poj 2985(并查集+线段树求K大数)

来源：互联网发布：2015年酒店行业数据编辑：程序博客网时间：2024/05/23 17:54

解题思路：这道题并查集很容易，合并时找到父节点就直接加上去就ok了。关键是如何求K大数，我一直在想用线段树怎么写，一开始想如果直接记录数的大小那肯定是没戏了，借鉴了一下别人的思路：区间[a,b]记录的是所有的数里面，等于a，a+1，a+2，......，b-1，b的个数。看到这里就应该明白了，这里线段树的用法是把它看做是一个1-n的数轴。到时候要修改某一个数，就直接在数轴上修改它。至于记录[a,b]的个数，是为了找到K大数。

参考博客：http://blog.sina.com.cn/s/blog_6fd8e0fe0100v89n.html

#include<iostream>#include<cstdio>#include<cstring>using namespace std;const int maxn = 200005;struct Segment{int l,r;int sum;}tree[maxn<<2];int n,m,fa[maxn],tot[maxn];int find(int x){if(fa[x] == x) return x;return fa[x] = find(fa[x]);}void build(int rt,int l,int r){tree[rt].l = l, tree[rt].r = r;if(tree[rt].l == 1) tree[rt].sum = n;else tree[rt].sum = 0;if(l == r) return;int mid = (l + r) >> 1;build(rt<<1,l,mid);build(rt<<1|1,mid+1,r);}void update(int rt,int pos,int val){tree[rt].sum += val;if(tree[rt].l == tree[rt].r) return;int mid = (tree[rt].l + tree[rt].r) >> 1;if(pos <= mid) update(rt<<1,pos,val);else update(rt<<1|1,pos,val);}int query(int rt,int k){if(tree[rt].l == tree[rt].r) return tree[rt].l;int mid = (tree[rt].l + tree[rt].r) >> 1;if(tree[rt<<1|1].sum >= k) return query(rt<<1|1,k);else return query(rt<<1,k - tree[rt<<1|1].sum);}int main(){int op,a,b,x,y;while(scanf("%d%d",&n,&m)!=EOF){for(int i = 1; i <= n; i++)fa[i] = i, tot[i] = 1;build(1,1,n);for(int i = 1; i <= m; i++){scanf("%d",&op);if(op){scanf("%d",&a);printf("%d\n",query(1,a));}else{scanf("%d%d",&a,&b);x = find(a);y = find(b);if(x == y) continue;fa[y] = x;update(1,tot[x],-1);update(1,tot[y],-1);update(1,tot[x]+tot[y],1);tot[x] += tot[y];tot[y] = 0;}}}return 0;}

用树状数组求k大数：

#include<iostream>#include<cstdio>#include<cstring>using namespace std;const int maxn = 200005;struct Tree{int n,c[maxn];void init(int n){this->n = n;memset(c,0,sizeof(c));}int lowbit(int x){return x & -x;}void update(int x,int d){while(x <= n){c[x] += d;x += lowbit(x);}}int sum(int x){int ans = 0;while(x > 0){ans += c[x];x -= lowbit(x);}return ans;}}tree;int n,m,fa[maxn],cnt[maxn];int find(int x){if(fa[x] == x) return x;return fa[x] = find(fa[x]);}int main(){int op;while(scanf("%d%d",&n,&m)!=EOF){tree.init(n);tree.update(1,n);for(int i = 1; i <= n; i++) fa[i] = i,cnt[i] = 1;while(m--){scanf("%d",&op);if(op == 0){int i,j;scanf("%d%d",&i,&j);int f1 = find(i);int f2 = find(j);if(f1 != f2){tree.update(cnt[f1],-1);tree.update(cnt[f2],-1);fa[f2] = f1;cnt[f1] += cnt[f2];tree.update(cnt[f1],1);}}else{int k,l = 1,r = n,mid,ans;scanf("%d",&k);while(l <= r){ mid = (l + r) >> 1;int tmp = tree.sum(n) - tree.sum(mid-1);if(tmp >= k){ans = mid;l = mid + 1;}else r = mid - 1;}printf("%d\n",ans);}}}return 0;}

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