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Commit b99d771

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‎SPOJ/COMDIV.cpp

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// Ivan Carvalho
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// Solution to https://www.spoj.com/problems/COMDIV/
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#include <bits/stdc++.h>
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using namespace std;
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const int MAXN = 1e6 + 10;
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int divisors[MAXN];
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int gcd(int x,int y){
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if(x < y) swap(x,y);
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if(y == 0) return x;
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return gcd(y,x%y);
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}
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int main(){
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for(int i = 1;i<MAXN;i++){
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for(int j = i;j<MAXN;j+=i) divisors[j]++;
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}
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int TC;
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scanf("%d",&TC);
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while(TC--){
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int a,b;
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scanf("%d %d",&a,&b);
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printf("%d\n",divisors[gcd(a,b)]);
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}
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return 0;
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}

‎SPOJ/FASTFLOW.cpp

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/*
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Tidal Flow Algorithm by M. Fontaine :
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https://ioinformatics.org/journal/v12_2018_25_41.pdf
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Implementation by I. Carvalho
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Solution to FASTFLOW : https://www.spoj.com/problems/FASTFLOW/
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Note : In this problem, node 1 is the source and node N is the Sink. The
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edges are also bidirectional
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*/
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#include <bits/stdc++.h>
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using namespace std;
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typedef long long ll;
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const int MAXN = 5010;
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const int MAXM = 30010;
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const ll INF = 1e18;
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struct edge{
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int to,rev; // node, index in the other adjacency list
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ll cap; // residual capacity
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};
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vector<edge> adjList[MAXN]; // adjacency list of the edges
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int Ev[MAXM],Ei[MAXM]; // BFS edge list
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int N,M,bfsPtr; // number of nodes
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int dist[MAXN],ok[MAXN];
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ll h[MAXN]; // heuristic of Tidal Flow
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ll p[MAXM]; // promised flow of Tidal Flow
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ll l[MAXN]; // amount of flow in pool of Tidal FLow
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ll TidalFlow(int edgeListSize){
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int source = 1, sink = N;
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fill(h,h+N+1,0); // initializing h[v], for all v
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h[source] = INF; // there is no bound in the flow that can reach
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the source
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for(int i = 0;i<edgeListSize;i++){
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int w = Ev[i]; // where it comes from
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int idx = Ei[i]; // index in the adjList
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int v = adjList[w][idx].to; // where it goes
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p[i] = min(adjList[w][idx].cap,h[w]); // the promised is
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the minimum of the heuristic and the capacity
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h[v] += p[i]; // we add the promised capacity to the
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heuristic
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}
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if(h[sink] == 0) return 0; // if the heuristic for the sink is
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0, then we are done
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fill(l,l+N+1,0); // initializing l[v], for all v
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l[sink] = h[sink]; // the amount of flow is the heuristic in the
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sink, initially
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for(int i = edgeListSize - 1;i>=0;i--){
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int w = Ev[i]; // where it comes from
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int idx = Ei[i]; // index in the adjList
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int v = adjList[w][idx].to; // where it goes
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// the promised is the minimum of the promised before,
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the diference between heuristic and available of the start or the
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available of the end
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p[i] = min(p[i], min(h[w] - l[w],l[v]));
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l[v] -= p[i];
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l[w] += p[i];
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}
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fill(h,h+N+1,0); // h[v] = 0, for all v
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h[source] = l[source]; // the amount of pool is the heuristic
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for(int i = 0;i<edgeListSize;i++){
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int w = Ev[i]; // where it comes from
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int idx = Ei[i]; // index in the adjList
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int v = adjList[w][idx].to; // where it goes
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int rev_idx = adjList[w][idx].rev; // index in the other
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adjList
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p[i] = min(p[i],h[w]);
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h[w] -= p[i];
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h[v] += p[i];
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adjList[w][idx].cap -= p[i]; // we update the residual
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capacity
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adjList[v][rev_idx].cap += p[i]; // update reverse edje
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capacity
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}
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return h[sink];
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}
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int BFS(){
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bfsPtr = 0;
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fill(ok,ok+N+1,0);
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int source = 1,sink = N;
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queue<int> bfs;
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bfs.push(source);
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ok[source] = 1;
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dist[source] = 0;
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while(!bfs.empty()){
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int v = bfs.front();
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bfs.pop();
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for(int i = 0;i<adjList[v].size();i++){
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if(adjList[v][i].cap == 0) continue;
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int u = adjList[v][i].to;
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if(ok[u]){
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if(dist[u] == dist[v] + 1){
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Ev[bfsPtr] = v;
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Ei[bfsPtr] = i;
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bfsPtr++;
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}
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continue;
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}
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ok[u] = 1;
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dist[u] = dist[v] + 1;
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bfs.push(u);
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Ev[bfsPtr] = v;
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Ei[bfsPtr] = i;
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bfsPtr++;
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}
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}
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return bfsPtr;
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}
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ll FordFulkerson(){
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ll flow = 0;
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while(true){
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ll augmenting = TidalFlow(BFS());
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if(augmenting == 0) break;
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else flow += augmenting;
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}
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return flow;
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}
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void addEdge(int u,int v,int cap){
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edge newedge;
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int uPtr = (int)adjList[u].size();
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int vPtr = (int)adjList[v].size();
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newedge.to = v;
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newedge.rev = vPtr;
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newedge.cap = cap;
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adjList[u].push_back(newedge);
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newedge.to = u;
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newedge.rev = uPtr;
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newedge.cap = cap;
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adjList[v].push_back(newedge);
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}
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int main(){
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scanf("%d %d",&N,&M);
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for(int i = 1;i<=M;i++){
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int u,v,w;
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scanf("%d %d %d",&u,&v,&w);
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addEdge(u,v,w);
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}
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printf("%lld\n",FordFulkerson());
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return 0;
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}

