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划分树--查询区间k-th number code

一、pku_2104
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#include<stdio.h>
#include<algorithm>

#define N 100000+100
#define M 21  // log(N)

using namespace std;

struct Node {
	int val,id;
} a[N];

int n,m,tr[M][N];

int cmp(Node aa, Node bb) {
	if(aa.val < bb.val || (aa.val == bb.val && aa.id < bb.id)) return 1;
	return 0;
}

void build_tree(int dep, int s, int t)
{
	if(s >= t) return;
	
	int i,j,k,mid = (s+t)/2;
	j = s; k = mid+1;
	
	for(i=s;i<=t;i++)
	{
	    if(tr[dep][i] <= mid)
	        tr[dep+1][j++] = tr[dep][i];
	    else
	        tr[dep+1][k++] = tr[dep][i];

	    tr[dep][i] = j-1;
	}
	
	build_tree(dep+1, s, mid);
	build_tree(dep+1, mid+1, t);
}

int find_tree(int dep, int s, int t, int i, int j, int k)
{
	if(s == t) return s;
	int ci, mid = (s+t)/2;
	
	int v = tr[dep][j]-(s-1);
	if(i > s) v = tr[dep][j] - tr[dep][i-1];
	
	if(v >= k)
	{
	    ci = s; if(i > s) ci = tr[dep][i-1]+1;
	    return find_tree(dep+1, s, mid, ci, tr[dep][j], k);
	}
	else
	{
	    ci = mid+1; if(i > s) ci = mid+1 + (i-1)-tr[dep][i-1];
	    return find_tree(dep+1, mid+1, t, ci, mid+j-tr[dep][j], k-v);
	}
	return 0;
}

int main()
{
	int i,j,k,ans;
	while(scanf("%d %d",&n,&m) != EOF)
	{
	    for(i=1;i<=n;i++) {
	        scanf("%d",&a[i].val); a[i].id = i;
	    }
	    
	    sort(a+1, a+1+n, cmp);
	    for(i=1;i<=n;i++) tr[0][a[i].id] = i;

	    build_tree(0, 1, n);
	    
	    while(m--)
	    {
	        scanf("%d %d %d",&i,&j,&k);
	        ans = find_tree(0, 1, n, i, j, k);
	        printf("%d\n",a[ans].val);
	    }
	}
	return 0;
}
二、hdu_2665
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#include<stdio.h>
#include<algorithm>

#define N 100000+100
#define M 21  // log(N)

using namespace std;

struct Node {
	int val,id;
} a[N];

int n,m,tr[M][N];

int cmp(Node aa, Node bb) {
	if(aa.val < bb.val || (aa.val == bb.val && aa.id < bb.id)) return 1;
	return 0;
}

void build_tree(int dep, int s, int t)
{
	if(s >= t) return;
   
	int i,j,k,mid = (s+t)/2;
	j = s; k = mid+1;
   
	for(i=s;i<=t;i++)
	{
	    if(tr[dep][i] <= mid)
	        tr[dep+1][j++] = tr[dep][i];
	    else
	        tr[dep+1][k++] = tr[dep][i];

	    tr[dep][i] = j-1;
	}
   
	build_tree(dep+1, s, mid);
	build_tree(dep+1, mid+1, t);
}

int find_tree(int dep, int s, int t, int i, int j, int k)
{
	if(s == t) return s;
	int ci, mid = (s+t)/2;
   
	int v = tr[dep][j]-(s-1);
	if(i > s) v = tr[dep][j] - tr[dep][i-1];
   
	if(v >= k)
	{
	    ci = s; if(i > s) ci = tr[dep][i-1]+1;
	    return find_tree(dep+1, s, mid, ci, tr[dep][j], k);
	}
	else
	{
	    ci = mid+1; if(i > s) ci = mid+1 + (i-1)-tr[dep][i-1];
	    return find_tree(dep+1, mid+1, t, ci, mid+j-tr[dep][j], k-v);
	}
	return 0;
}

int main()
{
	int i,j,k,ans,T;
	scanf("%d",&T);
	while(T--)
	{
	    scanf("%d %d",&n,&m);
	    for(i=1;i<=n;i++) {
	        scanf("%d",&a[i].val); a[i].id = i;
	    }
	   
	    sort(a+1, a+1+n, cmp);
	    for(i=1;i<=n;i++) tr[0][a[i].id] = i;

	    build_tree(0, 1, n);
	   
	    while(m--)
	    {
	        scanf("%d %d %d",&i,&j,&k);
	        ans = find_tree(0, 1, n, i, j, k);
	        printf("%d\n",a[ans].val);
	    }
	}
	return 0;
}
三、hdu_3727
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#include<stdio.h>
#include<algorithm>

