some dp problems

CSES - CSES Problem Set/Sorting_And_Searching/Traffic_Lights.cpp

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+//
+// Created by darian on 07.06.24.
+//
+
+#include <bits/stdc++.h>
+using namespace std;
+using ll = long long;
+
+//MISSING distances[p.second - p.first]--; !!!!!!
+//int main() {
+//    ll x; cin >> x;
+//    int n; cin >> n;
+//    map<ll, int> distances;
+//    distances[x] = 1;
+//    set<pair<ll, ll>> lines = {{0, x}};
+//
+//    for (int i{}; i < n; i++) {
+//        ll t; cin >> t;
+//        auto it = lines.lower_bound({t, t});
+//        --it;
+//        auto p = *it;
+//        lines.erase(p);
+//        lines.insert({p.first, t});
+//        lines.insert({t, p.second});
+//        distances[p.second - p.first]--;
+//        if (distances[p.second - p.first] == 0) distances.erase(p.second - p.first);
+//        distances[t - p.first]++;
+//        distances[p.second - t]++;
+//        cout << (*distances.rbegin()).first << endl;
+//    }
+//}
+//
+
+//slightly inspirated from usaco
+int main() {
+    ll x; cin >> x;
+    int n; cin >> n;
+
+    set<ll> lights{0, x};
+    map<ll, int> dist{{x, 1}};
+
+    for (int i{}; i < n; i++) {
+        ll a; cin >> a;
+        auto it = lights.upper_bound(a);
+        auto it2 = it;
+        it2--;
+
+        dist[a - *it2]++;
+        dist[*it - a]++;
+        dist[*it - *it2]--;
+        if (!dist[*it - *it2]) {
+            dist.erase(*it - *it2);
+        }
+        lights.insert(a);
+        cout << (*dist.rbegin()).first << endl;
+    }
+}
+
+
+//faster solution from usaco
+//#include <algorithm>
+//#include <iostream>
+//#include <vector>
+//
+//using std::cout;
+//using std::endl;
+//using std::vector;
+//
+//int main() {
+//    int street_len;
+//    int light_num;
+//    std::cin >> street_len >> light_num;
+//    vector<int> lights(light_num);
+//    for (int &l : lights) { std::cin >> l; }
+//
+//    vector<std::pair<int, int>> sorted_lights(light_num);
+//    for (int l = 0; l < light_num; l++) { sorted_lights[l] = {lights[l], l}; }
+//    std::sort(sorted_lights.begin(), sorted_lights.end());
+//
+//    // Given the light position, this array stores its position in
+//    // sorted_lights.
+//    vector<int> new_pos(light_num);
+//    for (int l = 0; l < light_num; l++) {
+//        new_pos[sorted_lights[l].second] = l;
+//    }
+//
+//    struct Light {
+//        int prev, next;
+//        int pos;
+//    };
+//    vector<Light> light_ll(light_num + 2);
+//    // First, we set our "lights" on the edges of the street.
+//    light_ll[0] = {-1, 1, 0};
+//    light_ll[light_num + 1] = {light_num, -1, street_len};
+//    for (int l = 0; l < light_num; l++) {
+//        light_ll[l + 1] = {l, l + 2, sorted_lights[l].first};
+//    }
+//
+//    // Find the longest passage once all the streetlights are added
+//    vector<int> gaps(light_num);
+//    int max_gap = 0;
+//    for (int l = 0; l <= light_num; l++) {
+//        max_gap = std::max(max_gap, light_ll[l + 1].pos - light_ll[l].pos);
+//    }
+//    gaps.back() = max_gap;
+//
+//    // Remove the streetlights in reverse order like as we did in the above
+//    // solution.
+//    for (int l = light_num - 1; l > 0; l--) {
+//        Light to_del = light_ll[new_pos[l] + 1];
+//        Light &left = light_ll[to_del.prev];
+//        Light &right = light_ll[to_del.next];
+//        // Re-assign the references to the next & previous node
+//        left.next = to_del.next;
+//        right.prev = to_del.prev;
+//
+//        max_gap = std::max(max_gap, right.pos - left.pos);
+//        gaps[l - 1] = max_gap;
+//    }
+//
+//    for (int i = 0; i < gaps.size() - 1; i++) { cout << gaps[i] << ' '; }
+//    cout << gaps.back() << endl;
+//}