hdu 3727 主席树+ 线段树
题目描述：
对一个序列进行维护，要求支持四种操作：1. 在结尾加入一个数。
2. 询问区间第K大的数
3. 询问大小为X的数在序列中的排名
4. 询问第K大的数
吐槽：
1. 真是捉了N久啊。。。。。。
2. 手动写内存池，与MLE只差400K。。。。。
算法分析：
操作3和4的话，离散化一下用树状数组/线段树搞就可以了。问题如何维护1和2。
好在更改的操作只是在结尾加入一个数，所以离线处理一下，用一个支持查询区间第K大的数据结构就行了。
于是这里选择了主席树。。。。
二分答案来找区间第K小。。。。
1 #include<iostream>
2 #include<cassert>
3 #include<cstring>
4 #include<algorithm>
5 #include<cstdio>
6 using namespace std;
7 const int N = 100005;
8 int num[N],now;
9 pair< int, int> hash[N];
10 int seg[N<<2],M;
11 // chairman tree
12 const int MAXN = 2000000;
13 int sum[MAXN],pl[MAXN],pr[MAXN],size,root[N];
14 int make_tree( int l, int r, int val){
15 int t = size++;
16 // cout<<l<<" "<<r<<" "<<val<<endl;
17 if(l == r) { sum[t] = val; return t;}
18 int m = l+r>>1;
19 pl[t] = make_tree(l,m,val);
20 pr[t] = make_tree(m+1,r,val);
21 sum[t] = sum[pl[t]] + sum[pr[t]];
22 return t;
23 }
24 int make_tree( int l, int r, int _pl, int _pr){
25 int t = size ++;
26 pl[t] = _pl; pr[t] =_pr;
27 sum[t] = sum[_pl] + sum[_pr];
28 return t;
29 }
30 int change( int L, int R, int pos, int at, int v){
31 if(L == R)
32 return make_tree(L,R,v);
33 int m = L+R >> 1;
34 if(at <=m ) return make_tree(L,R, change(L,m,pl[pos] , at, v),pr[pos]);
35 return make_tree(L, R , pl[pos] , change(m+1,R,pr[pos] ,at, v));
36 }
37 int ask( int l, int r, int pos, int L, int R){
38 if(l <= L && r >= R)
39 return sum[pos];
40 int mid = L+R >>1 , val = 0;
41 if(l <= mid) val += ask(l,r,pl[pos], L, mid);
42 if(r > mid) val += ask(l,r,pr[pos], mid+1,R);
43 return val;
44 }
45 // init()
46 int n;
47 void init(){
48 size = 0;
49 for( int i=0;i<n;i++)
50 hash[i] = make_pair(num[i] , i);
51 sort(hash, hash + n);
52 root[0] = make_tree(0,n-1,1);
53 for( int i=1; i<n; i++){
54 root[i] = change(0,n-1,root[i-1],hash[i-1].second , -1);
55 }
56 // cout<<size<<endl;
57 for( int i=30; i>=0; i--) if(n < (1<<i)) M = 1<<i;
58 for( int i=0; i<M*2; i++) seg[i] = 0;
59 }
60 // segment tree
61 void ins( int pos){
62 for(pos += M; pos; pos >>= 1)
63 seg[pos] ++;
64 }
65 int find_rank( int pos){
66 int ans = 0;
67 for(pos += M; pos; pos >>=1)
68 if(pos &1) ans += seg[pos ^ 1];
69 return ans +1;
70
71 }
72 int find_kth( int k){
73 int ans=1;
74 while(ans < M){
75 int l = ans <<1;
76 int r = ans <<1|1;
77 assert(seg[ans] >= k);
78 if(seg[l] >= k) ans = l;
79 else {
80 k -= seg[l];
81 ans = r;
82 }
83 }
84 return hash[ans-M].first;
85 }
86 // main
87 int find( int val){
88 int l = 0, r= n;
89 while(l<r){
90 int mid = l+r >>1;
91 if(val <= hash[mid].first) r = mid;
92 else l = mid+1;
93 }
94 return l;
95 }
96 int chk( int pos, int l, int r){
97 int val = ask(l,r,root[pos],0,n-1);
98 int ans = (r-l+1-val >> 1) + 1;
