Example of BS on real values

Author: shahayushd

Binary Search/1408C- Discrete Acceleration

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+#include <bits/stdc++.h>
+#include <string.h>
+#define int long long
+#define MAX (int)(1e7+5)
+#define MAX2D (int)(1e3+5)
+#define itn int
+#define inf 5e18
+#define MOD (int)(1e9 + 7)
+#define pb push_back
+#define mk make_pair
+#define all(x) x.begin(), x.end()
+#define rall(x) x.rbegin(),x.rend()
+#define pii pair<int, int>
+#define vii vector<pii>
+#define vi vector<int>
+#define vll vector<unsigned int>
+#define test \
+ int t; \
+ cin >> t; \
+ while (t--)
+#define fast \
+ ios_base ::sync_with_stdio(0); \
+ cin.tie(NULL); \
+ cout.tie(NULL)
+using namespace std;
+
+int n,L;
+const int N = 1e5+1;
+vector<double> a(N);
+double eps = 1e-6;
+
+bool good(double m) {
+ double t1 = m, t2 = m;
+ double speed1 = 1, speed2 = 1;
+ double pos1 = 0, pos2 = L;
+ for(int i=1;i<=n+1;i++) {
+ if(speed1*t1*1.0f >= 1.0f*((a[i]-a[i-1]))) pos1 += 1.0f*(a[i]-a[i-1]), t1 -= (1.0f*(a[i]-a[i-1]))/speed1, speed1++;
+ else pos1 += 1.0f*speed1*t1, t1 = 0;
+ t1 = max(t1, (double)0);
+ }
+ for(int i=n;i>=0;i--) {
+ if(speed2*t2*1.0f >= 1.0f*(a[i+1]-a[i])) pos2 -= 1.0f*(a[i+1]-a[i]), t2 -= (1.0f*(a[i+1]-a[i]))/speed2, speed2++;
+ else pos2 -= 1.0f*speed2*t2, t2 = 0;
+ t2 = max(t2, (double)0);
+ }
+ if((pos2-pos1) <= 0.00001) return true;
+ return false;
+}
+
+double f() {
+ double l = 0, r = L;
+ double ans = l;
+ for(int i=0;i<200 && l+eps <= r;i++) {
+ double mid = (l+r)*0.5f;
+ if(good(mid)) ans = mid, r = mid;
+ else l = mid;
+ }
+ return ans;
+}
+signed main()
+{
+ fast;
+ test {
+ cin>>n>>L;
+ a.resize(n+2);
+ for(int i=1;i<=n;i++) cin>>a[i];
+ a[0] = 0, a[n+1] = L; 
+ cout<<fixed<<setprecision(16);
+ cout<<f()<<"\n";
+ }
+ return 0; 
+}