"2017 Shandong round training Day2" Pair (Hall Theorem + tree line)

The length of a given number of columns and length of a number of columns , find the number of length can be continuous with the sub-series match.

Two columns can be matched, and if there is a scheme, the number of columns in the two may be paired off, the two numbers can be paired if and only if they are not less than if only .

The first row of three numbers .
The second row has numbers .
The third row has numbers .

A digital output, the number of length can be continuous with the sub-series match.

Sample input 1

5 2 10
5 3
1 8 5 5 7

Sample output 1

Sample input 2

2 2 6
2 3
3 4

Sample output 2

Sample input 3

4 2 10
5 5
9 3 8 9

Sample output 3

For data ;
for data ;
for data ;
for data .

SOLUTION:

A formula can be introduced by Hall Theorem

An interval of a pair

With the sum i represents the number of a connection point of the bi

If for each sum i satisfies sum i> = i can be a perfect match

CODE:

#include <bits/stdc++.h>

#define REP(i, a, b) for (int i = a; i <= b; ++i)
typedef long long ll;

using namespace std;

void File() {
    freopen("loj6062.in", "r", stdin);
    freopen("loj6062.out", "w", stdout);
}

const int maxn = 1.5e5 + 10;
int n, m, h, a[maxn], b[maxn], ans;

struct Segment_Tree {
#define mid ((l + r) >> 1)
#define lc rt << 1
#define rc rt << 1 | 1
#define lson lc, l, mid
#define rson rc, mid + 1, r
    int Min[maxn << 2], tag[maxn << 2];
    void pushdown(int rt) {
        Min[lc] += tag[rt];
        tag[lc] += tag[rt];
        Min[rc] += tag[rt];
        tag[rc] += tag[rt];
        tag[rt] = 0;
    }
    void build(int rt, int l, int r) {
        if (l == r)
            Min[rt] = -l;
        else {
            build(lson);
            build(rson);
            Min[rt] = min(Min[lc], Min[rc]);
        }
    }
    void modify(int rt, int l, int r, int L, int R, int x) {
        if (L > R)
            return;
        if (L <= l && r <= R) {
            Min[rt] += x;
            tag[rt] += x;
        } else {
            if (tag[rt])
                pushdown(rt);
            if (L <= mid)
                modify(lson, L, R, x);
            if (R >= mid + 1)
                modify(rson, L, R, x);
            Min[rt] = min(Min[lc], Min[rc]);
        }
    }
} T;

void init() {
    scanf("%d%d%d", &n, &m, &h);
    REP(i, 1, m) scanf("%d", &b[i]);
    sort(b + 1, b + m + 1);
    REP(i, 1, n) {
        scanf("%d", &a[i]);
        a[i] = lower_bound(b + 1, b + m + 1, h - a[i]) - b;
    }
    T.build(1, 1, m);
    REP(i, 1, m - 1) T.modify(1, 1, m, a[i], m, 1);
}

int main() {
   // File();
    init();
    REP(i, m, n) {
        T.modify(1, 1, m, a[i], m, 1);
        ans += (T.Min[1] >= 0);
        T.modify(1, 1, m, a[i - m + 1], m, -1);
    }
    printf("%d\n", ans);
    return 0;
}