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定义:dp[i][j] 表示 在前i个数中,使整个gcd值为j时最少取的数个数。
则有方程: gg = gcd(a[i],j)
gg == j : 添加这个数gcd不变,不添加, dp[i][j] = dp[i-1][j]
gg != j: t添加,更新答案, dp[i][gg] = dp[i-1][j] + 1
最后答案为dp[n][g] (g为原始的所有数的gcd)
时间复杂度: O(n*max(a[i]))
代码:
#include <iostream> #include <cstdio> #include <cstring> #include <cmath> #include <algorithm> using namespace std; #define N 1000007 int dp[703][10004]; int a[704]; int gcd(int a,int b) { if(!b) return a; return gcd(b,a%b); } int main() { int n,g,i,j; scanf("%d",&n); g = 0; int maxi = 1; for(i=1;i<=n;i++) for(j=0;j<=10004;j++) dp[i][j] = Mod; for(i=1;i<=n;i++) { scanf("%d",&a[i]); g = gcd(g,a[i]); maxi = max(maxi,a[i]); dp[i][a[i]] = 1; } //printf("%d\n",g); for(i=2;i<=n;i++) { for(j=0;j<=maxi;j++) { if(dp[i-1][j] != Mod) { int gg = gcd(a[i],j); if(gg == j) dp[i][gg] = min(dp[i][gg],dp[i-1][j]); else dp[i][gg] = min(dp[i][gg],dp[i-1][j] + 1); } } } printf("%d\n",n-dp[n][g]); return 0; }
UESTC 923 稳住GCD DP + GCD,布布扣,bubuko.com
标签:style blog http color os art
原文地址:http://www.cnblogs.com/whatbeg/p/3813537.html