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2014.12.14
挑战编程程序设计 搜索练习
8.6.1棋盘上的象
题目大意：在n*n的棋盘上放象，每个象的对角线上不能有别的象，求总共的方案数。
思路：搜索，肯定超时。dp~~排列组合~~又不会，只能打表了，好凶残。直接a（放0头象竟然是1种方案）。
#include<iostream>#include<cstdio>#include<cstring>using namespace std;int d1[20]={0},d2[20]={0},n,k;long long ans;void work(int i,int j,int di){ int dd1,dd2,yu; if (di>k) { ++ans; return; } if (i>n||j>n) return; yu=(n-i)*n+n-j+1; if (yu<k-di+1) return; dd1=i-j+8;dd2=i+j; if (d1[dd1]==0&&d2[dd2]==0) { ++d1[dd1];++d2[dd2]; if (j==n) work(i+1,1,di+1); else work(i,j+1,di+1); --d1[dd1];--d2[dd2]; } if (j==n) work(i+1,1,di); else work(i,j+1,di);}int main(){ while(scanf("%d%d",&n,&k)==2) { if (n==0&&k==0) break; ans=0; memset(d1,0,sizeof(d1)); memset(d2,0,sizeof(d2)); work(1,1,1); printf("%lld\n",ans); }}
#include<iostream>#include<cstdio>using namespace std;long long biao[9][65]={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,9,26,26,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,16,92,232,260,112,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,25,240,1124,2728,3368,1960,440,32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,36,520,3896,16428,39680,53744,38368,12944,1600,64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,49,994,10894,70792,282248,692320,1022320,867328,389312,81184,5792,128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,64,1736,26192,242856,1444928,5599888,14082528,22522960,22057472,12448832,3672448,489536,20224,256,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};int main(){ int n,k; while(scanf("%d%d",&n,&k)==2) { if (n==0&&k==0) break; printf("%lld\n",biao[n][k]); }}
8.6.3队伍
题目大意：n个人站队，恰有p个人比左边的人都高，恰有r个人比右边的人都高，求总的方案数。
思路：搜索，一开始是按位置搜的，超时妥妥的。之后改了搜索方法，从高的往小的放，如果当前的人放在已放过的左边；就相当于多了一个比左边人都高的，如果当前的人放在已放过的右边，就相当于多了一个比右边人都高的；如果放在之间的话，就没有变化。然后搜出来的相对要快，可是还是没法满足我们的要求，于是又用了打表，打了十分钟的表，终于a了。
#include<iostream>#include<cstdio>#include<cstring>using namespace std;int n;long long ans=0;bool use[14]={false};void work(int i,int ll,int rr,int le,int re){ int j; if (i>n&&le==0&&re==0) { ++ans; return; } if (ll-1<le) return; if (n-rr<re) return; if (i==1) { for (j=le;j<=n-re+1;++j) { use[j]=true; work(i+1,j,j,le-1,re-1); use[j]=false; } } else { for (j=le;j<=n-re+1;++j) { if (j<1||j>n) continue; if (!use[j]) { use[j]=true; if (j<ll&&le>0) work(i+1,j,rr,le-1,re); if (j>ll&&j<rr) work(i+1,ll,rr,le,re); if (j>rr&&re>0) work(i+1,ll,j,le,re-1); use[j]=false; } } }}int main(){ int i,j,ci,t,l,r; scanf("%d",&t); for (ci=1;ci<=t;++ci) { scanf("%d%d%d",&n,&l,&r); memset(use,false,sizeof(use)); ans=0; work(1,n+1,0,l,r); printf("%lld\n",ans); }}
#include<iostream>#include<cstdio>using namespace std;long long 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main(){ int ci,n,l,r; scanf("%d",&ci); while(ci) { scanf("%d%d%d",&n,&l,&r); printf("%lld\n",ans[n][l][r]); --ci; }}
8.6.5拔河
题目大意：有n个人拔河，将这n个人尽量平分，使两队的人不相差多于1个，然后使两队的体重数相差尽量小，输出分配方案。
思路：之前做过这个题，用的是背包。用容积为总容积一半的背包，装一半的物品，然后用布尔数组保存这些，最后从一半容积处穷举，找到最优解就可以了。
#include<iostream>#include<cstdio>#include<cstring>using namespace std;bool f[101][45001]={false};int a[101]={0};int main(){ int i,j,sum=0,n,k,q,cha,summ,ci; scanf("%d",&ci); while(ci) { cin>>n; sum=0; memset(f,false,sizeof(f)); if (n%2==0) k=n/2; else k=n/2+1; for (i=1;i<=n;++i) { cin>>a[i]; sum+=a[i]; } if (sum%2==0) summ=sum/2; else summ=sum/2+1; for (i=0;i<=n;++i) f[i][0]=true; for (i=1;i<=n;++i) for (j=summ;j>=a[i];--j) for (q=k;q>=1;--q) f[q][j]=f[q][j]||f[q-1][j-a[i]]; for (j=summ;j>=0;--j) if (f[k][j]) { cout<<min(j,sum-j)<<" "<<max(j,sum-j)<<endl; break; } if (ci>1) cout<<endl; --ci; }}
2014.12.14
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