题目链接

传送门

A题

题面

代码实现如下

#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> piL;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;

#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("in","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)

const double eps = 1e-8;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;

int main() {
    printf("6\n28\n496\n8128\n33550336\n");
    return 0;
}

C题

题面

题意

定义\(F\)函数为斐波那契数列，给你一个\(W\)，要你构造一个集合\(S\)使得集合内的元素\(f_i\)满足：
\[ W=\sum_{f_i\in S}F[F[f_i]] \]
如果不满足输出\(-1\)，否则输出字典序最小的一个集合。

思路

对于\(n\)很大的时候我们先将它一直减最大的小于等于\(n\)的斐波那契数，直到\(n\leq20\)，然后用二进制来枚举选哪些斐波那契数来凑这个\(n\)。
今年湖南多校对抗赛第一场的一道题和这题很像,题解请戳这里。
对\(java\)和\(python\)不太熟悉，所以代码写的有点挫\(\dots\dots\)

\(java\)代码实现如下

import java.util.*;
import java.math.*;

public class Main {
    static BigInteger pw[] = new BigInteger[40];
    static BigInteger f[] = new BigInteger[3];
    static BigInteger a[][] = new BigInteger[3][3];

    public static void mul(BigInteger f[], BigInteger a[][]) {
        BigInteger c[] = new BigInteger[3];
        for(int i = 0; i < 2; ++i) c[i] = BigInteger.ZERO;
        for(int i = 0; i < 2; ++i) {
            for(int j = 0; j < 2; ++j) {
                c[i] = c[i].add(f[j].multiply(a[j][i]));
            }
        }
        for(int i = 0; i < 2; ++i) f[i] = c[i];
    }

    public static void mulself(BigInteger a[][]) {
        BigInteger c[][] = new BigInteger[3][3];
        for(int i = 0; i < 2; ++i) {
            for(int j = 0; j < 2; ++j) {
                c[i][j] = BigInteger.ZERO;
            }
        }
        for(int i = 0; i < 2; ++i) {
            for(int j = 0; j < 2; ++j) {
                for(int k = 0; k < 2; ++k) {
                    c[i][j] = c[i][j].add(a[i][k].multiply(a[k][j]));
                }
            }
        }
        for(int i = 0; i < 2; ++i) {
            for(int j = 0; j < 2; ++j) {
                a[i][j] = c[i][j];
            }
        }
    }

    public static void init() {
        pw[1] = BigInteger.ONE;
        pw[2] = BigInteger.ONE;
        for(int i = 3; i <= 30; ++i) {
            pw[i] = pw[i-1].add(pw[i-2]);
        }
        for(int cnt = 1; cnt <= 30; ++cnt) {
            if(cnt <= 4) {
                if(cnt <= 3) pw[cnt] = BigInteger.ONE;
                else pw[cnt] = BigInteger.valueOf(2);
                continue;
            }
            f[0] = BigInteger.ONE;
            f[1] = BigInteger.ONE;
            a[0][0] = BigInteger.ONE; a[0][1] = BigInteger.ONE;
            a[1][0] = BigInteger.ONE; a[1][1] = BigInteger.ZERO;
            BigInteger x = pw[cnt];
            x = x.subtract(BigInteger.valueOf(2));
            while(x.compareTo(BigInteger.ZERO) > 0) {
                if(x.mod(BigInteger.valueOf(2)).equals(BigInteger.ONE)) {
                    mul(f, a);
                }
                mulself(a);
                x = x.divide(BigInteger.valueOf(2));
            }
            pw[cnt] = f[0];
        }
    }

