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  • POJ 2104 K-th Number 静态主席树(裸

    题目链接:点击打开链接

    题意:

    给定n长的序列。q个询问

    以下n个数字给出序列

    每一个询问[l, r] k ,输出该区间中第k大的数

    先建一个n个节点的空树。然后每次从后往前新建一棵树,依附原来的空树建。询问就是在树上二分。


    #include <stdio.h>
    #include <stdlib.h>
    #include <algorithm>
    #include <vector>
    #include <iostream>
    #include <cstring>
    using namespace std;
    
    const int N = 100010;
    const int M = N * 30;
    int n, q, tot;
    int a[N];
    int T[M], lson[M], rson[M], c[M];
    vector<int>G;
    
    void input(){
    	G.clear();
    	for (int i = 1; i <= n; i++)scanf("%d", &a[i]), G.push_back(a[i]);
    	sort(G.begin(), G.end());
    	G.erase(unique(G.begin(), G.end()), G.end());
    	for (int i = 1; i <= n; i++)a[i] = lower_bound(G.begin(), G.end(), a[i]) - G.begin() + 1;
    }
    int build(int l, int r){
    	int root = tot++;
    	c[root] = 0;
    	if (l != r){
    		int mid = (l + r) >> 1;
    		lson[root] = build(l, mid);
    		rson[root] = build(mid + 1, r);
    	}
    	return root;
    }
    int updata(int root, int pos, int val){
    	int newroot = tot++, tmp = newroot;
    	c[newroot] = c[root] + val;
    	int l = 1, r = G.size();
    	while (l <= r){
    		int mid = (l + r) >> 1;
    		if (pos <= mid){
    			lson[newroot] = tot++; rson[newroot] = rson[root];
    			newroot = lson[newroot]; root = lson[root];
    			r = mid - 1;
    		}
    		else {
    			rson[newroot] = tot++; lson[newroot] = lson[root];
    			newroot = rson[newroot]; root = rson[root];
    			l = mid + 1;
    		}
    		c[newroot] = c[root] + val;
    	}
    	return tmp;
    }
    int query(int L, int R, int k){
    	int l = 1, r = G.size(), ans = l;
    	while (l <= r){
    		int mid = (l + r) >> 1;
    		if (c[lson[L]] - c[lson[R]] >= k){
    			ans = mid;
    			r = mid - 1;
    			L = lson[L];
    			R = lson[R];
    		}
    		else {
    			l = mid + 1;
    			k -= c[lson[L]] - c[lson[R]];
    			L = rson[L]; 
    			R = rson[R];
    		}
    	}
    	return ans;
    }
    int main(){
    	while (~scanf("%d%d", &n, &q)){
    		input();
    		tot = 0;
    		T[n + 1] = build(1, G.size());
    		for (int i = n; i; i--)
    			T[i] = updata(T[i + 1], a[i], 1);
    		while (q--){
    			int l, r, k; scanf("%d %d %d", &l, &r, &k);
    			printf("%d
    ", G[query(T[l], T[r+1], k)- 1]);
    		}
    	}
    	return 0;
    }
    


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  • 原文地址:https://www.cnblogs.com/liguangsunls/p/6958962.html
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