POJ 3090 Visible Lattice Points legal Lee Series | | By the meter

Because the image is symmetrical about the diagonal. So we just look at the Triangle area.

Consider the x-axis as the denominator, the point of the circle as a molecule

{1/2},{1/3,1/2},{1/4,3/4},{1/5,2/5,3/5,4/5}, in turn

Written in the prefix and the form is {1/3,2/3},{},{a,A,1/3,2/3,1/4,3/4},{,1/ 3,2/3,1/4,3/4,1/5,2/5,3/5,4/5}

Found. This is a series of Valeo, that is, the number added by K is phi[k].

The final answer *2+ (0,1) + (1,0), (three) the point is good

#include <iostream> #include <cstdio> #include <cmath>using namespace std; #define N 1009int Phi[n];int Farey[n]={0,0,1};void init () {    int i, J;    for (i = 1; i < N; i++)        phi[i] = i;    for (i = 2; i < N, i++)        if (i = = Phi[i]) for            (j = i; J < N; J + = i)                phi[j] = (Phi[j]/i) * (i-1);} int main () {    init ();    for (int i=3;i<n;i++)    {        farey[i]=farey[i-1]+phi[i];    }    int cas,n,ca=1;    scanf ("%d", &cas);    while (cas--)    {        scanf ("%d", &n);        printf ("%d%d%d\n", ca++,n,farey[n]*2+3);    }    return 0;}

If This rule is not found, it is also possible to recursively make a table, like a matrix and storage, using GCD to infer whether the current point is blocked by the previous point.

#include <iostream> #include <cstdio> #include <cmath> #include <cstring> #include <cstdlib >using namespace Std;int mp[1005][1005];bool vis[1005][1005];int gcd (int a,int b) {return a%b==0?b:gcd (b,a%b);}    int A[1005][1005];int Main () {memset (vis,0,sizeof (VIS));    int ans=0;            for (int i=1;i<=1000;i++) {for (int j=1;j<=1000;j++) {int gg=gcd (I,J);                if (Vis[i/gg][j/gg]) {a[i][j]+=a[i-1][j]+a[i][j-1];                A[I][J]-=A[I-1][J-1];            Continue                } else {vis[i][j]=1;                a[i][j]+=a[i-1][j]+a[i][j-1]+1;            A[I][J]-=A[I-1][J-1];    }}} int n;    int ca=1;    int CAs;    scanf ("%d", &cas);        while (cas--) {scanf ("%d", &n);    printf ("%d%d%d\n", ca++,n,a[n][n]+2); } return 0;}

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POJ 3090 Visible Lattice Points legal Lee Series | | By the meter