    public static void main(String[] args) {
        init();
        Vector<Integer> ans = new Vector<Integer>();
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-- != 0) {
            BigInteger n = sc.nextBigInteger();
            ans.clear();
            int idx = 30, flag = 1;
            while(true) {
                if(n.compareTo(BigInteger.valueOf(20))<=0) break;
                int p = -1;
                for(int i = idx; i >= 1; --i) {
                    if(n.compareTo(pw[i]) >= 0) {
                        p = i;
                        break;
                    }
                }
                if(p == -1) {
                    flag = 0;
                    break;
                }
                n = n.subtract(pw[p]);
                idx = p - 1;
                ans.add(p);
                if(n.equals(BigInteger.ZERO)) break;
            }
            if(flag == 0) {
                System.out.println(-1);
            } else {
                if(n.equals(BigInteger.ZERO)) {
                    int vis = 0;
                    for(int i = ans.size() - 1; i >= 0; --i) {
                        if(vis == 1) System.out.print(" ");
                        vis = 1;
                        System.out.print(ans.elementAt(i));
                    }
                    System.out.println();
                } else {
                    idx = 6;
                    int tot = 1<<idx, pp = 0;
                    for(int i = 1; i < tot; ++i) {
                        BigInteger nw = BigInteger.ZERO;
                        for(int j = 1; j <= idx; ++j) {
                            if((i & (1<<(j-1))) > 0) {
                                nw = nw.add(pw[j]);
                            }
                        }
                        if(n.equals(nw)) {
                            for(int j = idx; j >= 1; --j) {
                                if((i & (1<<(j-1))) > 0) {
                                    ans.add(j);
                                }
                            }
                            pp = 1;
                            break;
                        }
                    }
                    if(pp == 0) System.out.println(-1);
                    else {
                        int vis = 0;
                        for(int i = ans.size() - 1; i >= 0; --i) {
                            if(vis == 1) System.out.print(" ");
                            vis = 1;
                            System.out.print(ans.elementAt(i));
                        }
                        System.out.println();
                    }
                }
            }
        }
        sc.close();
    }
}

\(python\)代码实现如下

def __mul__(f, a):
    c = [0] * 3
    for i in range(2):
        for j in range(2):
            c[i] = c[i] + f[j] * a[j][i]
    return c

def __mulself__(a):
    c = [[0] * 3 for i in range(3)]
    for i in range(2):
        for j in range(2):
            for k in range(2):
                c[i][j] = c[i][j] + a[i][k] * a[k][j]
    return c

pw = [0]*36
pw[1] = pw[2] = 1
for i in range(3, 31):
    pw[i] = pw[i-1] + pw[i-2]
pw[3] = 1
pw[4] = 2
f = [0] * 3
a = [[0] * 3 for i in range(2)]
for i in range(5, 31):
    x = pw[i]
    x -= 2
    f[0] = f[1] = 1
    a[0][0] = a[0][1] = a[1][0] = 1
    a[1][1] = 0
    while(x > 0):
        if(x & 1):
            f = __mul__(f, a)
        a = __mulself__(a)
        x >>= 1
    pw[i] = f[0]
T = eval(input())
for icase in range(T):
    n = eval(input())
    ans = []
    idx = 30
    flag = 1
    while(True):
        if(n <= 20):
            break;
        p = -1
        for i in range(idx, 0, -1):
            if(n >= pw[i]):
                p = i
                break
        if(p == -1):
            flag = 0
            break
        n -= pw[p]
        idx = p - 1
        ans.append(p)
        if(n == 0):
            break;
    if(flag == 0):
        print(-1)
    else:
        pp = False
        if(n == 0):
            pp = True
        else:
            idx = 6
            tot = 1<<idx
            pp = False
            for i in range(1, tot):
                nw = 0
                for j in range(1, idx + 1):
                    if((i & (1<<(j-1))) > 0):
                        nw += pw[j]
                if(n == nw):
                    for j in range(idx, 0, -1):
                        if ((i & (1 << (j - 1))) > 0):
                            ans.append(j)
                    pp = True
                    break
        if(pp):
            ans.sort()
            for i in range(len(ans)):
                print(ans[i], end="")
                if(i != len(ans) - 1):
                    print(end=" ")
                else:
                    print()
        else:
            print(-1)