99 // cout<<(ans)<<endl;
100 return ans;
101 }
102 struct Query{
103 char cmd[20];
104 int l,r,v;
105 } query[N*5];
106 int main(){
107 int _test = 0,Q;
108 while(~scanf("%d",&Q)){
109 n = 0;
110 for( int i=0; i<Q;i++){
111 scanf("%s",query[i].cmd);
112 if(!strcmp(query[i].cmd, "Insert")){
113 scanf("%d",&query[i].v);
114 num[n++] = query[i].v;
115 }
116 else {
117 char x = query[i].cmd[strlen(query[i].cmd) -1];
118 if(x =='1')
119 scanf("%d%d%d",&query[i].l , &query[i].r ,&query[i].v);
120 else scanf("%d",&query[i].v);
121 }
122 }
123 init();
124 long long Q1 = 0, Q2= 0, Q3 = 0;
125 printf("Case %d:\n", ++ _test);
126 for( int i=0;i<Q;i++){
127 if(!strcmp(query[i].cmd,"Insert")){
128 ins(find(query[i].v));
129 }
130 else {
131 char x = query[i].cmd[strlen(query[i].cmd) -1];
132 if(x == '1'){
133 int L = query[i].l-1, R = query[i].r-1 , k = query[i].v;
134 int l = 0, r = n;
135 // cout<<"qeury_1 "<<L<<" "<<R<<" "<<k<<endl;
136 while(l < r){
137 int m = l+r >>1;
138 // cout<<l<<" "<<r<<" "<<m<<" "<<hash[m].first<<endl;
139 if(chk(m,L,R) > k) r = m ;
140 else l = m+1;
141 }
142 l--;
143 int v1 = hash[l].first;
144 Q1 += v1;
145 // cout<<v1<<endl;
146 }
147 else if(x=='2'){
148 int u = find(query[i].v);
149 int v2 = find_rank(u);
150 // cout<<v2<<endl;
151 Q2 += v2;
152 }
153 else {
154 int v3 = find_kth(query[i].v);
155 Q3 += v3;
156 // cout<<v3<<endl;
157 }
158 }
159 }
160 cout<<Q1<<endl<<Q2<<endl<<Q3<<endl;
161 // cout<<size<<endl;
162 }
163 }
164
2 #include<cassert>
3 #include<cstring>
4 #include<algorithm>
5 #include<cstdio>
6 using namespace std;
7 const int N = 100005;
8 int num[N],now;
9 pair< int, int> hash[N];
10 int seg[N<<2],M;
11 // chairman tree
12 const int MAXN = 2000000;
13 int sum[MAXN],pl[MAXN],pr[MAXN],size,root[N];
14 int make_tree( int l, int r, int val){
15 int t = size++;
16 // cout<<l<<" "<<r<<" "<<val<<endl;
17 if(l == r) { sum[t] = val; return t;}
18 int m = l+r>>1;
19 pl[t] = make_tree(l,m,val);
20 pr[t] = make_tree(m+1,r,val);
21 sum[t] = sum[pl[t]] + sum[pr[t]];
22 return t;
23 }
24 int make_tree( int l, int r, int _pl, int _pr){
25 int t = size ++;
26 pl[t] = _pl; pr[t] =_pr;
27 sum[t] = sum[_pl] + sum[_pr];
28 return t;
29 }
30 int change( int L, int R, int pos, int at, int v){
31 if(L == R)
32 return make_tree(L,R,v);
33 int m = L+R >> 1;
34 if(at <=m ) return make_tree(L,R, change(L,m,pl[pos] , at, v),pr[pos]);
35 return make_tree(L, R , pl[pos] , change(m+1,R,pr[pos] ,at, v));
36 }
37 int ask( int l, int r, int pos, int L, int R){
38 if(l <= L && r >= R)
39 return sum[pos];
40 int mid = L+R >>1 , val = 0;
41 if(l <= mid) val += ask(l,r,pl[pos], L, mid);