‎SPOJ/GCDEX.cpp

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// Ivan Carvalho
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// Solution to https://www.spoj.com/problems/GCDEX/
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#include <bits/stdc++.h>
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using namespace std;
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typedef long long ll;
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const int MAXN = 1e6 + 10;
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ll G[MAXN];
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int isNotPrime[MAXN],phi[MAXN];
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int main(){
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// Initializing
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for(int i = 1;i<MAXN;i++){
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phi[i] = i;
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}
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// Calculating phi
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for(int i = 2;i<MAXN;i++){
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if(isNotPrime[i]) continue;
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phi[i]--;
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for(int j = 2*i;j<MAXN;j+=i){
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phi[j] -= phi[j]/i;
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isNotPrime[j] = 1;
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}
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}
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// Calculating G
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for(int i = 1;i<MAXN;i++){
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for(int j = 2*i;j<MAXN;j+=i){
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G[j] += 1LL*i*phi[j/i];
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}
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}
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for(int i = 2;i<MAXN;i++) G[i] += G[i-1]; // pref sum
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int N;
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while(scanf("%d",&N) && N){
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printf("%lld\n",G[N]);
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}
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return 0;
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}

‎SPOJ/LCMSUM.cpp

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// Ivan Carvalho
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// Solution to https://www.spoj.com/problems/LCMSUM/
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#include <bits/stdc++.h>
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using namespace std;
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typedef long long ll;
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const int MAXN = 1000010;
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ll lcmSum[MAXN],sumOfCoprimes[MAXN];
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ll mobius[MAXN],isNotPrime[MAXN];
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ll fast_sum(ll x){
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return (x*(x+1))/2;
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}
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int main(){
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//cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(0);
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// Initializing values
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for(int i = 1;i<MAXN;i++){
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mobius[i] = 1;
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}
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// Calcuting primes and mobius function
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for(int i = 2;i<MAXN;i++){
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if(isNotPrime[i]) continue;
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mobius[i] *= -1;
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for(int j = 2*i;j<MAXN;j+=i){
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mobius[j] *= -1;
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isNotPrime[j] = 1;
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}
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ll sq = 1LL*i*i;
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for(ll j = sq;j<MAXN;j+=sq) mobius[j] = 0;
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}
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// Calculating the sum of coprimes
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for(int i = 1;i<MAXN;i++){
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if(mobius[i] == 0) continue;
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for(int j = i;j<MAXN;j+=i){
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sumOfCoprimes[j] +=
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1LL*fast_sum(j/i)*i*mobius[i];
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}
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}
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// Calculating the LCM sum
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for(ll i = 1;i<MAXN;i++){
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for(ll j = i;j<MAXN;j+=i){
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lcmSum[j] += j*sumOfCoprimes[j/i];
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}
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}
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int TC;
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scanf("%d",&TC);
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for(int i = 1;i<=TC;i++){
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int N;
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scanf("%d",&N);
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printf("%lld\n",lcmSum[N]);
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}
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return 0;
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}

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