#define N 100000+100
#define M 21  // log(N)

typedef long long LL;

using namespace std;

struct Input {
	int sta,s,t,k;
} q[N+N+N];

struct Node {
	int val,id;
} a[N];

int n,m,tr[M][N],C[N],b[N];

int cmp(Node aa, Node bb) {
	if(aa.val < bb.val || (aa.val == bb.val && aa.id < bb.id)) return 1;
	return 0;
}

int lowbit(int x) {
	return x&(-x);
}

void change(int x, int y) {
	while(x <= n) {
	    C[x] += y; x += lowbit(x);
	}
}

int cal(int x) {
	int t=0;
	while(x > 0) {
	    t += C[x]; x -= lowbit(x);
	}
	return t;
}

void build_tree(int dep, int s, int t)
{
	if(s >= t) return;
   
	int i,j,k,mid = (s+t)/2;
	j = s; k = mid+1;
   
	for(i=s;i<=t;i++)
	{
	    if(tr[dep][i] <= mid)
	        tr[dep+1][j++] = tr[dep][i];
	    else
	        tr[dep+1][k++] = tr[dep][i];

	    tr[dep][i] = j-1;
	}
   
	build_tree(dep+1, s, mid);
	build_tree(dep+1, mid+1, t);
}

int find_tree(int dep, int s, int t, int i, int j, int k)
{
	if(s == t) return s;
	int ci, mid = (s+t)/2;
   
	int v = tr[dep][j]-(s-1);
	if(i > s) v = tr[dep][j] - tr[dep][i-1];
   
	if(v >= k)
	{
	    ci = s; if(i > s) ci = tr[dep][i-1]+1;
	    return find_tree(dep+1, s, mid, ci, tr[dep][j], k);
	}
	else
	{
	    ci = mid+1; if(i > s) ci = mid+1 + (i-1)-tr[dep][i-1];
	    return find_tree(dep+1, mid+1, t, ci, mid+j-tr[dep][j], k-v);
	}
	return 0;
}

int main()
{
	int i,k,T,low,up,mid,cas=0;
	LL ans[5];
	char ch[33];
   
	while(scanf("%d",&T) != EOF)
	{
	   
	    n = 0; m = 0;
	    for(i=1;i<=T;i++)
	    {
	        scanf("%s", ch);
	        if(ch[0] == 'I')
	        {
	            q[i].sta = 0;
	            n++; scanf("%d", &a[n].val); a[n].id = n;
	        }
	        else
	        {
	            q[i].sta = ch[6] - 48;
	            if(ch[6] == '1') scanf("%d %d %d",&q[i].s,&q[i].t,&q[i].k);
	            else
	                scanf("%d",&q[i].k);
	        }
	    }
	   
	    sort(a+1, a+1+n, cmp);
	    for(i=1;i<=n;i++)
	    {
	        b[a[i].id] = tr[0][a[i].id] = i;
	        C[i] = 0;
	    }
	    C[0] = 0;

	    build_tree(0, 1, n);
	   
	    ans[1] = ans[2] = ans[3] = 0;
	   
	    m = 0;
	   
	    for(i=1;i<=T;i++)
	    {
	        if(q[i].sta == 0)
	        {
	            m++;
	            change(b[m], 1);
	        }
	        else
	        if(q[i].sta == 1)
	        {
	            k = find_tree(0, 1, n, q[i].s, q[i].t, q[i].k);
	            ans[1] += a[k].val;
	        }
	        else
	        if(q[i].sta == 2)
	        {
	            low = 1; up = n;
	            while(low < up) {
	                mid = (low + up)/2;
	                if(a[mid].val < q[i].k) low = mid+1; else up = mid;
	            }
	            mid = (low + up)/2;
	            ans[2] += cal(mid);
	        }
	        else
	        if(q[i].sta == 3)
	        {
	            low = 1; up = n;
	            while(low < up) {
	                mid = (low + up)/2;
	                if(cal(mid) < q[i].k) low = mid+1; else up = mid;
	            }
	            mid = (low + up)/2;
	            ans[3] += a[mid].val;
	        }
	    }
	    cas++;
	    printf("Case %d:\n%lld\n%lld\n%lld\n",cas,ans[1],ans[2],ans[3]);
	}
	return 0;
}
四、hdu_3473
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#include<stdio.h>
#include<algorithm>