H题

题面

题意

给你一个\(2\times n\)的矩阵，你初始时在\((1,1)\)处，每次移动可以往周围八个方向移动，问你到达右下角的方案数是多少。

思路

我们假设前i-1列都已经求好了方案数，那么\(dp[i][j]\)表示第\(i\)列第\(j\)行的方案数，则\(dp[i][1]=dp[i-1][1]+dp[i-1][2],dp[i][2]=dp[i-1][1]+dp[i-1][2]+dp[i][1]\)，因此\(dp[i][2]=2*(dp[i-1][1]+dp[i-1][2])=4\times 3^{i-2}\)。

代码实现如下

#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> piL;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;

#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("in","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)

const double eps = 1e-8;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;

int n;

LL qpow(LL x, int n) {
    LL res = 1;
    while(n) {
        if(n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

int main() {
    scanf("%d", &n);
    if(n == 1) return printf("1\n") * 0;
    printf("%lld\n", 4LL * qpow(3, n - 2) % mod);
    return 0;
}

I题

题面

思路

我们先用单调栈来求出以\(a_i\)为区间最小值的左右端点，然后再用线段树来维护前\(i\)个前缀和的最大值和最小值，然后对于每个数进行查询即可。

代码实现如下

#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> pil;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;

#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("D://code//in.txt","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)

const double eps = 1e-8;
const int mod = 1000000007;
const int maxn = 5e5 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;

int n;
stack<int> s;
LL sum[maxn];
int a[maxn], l[maxn], r[maxn];

struct node {
    int l, r;
    LL mx, mn;
}segtree[maxn<<2];

void push_up(int rt) {
    segtree[rt].mx = max(segtree[lson].mx, segtree[rson].mx);
    segtree[rt].mn = min(segtree[lson].mn, segtree[rson].mn);
}

void build(int rt, int l, int r) {
    segtree[rt].l = l, segtree[rt].r = r;
    if(l == r) {
        segtree[rt].mx = segtree[rt].mn = sum[l];
        return;
    }
    int mid = (l + r) >> 1;
    build(lson, l, mid); build(rson, mid + 1, r);
    push_up(rt);
}

LL query(int rt, int l, int r, int op) {
    if(segtree[rt].l == l && segtree[rt].r == r) {
        if(op == 1) return segtree[rt].mx;
        else return segtree[rt].mn;
    }
    int mid = (segtree[rt].l + segtree[rt].r) >> 1;
    if(r <= mid) return query(lson, l, r, op);
    else if(l > mid) return query(rson, l, r, op);
    else {
        if(op == 1) return max(query(lson, l, mid, op), query(rson, mid + 1, r, op));
        else return min(query(lson, l, mid, op), query(rson, mid + 1, r, op));
    }
}

int main(){
#ifndef ONLINE_JUDGE
    FIN;
#endif
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i) {
        scanf("%d", &a[i]);
        l[i] = r[i] = i;
        sum[i] = sum[i-1] + a[i];
    }
    for(int i = 1; i <= n; ++i) {
        while(s.size() && a[s.top()] > a[i]) {
            r[s.top()] = i - 1;
            s.pop();
        }
        s.push(i);
    }
    while(s.size()) {
        r[s.top()] = n;
        s.pop();
    }
    for(int i = n; i >= 1; --i) {
        while(s.size() && a[s.top()] > a[i]) {
            l[s.top()] = i + 1;
            s.pop();
        }
        s.push(i);
    }
    while(s.size()) {
        l[s.top()] = 1;
        s.pop();
    }
    build(1, 0, n);
    LL ans = -INF, tmp;
    for(int i = 1; i <= n; ++i) {
        if(a[i] < 0) {
            tmp = query(1, i, r[i], 2) - query(1, l[i] - 1, i, 1);
        } else {
            tmp = query(1, i, r[i], 1) - query(1, l[i]-1, i, 2);
        }
        ans = max(ans, tmp * a[i]);
    }
    printf("%lld\n", ans);
    return 0;
}

