean all the cities of the country are placed on a single straight line - the x -axis. Thus every city's position can be defined by a single coordinate, xi, the distance from the left borderline of the country. You can treat all cities as single points. Unfortunately, the dictator of telecommunication of EV (Mr. S. Treat Jr.) do

View Solution →## Subsequence Weighting

A subsequence of a sequence is a sequence which is obtained by deleting zero or more elements from the sequence. You are given a sequence A in which every element is a pair of integers i.e A = [(a1, w1), (a2, w2),..., (aN, wN)]. For a subseqence B = [(b1, v1), (b2, v2), ...., (bM, vM)] of the given sequence : We call it increasing if for every i (1 <= i < M ) , bi < bi+1. Weight(B) =

View Solution →## Kindergarten Adventures

Meera teaches a class of n students, and every day in her classroom is an adventure. Today is drawing day! The students are sitting around a round table, and they are numbered from 1 to n in the clockwise direction. This means that the students are numbered 1, 2, 3, . . . , n-1, n, and students 1 and n are sitting next to each other. After letting the students draw for a certain period of ti

View Solution →## Mr. X and His Shots

A cricket match is going to be held. The field is represented by a 1D plane. A cricketer, Mr. X has N favorite shots. Each shot has a particular range. The range of the ith shot is from Ai to Bi. That means his favorite shot can be anywhere in this range. Each player on the opposite team can field only in a particular range. Player i can field from Ci to Di. You are given the N favorite shots of M

View Solution →