Solved problem 265D from codeforces

Author: AliOsm

CodeForces/265D. Good Sequences.cpp

@@ -0,0 +1,64 @@
+/*
+  Idea:
+    - Dynamic programming with Prime factorization.
+    - Any two numbers share at least one prime factor, then the GCD between them
+      not equal to 1.
+    - Based on the previous point we can start a DP from each index and try
+      to add a new number to the sequence based on the prime factorization of the 
+      current number.
+*/
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int const N = 1e5 + 1;
+int n, a[N], dp[N];
+vector<vector<int> > g, d;
+
+int rec(int idx) {
+  if(idx == n)
+  	return 0;
+
+  int &ret = dp[idx];
+  if(ret != -1)
+  	return ret;
+  ret = 0;
+
+  for(int i = 0, cur; i < d[idx].size(); ++i) {
+  	cur = upper_bound(g[d[idx][i]].begin(), g[d[idx][i]].end(), idx) - g[d[idx][i]].begin();
+  	if(cur != g[d[idx][i]].size())
+  		ret = max(ret, rec(g[d[idx][i]][cur]) + 1);
+  }
+
+  return ret;
+}
+
+int main() {
+	g.resize(N);
+	d.resize(N);
+
+  scanf("%d", &n);
+  for(int i = 0; i < n; ++i) {
+    scanf("%d", a + i);
+
+    int x = a[i], sqrtx = sqrt(x);
+    for(int j = 2, fr; j <= sqrtx; ++j) {
+    	fr = 0;
+    	while(x % j == 0)
+    		++fr, x /= j;
+    	if(fr != 0)
+    		g[j].push_back(i), d[i].push_back(j);
+    }
+    if(x != 1)
+    	g[x].push_back(i), d[i].push_back(x);
+  }
+
+  memset(dp, -1, sizeof dp);
+  int res = 0;
+  for(int i = 0; i < n; ++i)
+    res = max(res, rec(i) + 1);
+  printf("%d\n", res);
+
+  return 0;
+}

CodeForces/README.md

@@ -97,6 +97,7 @@
 - [262A. Roma and Lucky Numbers](http://codeforces.com/problemset/problem/262/A)
 - [263A. Beautiful Matrix](http://codeforces.com/problemset/problem/263/A)
 - [263D. Cycle in Graph](http://codeforces.com/contest/263/problem/D)
+- [265D. Good Sequences](http://codeforces.com/contest/265/problem/D)
 - [266A. Stones on the Table](http://codeforces.com/problemset/problem/266/A)
 - [266B. Queue at the School](http://codeforces.com/problemset/problem/266/B)
 - [268A. Games](http://codeforces.com/problemset/problem/268/A)