Super Mario 树状数组离线 || 线段树

Super Mario

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 5560    Accepted Submission(s): 2532

Problem Description

Mario is world-famous plumber. His “burly” figure and amazing jumping ability reminded in our memory. Now the poor princess is in trouble again and Mario needs to save his lover. We regard the road to the boss’s castle as a line (the length is n), on every integer point i there is a brick on height hi. Now the question is how many bricks in [L, R] Mario can hit if the maximal height he can jump is H.

 

Input

The first line follows an integer T, the number of test data.
For each test data:
The first line contains two integers n, m (1 <= n <=10^5, 1 <= m <= 10^5), n is the length of the road, m is the number of queries.
Next line contains n integers, the height of each brick, the range is [0, 1000000000].
Next m lines, each line contains three integers L, R,H.( 0 <= L <= R < n 0 <= H <= 1000000000.)

 

Output

For each case, output "Case X: " (X is the case number starting from 1) followed by m lines, each line contains an integer. The ith integer is the number of bricks Mario can hit for the ith query.

 

Sample Input

1 10 10 0 5 2 7 5 4 3 8 7 7 2 8 6 3 5 0 1 3 1 1 9 4 0 1 0 3 5 5 5 5 1 4 6 3 1 5 7 5 7 3

 

Sample Output

Case 1: 4 0 0 3 1 2 0 1 5 1

 

http://acm.hdu.edu.cn/showproblem.php?pid=4417

一开始的时候，很难想，和以前的树状数组不同，但是有一点是固定的。

既然要是区间里的个数，那么就肯定离不开L, R

开始的时候还以为学以前的区间统计不同数字的个数一样。对R排序，然后每个压进树状数组。

但是这样不行，查询元素的变得十分麻烦。

比如1、5、7、3

我把这些元素都压进去了，然后查询[3, 4]小于等于6的个数，就会很麻烦。

既要减去[1, 2]的，也有些数字比6大。、

主要是没用上L和R。这两个是必须用的，都是getsum(R) - getsum(L - 1)进而得到答案。都是这个套路。

那么就是看看[L, R]这一段连续的区间，有多少个数是小于等于val的。那么我们先保证，现在每一个压进树状

数组的元素都是<=val的，这个可以保证，然后更新数字的时候，就是跟新他们的位置，所以这时候查询就直接来就行了。

这一招保证每一次query的时候元素都是合法的技巧，以前用过一次，可惜忘记了。

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <assert.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;


#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
const int maxn = 1e5 + 20;
int c[maxn];
int n, m;
int lowbit(int x) {
    return x & (-x);
}
void UpDate(int pos, int val) {
    while (pos <= n) {
        c[pos] += val;
        pos += lowbit(pos);
    }
}
int getsum(int pos) {
    int ans = 0;
    assert(pos >= 0);
    while (pos) {
        ans += c[pos];
        pos -= lowbit(pos);
    }
    return ans;
}
struct haha {
    int val, id;
    bool operator < (const struct haha & rhs) const {
        return val < rhs.val;
    }
}a[maxn];
struct node {
    int L, R, id, val;
    bool operator < (const struct node & rhs) const {
        return val < rhs.val;
    }
}query[maxn];
int ans[maxn];
void init() {
    memset(c, 0, sizeof c);
}
void work() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; ++i) {
        scanf("%d", &a[i].val);
        a[i].id = i;
    }
    sort(a + 1, a + 1 + n);
    for (int i = 1; i <= m; ++i) {
        scanf("%d%d%d", &query[i].L, &query[i].R, &query[i].val);
        query[i].L++;
        query[i].R++;
        query[i].id = i;
    }
    sort(query + 1, query + 1 + m);
    int now = 1;
    for (int i = 1; i <= m; ++i) {
        while (now <= n && query[i].val >= a[now].val) {
            UpDate(a[now].id, 1);
            now++;
        }
        ans[query[i].id] = getsum(query[i].R) - getsum(query[i].L - 1);
    }
    static int f = 0;
    printf("Case %d:
", ++f);
    for (int i = 1; i <= m; ++i) {
        printf("%d
", ans[i]);
    }
}

int main() {
#ifdef local
    freopen("data.txt", "r", stdin);
//    freopen("data.txt", "w", stdout);
#endif
    int t;
    scanf("%d", &t);
    while (t--) {
        init();
        work();
    }
    return 0;
}

我这个线段树不是其他线段树。

我的每个节点都保存了所有区间的数字。并且排序

就是把归并排序的过程记录下来了。

然后对于每一个个查询。

1、如果区间全部包含了，那么直接二分查找即可。

2、递归搜索。

注意pushUp的时候，要先vector<>.resize();

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <assert.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;


#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
#define root 1, n, 1
#define lson L, mid, cur << 1
#define rson mid + 1, R, cur << 1 | 1
const int maxn = 1e5 + 20;
vector<int>seg[maxn << 2];
int a[maxn];
int n, m;
void pushUp(int cur) {
//    cout << "ff" << endl;
//    cout << seg[cur << 1].size() << endl;
    merge(seg[cur << 1].begin(), seg[cur << 1].end(), seg[cur << 1 | 1].begin(), seg[cur << 1 | 1].end(), seg[cur].begin());
}
void build(int L, int R, int cur) {
    if (L == R) {
        seg[cur].clear();
        seg[cur].push_back(a[L]);
        return;
    }
    int mid = (L + R) >> 1;
    build(lson);
    build(rson);
    seg[cur].resize(R - L + 1);
    pushUp(cur);
}
int query(int be, int en, int val, int L, int R, int cur) {
    if (L >= be && R <= en) {
        if (val >= seg[cur].back()) {
            return R - L + 1;
        } else {
            int pos = upper_bound(seg[cur].begin(), seg[cur].end(), val) - seg[cur].begin();
            return pos;
        }
    }
    int mid = (L + R) >> 1;
    int lans = 0, rans = 0;
    if (mid >= be) {
        lans = query(be, en, val, lson);
    }
    if (mid < en) {
        rans = query(be, en, val, rson);
    }
    return lans + rans;
}
void upDate(int pos, int val, int L, int R, int cur) {
    if (L == R) {
        if (pos == L) {
            seg[cur].clear();
            seg[cur].push_back(val);
        }
        return;
    }
    int mid = (L + R) >> 1;
    if (pos <= mid) upDate(pos, val, lson);
    else upDate(pos, val, rson);
    pushUp(cur);
}
void work() {
    scanf("%d%d", &n, &m);
//    cout << n << " " << m << endl;
    for (int i = 1; i <= n; ++i) {
        scanf("%d", &a[i]);
    }
    build(root);
//    for (int i = 0; i < seg[1].size(); ++i) {
//        cout << seg[1][i] << " ";
//    }
//    cout << endl;
//    cout << "ff" << endl;
    static int f = 0;
    printf("Case %d:
", ++f);
    while (m--) {
        int be, en, x;
        scanf("%d%d%d", &be, &en, &x);
        be++;
        en++;
        int res = query(be, en, x, root);
        printf("%d
", res);
    }
}

int main() {
#ifdef local
    freopen("data.txt", "r", stdin);
//    freopen("data.txt", "w", stdout);
#endif
    int t;
    scanf("%d", &t);
    while (t--) work();
    return 0;
}