J题

题面

题意

给你一棵有\(n\)个结点的树，问你\(u,v\)之间所有的边权小于等于\(k\)的数量。

思路

主席树板子题。

代码实现如下

#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> piL;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;

#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("in","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)

const double eps = 1e-8;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;

vector<int> v;
int n, q, x, y, w, len, cnt, tot;
int head[maxn], root[maxn], fa[maxn][30], deep[maxn];

struct edge {
    int v, w, next;
}ed[maxn<<1];

void add(int u, int v, int w) {
    ed[tot].v = v;
    ed[tot].w = w;
    ed[tot].next = head[u];
    head[u] = tot++;
}

int getid(int x) {
    return lower_bound(v.begin(), v.end(), x) - v.begin() + 1;
}

struct node {
    int l, r, sum;
}tree[maxn*40];

void update(int l, int r, int& x, int y, int pos) {
    tree[++cnt] = tree[y], tree[cnt].sum++, x = cnt;
    if(l == r) return;
    int mid = (l + r) >> 1;
    if(mid >= pos) update(l, mid, tree[x].l, tree[y].l, pos);
    else update(mid + 1, r, tree[x].r, tree[y].r, pos);
}

int query(int l, int r, int x, int y, int pos) {
    if(r <= pos) return tree[y].sum - tree[x].sum;
    if(l == r) return tree[y].sum - tree[x].sum;
    int mid = (l + r) >> 1;
    if(pos <= mid) return query(l, mid, tree[x].l, tree[y].l, pos);
    else return tree[tree[y].l].sum - tree[tree[x].l].sum + query(mid + 1, r, tree[x].r, tree[y].r, pos);
}

void dfs(int u, int d, int p) {
    deep[u] = d;
    fa[u][0] = p;
    for(int i = head[u]; ~i; i = ed[i].next) {
        int v = ed[i].v;
        if(v != p) {
            update(1, len, root[v], root[u], getid(ed[i].w));
            dfs(v, d + 1, u);
        }
    }
}

void lca() {
    for(int i = 1; i <= n; i++) {
        for(int j = 1; (1 << j) <= n; j++) {
            fa[i][j] = -1;
        }
    }
    for(int j = 1; (1 << j) <= n; j++) {
        for(int i = 1; i <= n; i++) {
            if(fa[i][j-1] != -1) {
                fa[i][j] = fa[fa[i][j-1]][j-1];
            }
        }
    }
}

int cal(int u, int v) {
    if(deep[u] < deep[v]) swap(u, v);
    int k;
    for(k = 0; (1 << (1 + k)) <= deep[u]; k++);
    for(int i = k; i >= 0; i--) {
        if(deep[u] - (1 << i) >= deep[v]) {
            u = fa[u][i];
        }
    }
    if(u == v) return u;
    for(int i = k; i >= 0; i--) {
        if(fa[u][i] != -1 && fa[u][i] != fa[v][i]) {
            u = fa[u][i];
            v = fa[v][i];
        }
    }
    return fa[u][0];
}

struct que {
    int u, v, w;
}ask[maxn];

int main() {
    scanf("%d%d", &n, &q);
    for(int i = 1; i <= n; ++i) {
        head[i] = -1;
    }
    for(int i = 1; i < n; ++i) {
        scanf("%d%d%d", &x, &y, &w);
        v.push_back(w);
        add(x, y, w); add(y, x, w);
    }
    for(int i = 1; i <= q; ++i) {
        scanf("%d%d%d", &ask[i].u, &ask[i].v, &ask[i].w);
        v.push_back(ask[i].w);
    }
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
    len = v.size();
    dfs(1, 1, 0);
    lca();
    for(int i = 1; i <= q; ++i) {
        int p = cal(ask[i].u, ask[i].v);
        printf("%d\n", query(1, len, root[p], root[ask[i].u], getid(ask[i].w)) + query(1, len, root[p], root[ask[i].v], getid(ask[i].w)));
    }
    return 0;
}