42 if(r > mid) val += ask(l,r,pr[pos], mid+1,R);
43 return val;
44 }
45 // init()
46 int n;
47 void init(){
48 size = 0;
49 for( int i=0;i<n;i++)
50 hash[i] = make_pair(num[i] , i);
51 sort(hash, hash + n);
52 root[0] = make_tree(0,n-1,1);
53 for( int i=1; i<n; i++){
54 root[i] = change(0,n-1,root[i-1],hash[i-1].second , -1);
55 }
56 // cout<<size<<endl;
57 for( int i=30; i>=0; i--) if(n < (1<<i)) M = 1<<i;
58 for( int i=0; i<M*2; i++) seg[i] = 0;
59 }
60 // segment tree
61 void ins( int pos){
62 for(pos += M; pos; pos >>= 1)
63 seg[pos] ++;
64 }
65 int find_rank( int pos){
66 int ans = 0;
67 for(pos += M; pos; pos >>=1)
68 if(pos &1) ans += seg[pos ^ 1];
69 return ans +1;
70
71 }
72 int find_kth( int k){
73 int ans=1;
74 while(ans < M){
75 int l = ans <<1;
76 int r = ans <<1|1;
77 assert(seg[ans] >= k);
78 if(seg[l] >= k) ans = l;
79 else {
80 k -= seg[l];
81 ans = r;
82 }
83 }
84 return hash[ans-M].first;
85 }
86 // main
87 int find( int val){
88 int l = 0, r= n;
89 while(l<r){
90 int mid = l+r >>1;
91 if(val <= hash[mid].first) r = mid;
92 else l = mid+1;
93 }
94 return l;
95 }
96 int chk( int pos, int l, int r){
97 int val = ask(l,r,root[pos],0,n-1);
98 int ans = (r-l+1-val >> 1) + 1;
99 // cout<<(ans)<<endl;
100 return ans;
101 }
102 struct Query{
103 char cmd[20];
104 int l,r,v;
105 } query[N*5];
106 int main(){
107 int _test = 0,Q;
108 while(~scanf("%d",&Q)){
109 n = 0;
110 for( int i=0; i<Q;i++){
111 scanf("%s",query[i].cmd);
112 if(!strcmp(query[i].cmd, "Insert")){
113 scanf("%d",&query[i].v);
114 num[n++] = query[i].v;
115 }
116 else {
117 char x = query[i].cmd[strlen(query[i].cmd) -1];
118 if(x =='1')
119 scanf("%d%d%d",&query[i].l , &query[i].r ,&query[i].v);
120 else scanf("%d",&query[i].v);
121 }
122 }
123 init();
124 long long Q1 = 0, Q2= 0, Q3 = 0;
125 printf("Case %d:\n", ++ _test);
126 for( int i=0;i<Q;i++){
127 if(!strcmp(query[i].cmd,"Insert")){
128 ins(find(query[i].v));
129 }
130 else {
131 char x = query[i].cmd[strlen(query[i].cmd) -1];
132 if(x == '1'){
133 int L = query[i].l-1, R = query[i].r-1 , k = query[i].v;
134 int l = 0, r = n;
135 // cout<<"qeury_1 "<<L<<" "<<R<<" "<<k<<endl;
136 while(l < r){
137 int m = l+r >>1;
138 // cout<<l<<" "<<r<<" "<<m<<" "<<hash[m].first<<endl;
139 if(chk(m,L,R) > k) r = m ;
140 else l = m+1;
141 }
142 l--;
143 int v1 = hash[l].first;
144 Q1 += v1;
145 // cout<<v1<<endl;
146 }
147 else if(x=='2'){
148 int u = find(query[i].v);
149 int v2 = find_rank(u);
150 // cout<<v2<<endl;
151 Q2 += v2;
152 }
153 else {
154 int v3 = find_kth(query[i].v);
155 Q3 += v3;
156 // cout<<v3<<endl;
157 }
158 }
159 }
160 cout<<Q1<<endl<<Q2<<endl<<Q3<<endl;
161 // cout<<size<<endl;
162 }
163 }
164