#define N 100000+100
#define M 21  // log(N)

typedef long long LL;

using namespace std;

struct Node {
	int val,id;
} a[N];

int n,m,pos,tr[M][N];
LL less,more, sum[M][N];

int cmp(Node aa, Node bb) {
	if(aa.val < bb.val || (aa.val == bb.val && aa.id < bb.id)) return 1;
	return 0;
}

void build_tree(int dep, int s, int t)
{
	if(s >= t) return;
   
	int i,j,k, mid = (s+t)/2;
	LL s1,s2;
   
	j = s; k = mid+1;
	s1 = s2 = 0;
   
	for(i=s;i<=t;i++)
	{
	    if(tr[dep][i] <= mid)
	    {
	        s1 += a[tr[dep][i]].val;
	        sum[dep][j] = s1;
	        tr[dep+1][j++] = tr[dep][i];
	    }
	    else
	    {
	        s2 += a[tr[dep][i]].val;
	        sum[dep][k] = s2;
	        tr[dep+1][k++] = tr[dep][i];
	    }

	    tr[dep][i] = j-1;
	}
   
	build_tree(dep+1, s, mid);
	build_tree(dep+1, mid+1, t);
}

void find_tree(int dep, int s, int t, int i, int j, int k)
{
	if(s == t) { pos = s; return ; }
	int ci,cj,  mid = (s+t)/2;
	LL s1,s2;
   
	int v = tr[dep][j]-(s-1);
	if(i > s) v = tr[dep][j] - tr[dep][i-1];
   
	if(v >= k)
	{
	    ci = s; if(i > s) ci = tr[dep][i-1]+1;
	    find_tree(dep+1, s, mid, ci, tr[dep][j], k);
	   
	   
	    if(i == s) ci = 0; else ci = (i-1)-tr[dep][i-1];
	    if(ci == 0) s1 = 0; else s1 = sum[dep][mid+ci];
	   
	    cj = j-tr[dep][j];
	    if(cj == 0) s2 = 0; else s2 = sum[dep][mid+cj];
	   
	    more += (s2-s1);
	}
	else
	{
	    ci = mid+1; if(i > s) ci = mid+1 + (i-1)-tr[dep][i-1];
	    find_tree(dep+1, mid+1, t, ci, mid+j-tr[dep][j], k-v);
	   
	   
	    if(i > s) ci = tr[dep][i-1]; else ci = s-1;
	    if(ci < s) s1 = 0; else s1 = sum[dep][ci];
	   
	    cj = tr[dep][j]; 
	    if(cj < s) s2 = 0; else s2 = sum[dep][cj];
	   
	    less += (s2-s1);
	}
}

int main()
{
	int i,j,k,T,cas=0;
	scanf("%d",&T);
	while(T--)
	{
	    scanf("%d",&n);
	    for(i=1;i<=n;i++) {
	        scanf("%d",&a[i].val); a[i].id = i;
	    }
	   
	    sort(a+1, a+1+n, cmp);
	   
	    sum[0][0] = 0;
	    for(i=1;i<=n;i++)
	    {
	        tr[0][a[i].id] = i;
	        sum[0][i] = sum[0][i-1] + a[i].val;
	    }

	    build_tree(0, 1, n);
	   
	    cas++;
	    printf("Case #%d:\n", cas);
	   
	    scanf("%d",&m);
	    while(m--)
	    {
	        scanf("%d %d",&i,&j);
	        i++; j++; k = (j-i+2)/2;
	        less = 0; more = 0;
	        find_tree(0, 1, n, i, j, k);
	       
	        //printf("%d %lld %lld\n",a[pos].val,less,more);
	       
	        printf("%lld\n", (LL)(k-1)*(LL)a[pos].val-less + more-(LL)(j-i+1-k)*(LL)a[pos].val);
	    }
	    printf("\n");
	}
	return 0;
}

Posted by kk algorithm, base

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