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Social Distancing.cpp
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Social Distancing.cpp
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// Problem: http://www.usaco.org/index.php?page=viewproblem2&cpid=1038
// Solved on January 24th 2023
#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <math.h>
using namespace std;
int n, m;
pair<long long, long long> intervals[100001];
bool check(long long d) {
long long current = intervals[0].first;
int currentInterval = 0;
for (int i = 1; i < n; i++) {
current += d;
//Incrementing the interval until it reaches the next one
while (currentInterval < m && current > intervals[currentInterval].second) {
currentInterval++;
}
if (currentInterval == m) {
return false;
}
if (intervals[currentInterval].first > current) {
current = intervals[currentInterval].first;
}
}
return true;
}
int main()
{
freopen("socdist.in", "r", stdin);
freopen("socdist.out", "w", stdout);
//Taking in n and m
cin >> n >> m;
//Adding the intervals into the pair variable
for (int i = 0; i < m; i++) {
cin >> intervals[i].first >> intervals[i].second;
}
//Sort the intervals in increasing order
sort(intervals, intervals + m);
//Set the low and high variables
long long low = 1;
long long high = pow(10, 18);
//Using binary search and the check function
while (low + 1 < high) {
long long middle = (low + high) / 2;
if (check(middle)) {
low = middle;
}
else {
high = middle;
}
}
cout << low << endl;
}