CodeForces 264B Good Sequences dp，codeforces264b

CodeForces 264B Good Sequences dp，codeforces264b

題目連結：點擊開啟連結

題意：

給定n個數，

構造一個序列（只能選給出的n個數，但數字可重複用）

使得序列嚴格遞增且相鄰的兩個數字不互質

思路：

因為是嚴格遞增，所以給輸入的n個數排個序，相當於選n個數中的子序列了。

把每個數都分解質因數，然後用質因數轉移方程即可。

import java.io.BufferedReader;import java.io.InputStreamReader;import java.io.PrintWriter;import java.math.BigInteger;import java.text.DecimalFormat;import java.util.ArrayDeque;import java.util.ArrayList;import java.util.Arrays;import java.util.Collection;import java.util.Collections;import java.util.Comparator;import java.util.Deque;import java.util.HashMap;import java.util.Iterator;import java.util.LinkedList;import java.util.Map;import java.util.PriorityQueue;import java.util.Scanner;import java.util.Stack;import java.util.StringTokenizer;import java.util.TreeMap;import java.util.TreeSet;import java.util.Queue;import java.io.File;import java.io.FileInputStream;import java.io.FileNotFoundException;import java.io.FileOutputStream;public class Main {int[] prime = new int[N], len = new int[N]; int primenum;//有primenum個素數 math.hvoid PRIME(int Max_Prime){primenum=0;prime[primenum++]=2;for(int i=3;i<=Max_Prime;i+=2)for(int j=0;j<primenum;j++)if(i%prime[j]==0)break;else if(prime[j]>sqrt((double)i) || j==primenum-1){prime[primenum++]=i;break;}}int n;int[] a = new int[N];ArrayList<Integer> G = new ArrayList();void go(int x){G.clear();for(int i = 0; prime[i]*prime[i]<= x; i++){if(x%prime[i] == 0){G.add(prime[i]);while(x%prime[i]==0)x/=prime[i];}}if(x>1)G.add(x);}void work() throws Exception{n = Int();for(int i = 0; i < n; i++)a[i] = Int();for(int i = 0; i < N; i++)len[i] = 0;Arrays.sort(a, 0, n);PRIME(100000);for(int i = 0; i < n; i++){go(a[i]);int mx = 0;for(int j = 0; j < G.size(); j++){mx = max(len[G.get(j)] , mx);}for(int j = 0; j < G.size(); j++)len[G.get(j)] = mx+1;}int ans = 1;for(int i = 0; i < N; i++)ans = max(ans, len[i]);out.println(ans);}    public static void main(String[] args) throws Exception{        Main wo = new Main();    in = new BufferedReader(new InputStreamReader(System.in));    out = new PrintWriter(System.out);  //  in = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));  //  out = new PrintWriter(new File("output.txt"));        wo.work();        out.close();    }static int N = 100005;static int M = 101;DecimalFormat df=new DecimalFormat("0.0000");static int inf = (int)1e8;static long inf64 = (long) 1e18*2;static double eps = 1e-8;static double Pi = Math.PI;static int mod = (int)1e9 + 7 ;private String Next() throws Exception{    while (str == null || !str.hasMoreElements())        str = new StringTokenizer(in.readLine());    return str.nextToken();    }    private int Int() throws Exception{    return Integer.parseInt(Next());    }    private long Long() throws Exception{    return Long.parseLong(Next());    }    private double Double() throws Exception{    return Double.parseDouble(Next());    }    StringTokenizer str;    static Scanner cin = new Scanner(System.in);    static BufferedReader in;    static PrintWriter out;  /*  class Edge{int from, to, dis, nex;Edge(){}Edge(int from, int to, int dis, int nex){this.from = from;this.to = to;this.dis = dis;this.nex = nex;}}Edge[] edge = new Edge[M<<1];int[] head = new int[N];int edgenum;void init_edge(){for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;}void add(int u, int v, int dis){edge[edgenum] = new Edge(u, v, dis, head[u]);head[u] = edgenum++;}/**/int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;int pos = r;r--;while (l <= r) {int mid = (l + r) >> 1;if (A[mid] <= val) {l = mid + 1;} else {pos = mid;r = mid - 1;}}return pos;}int Pow(int x, int y) {int ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}double Pow(double x, int y) {double ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}int Pow_Mod(int x, int y, int mod) {int ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;ans %= mod;y >>= 1;x = x * x;x %= mod;}return ans;}long Pow(long x, long y) {long ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}long Pow_Mod(long x, long y, long mod) {long ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;ans %= mod;y >>= 1;x = x * x;x %= mod;}return ans;}int gcd(int x, int y){if(x>y){int tmp = x; x = y; y = tmp;}while(x>0){y %= x;int tmp = x; x = y; y = tmp;}return y;}int max(int x, int y) {return x > y ? x : y;}int min(int x, int y) {return x < y ? x : y;}double max(double x, double y) {return x > y ? x : y;}double min(double x, double y) {return x < y ? x : y;}long max(long x, long y) {return x > y ? x : y;}long min(long x, long y) {return x < y ? x : y;}int abs(int x) {return x > 0 ? x : -x;}double abs(double x) {return x > 0 ? x : -x;}long abs(long x) {return x > 0 ? x : -x;}boolean zero(double x) {return abs(x) < eps;}double sin(double x){return Math.sin(x);}double cos(double x){return Math.cos(x);}double tan(double x){return Math.tan(x);}double sqrt(double x){return Math.sqrt(x);}}