Create 3710. Maximum Partition Factor (#908)

Author: Chayandas07

3710_Maximu_partition_factor.cpp

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+/**
+ * LeetCode Biweekly Contest Problem - LC 3710
+ * 
+ * Problem Statement (inferred from code):
+ * Given a set of points, partition them into at most 2 groups such that 
+ * within each group, any pair of points has a Manhattan distance ≥ D, 
+ * and both groups are bipartite (no odd-length cycles).
+ *
+ * Goal: Find the **maximum possible D** such that the above condition holds.
+ *
+ * Approach:
+ * - Binary search on distance D.
+ * - For each candidate D, create an undirected graph where an edge exists 
+ *   between two points if their distance is **less than D**.
+ * - If this graph is **bipartite**, it's a valid partition for D.
+ * - Return the largest D that satisfies this.
+ */
+
+ typedef long long ll;
+
+class dsu {
+public:
+    ll n;
+    vector<ll> par;
+    vector<vector<ll>> gd;
+
+    // Constructor to initialize DSU with N nodes
+    dsu(ll N) {
+        n = N;
+        par.resize(N, 0);
+        gd.resize(N);
+        for (ll i = 0; i < n; i++) {
+            par[i] = i;       // Each node is its own parent
+            gd[i].push_back(i); // Each group starts with one element
+        }
+    }
+
+    // Find with path compression
+    ll find(ll u) {
+        if (par[u] != u)
+            return par[u] = find(par[u]);
+        return u;
+    }
+
+    // Union two sets
+    void comb(ll u, ll v) {
+        ll ru = find(u), rv = find(v);
+        if (ru != rv) {
+            par[rv] = ru;
+            gd[ru].push_back(rv); // Merge group
+        }
+    }
+
+    // Check if number of disjoint sets is at most 2
+    bool f() {
+        vector<ll> vis(n, 0);
+        ll ct = 0;
+        for (ll i = 0; i < n; i++) {
+            ll ri = find(i);
+            if (vis[ri]) continue;
+            vis[ri] = 1;
+            ct++;
+        }
+        return ct <= 2;
+    }
+};
+#include<bits/stdc++.h>
+using namespace std;
+class Solution {
+public:
+    // Check if the undirected graph is bipartite
+    bool isBipartite(const std::vector<std::vector<ll>>& adj, ll N) {
+        std::vector<int> c(N, 0);  // Color array: 0 = unvisited, 1 or 2 = color
+
+        for (ll i = 0; i < N; ++i) {
+            if (c[i] != 0) continue;
+
+            std::queue<ll> q;
+            q.push(i);
+            c[i] = 1;  // Start coloring with 1
+
+            while (!q.empty()) {
+                ll u = q.front();
+                q.pop();
+
+                for (ll v : adj[u]) {
+                    if (c[v] == 0) {
+                        c[v] = 3 - c[u];  // Alternate color
+                        q.push(v);
+                    } else if (c[v] == c[u]) {
+                        return false; // Same color on both ends — not bipartite
+                    }
+                }
+            }
+        }
+        return true;
+    }
+
+    // Check if it's possible to partition at distance ≥ dist
+    bool ispos(vector<vector<ll>>& adj, ll& dist, ll& N) {
+        vector<vector<ll>> edges(N);
+
+        // Build graph: edge if distance < dist
+        for (ll i = 0; i < N; i++) {
+            for (int j = i + 1; j < N; j++) {
+                if (adj[j][i] < dist) {
+                    edges[i].push_back(j);
+                    edges[j].push_back(i);
+                }
+            }
+        }
+
+        // Check if the graph is bipartite
+        return isBipartite(edges, N);
+    }
+
+    // Manhattan distance between two points
+    ll g(vector<int>& p1, vector<int>& p2) {
+        return abs(p1[0] - p2[0]) + abs(p1[1] - p2[1]);
+    }
+
+    int maxPartitionFactor(vector<vector<int>>& pts) {
+        ll n = pts.size();
+        if (n <= 2) return 0ll;
+
+        vector<vector<ll>> adj(n, vector<ll>(n, LLONG_MAX));
+        ll MX = 1;
+
+        // Precompute all pairwise Manhattan distances
+        for (int i = 0; i < n; i++) {
+            for (int j = i + 1; j < n; j++) {
+                ll MD = g(pts[i], pts[j]);
+                adj[i][j] = adj[j][i] = MD;
+                MX = max(MD, MX);  // Track max distance
+            }
+        }
+
+        // Binary search over possible D
+        ll lo = 0, hi = MX;
+        while (lo < hi) {
+            ll mid = (lo + hi + 1) / 2;
+            if (ispos(adj, mid, n)) {
+                lo = mid;  // Valid partition, try higher
+            } else {
+                hi = mid - 1;  // Invalid, reduce D
+            }
+        }
+
+        return hi;
+    }
+};