ural 1091. Tmutarakan Exams 和 codeforces 295 B. Greg and Graph

ural 1091 题目链接:http://acm.timus.ru/problem.aspx?space=1&num=1091

题意是从1到n的集合里选出k个数,使得这些数满足gcd大于1

解法:

因子有2的数: 2,4,6,8,10,12,14.。。

因子有3的数:3,6,9,12,15,18,21.。。

因子有5的数:5,10,15,18,21,24.。。

可以看出这里求出的集合时会有重复的,得去从。可惜没有学过容斥原理。不过解决这题还是没问题的。

50以内的素因子有:2, 3, 5, 7, 11, 13, 17, 19, 23只有这些素因子才可能产生集合元素大于2的集合

排除重复度为2的集合: 6{2,3(因子2和因子3造成集合重复)}, 10{2,5},14{2,7}, 22{2, 11}, 15{3,5},21{3,7}

代码为:

IN = lambda : map(int, raw_input().split() )
prime = [2, 3, 5, 7, 11, 13, 17, 19, 23]
x = [6, 10, 14, 22, 15, 21] k, s = IN()
c =[ [0]*(s+1) for i in xrange(s+1) ]
for i in xrange(s+1):
c[i][1] = i; c[i][0] = 1; c[i][i]=1
for i in xrange(1,s+1):
for j in xrange(1, i):
c[i][j] = c[i-1][j]+c[i-1][j-1] sum = 0
for v in prime:
if s/v<k: break
sum += c[s/v][k]
for v in x:
if s/v<k: break
sum -= c[s/v][k] print sum if sum<10000 else 10000

cf 295B http://codeforces.com/problemset/problem/295/B

题意是:按照一定顺序删除点并删除与点相连的线,求删除该点前的点集合里两两点的最短距离。

这题我以前看到过类似的,很自然就想到了从后往前处理,每次把这个点加进去循环更新距离,这个类似floyed

python代码:肯能是python效率问题吧,这个代码过不了。TLE,但是换成c++就过了

from sys import stdin,stdout
IN = lambda: [ int(x) for x in stdin.readline().split() ]
n = int( stdin.readline().strip() )
edge = []
for i in xrange(n):
edge.append( IN() )
x = IN()
ans = [0]*n for k in xrange(n-1, -1, -1):
for i in xrange(n):
for j in xrange(n):
edge[i][j] = min( edge[i][j], edge[i][x[k] -1] + edge[x[k]-1 ][j] )
for i in xrange(k, n):
for j in xrange(k, n):
ans[k] += edge[x[i]-1 ][x[j]-1 ]
print ' '.join( map(str,ans ) )

c++ code:

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std; #define maxn 505
int n, edge[maxn][maxn];
int x[maxn];
long long ans[maxn]; int main(int argc, char**argv){
cin >> n;
for ( int i=; i<n; ++i )
for ( int j=; j<n; ++j )
cin >> edge[i][j];
for ( int i=; i<n; ++i ) cin >>x[i];
for ( int k=n-; k>=; --k ){
for ( int i=; i<n; ++i )
for ( int j=; j<n; ++j )
edge[i][j] = min( edge[i][j], edge[i][x[k]- ]+ edge[x[k]-][j] );
ans[k] = ;
for ( int i=k; i<n; ++i )
for ( int j=i+; j<n; ++j )
ans[k] += edge[x[i]- ][x[j]- ]+edge[x[j]- ][x[i]- ];
}
for ( int i=; i<n; ++i )
printf("%I64d ", ans[i]);
}
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