K题

题面

题意

首先定义一下函数:
\(f(l,r):\bigoplus a_i(l\leq i \leq r)\)
\(g(l,r):\bigoplus f(x,y)(l\leq x\leq y\leq r)\)
\(w(l,r):\bigoplus g(x,y)(l\leq x\leq y\leq r)\)
给你\(n\)个数，\(q\)次查询，每次查询\(l,r\)间的\(w(l,r)\)的值。

思路

打表找规律即可。
我们首先打表发现：
\[ \text{当}r-l+1\text{为偶数时},g(l,r)=0\\ \text{当}r-l+1\text{为奇数时},g(l,r)=l\bigoplus (l+2)\bigoplus (l+4)\bigoplus\dots \]
然后就可以用下述代码打出\(w(l,,r)\)的解，最后用前缀和预处理一下就行。

打表代码如下

#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> piL;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;

#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("in","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)

const double eps = 1e-8;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;

map<int, int> mp;

int main() {
    for(int i = 1; i <= 25; ++i) { //区间长度
        mp.clear();
        for(int j = 1; j <= i; j += 2) {  //g的长度
            for(int s = 1; s <= i; ++s) {
                if(s + j - 1 > i) break;
                for(int k = s; k <= i; k += 2) {
                    if(k + j - 1 > i) break;
                    mp[k] ++;
                    if(mp[k] % 2 == 0) mp[k] = 0;
                }
            }
        }
        printf("[%d]:", i);
        for(int j = 1; j <= i; ++j) {
            if(mp[j]) printf("%d ", j);
        }
        printf("\n");
    }
    return 0;
}

代码实现如下

#include <set>
#include <map>
#include <deque>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<LL, LL> pLL;
typedef pair<LL, int> pLi;
typedef pair<int, LL> piL;;
typedef pair<int, int> pii;
typedef unsigned long long uLL;

#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) x&(-x)
#define name2str(name) (#name)
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
#define FIN freopen("in","r",stdin)
#define IO ios::sync_with_stdio(false),cin.tie(0)

const double eps = 1e-8;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 7;
const double pi = acos(-1);
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;

int t, n, q;
int a[maxn];
int sum[4][maxn];

int main() {
    scanf("%d", &t);
    while(t--) {
        scanf("%d", &n);
        a[0] = 0;
        memset(sum, 0, sizeof(sum));
        for(int i = 1; i <= n; ++i) {
            scanf("%d", &a[i]);
        }
        for(int i = 0; i < 4; ++i) {
            sum[i][i] = a[i];
            for(int j = i; j + 4 <= n; j += 4) {
                sum[i][j+4] = sum[i][j] ^ a[j+4];
            }
        }
        scanf("%d", &q);
        int l, r;
        while(q--) {
            scanf("%d%d", &l, &r);
            int len = r - l + 1;
            if(len % 4 == 1) {
                 int num = l % 4;
                 int s = 0, t = r;
                 if(l >= 4) {
                    s = l - 4;
                 }
                 t = l + len / 4 * 4;
                 if(t > r) t -= 4;
                 printf("%d\n", sum[num][t] ^ sum[num][s]);
            } else if(len %  4 == 3) {
                int num = (l + 1) % 4;
                int s = 0, t = r;
                if(l >= 4) {
                    s = (l + 1) - 4;
                }
                t = (l + 1) + len / 4 * 4;
                if(t > r) t -= 4;
                printf("%d\n", sum[num][t] ^ sum[num][s]);
            } else if(len % 4 == 0) {
                printf("0\n");
            } else {
                int num1 = l % 4;
                int s1 = 0, t1 = r;
                if(l >= 4) {
                    s1 = l - 4;
                }
                t1 = l + len / 4 * 4;
                if(t1 > r) t1 -= 4;

                int num2 = (l + 1) % 4;
                int s2 = 0, t2 = r;
                if(l >= 4) {
                    s2 = (l + 1) - 4;
                }
                t2 = (l + 1) + len / 4 * 4;
                if(t2 > r) t2 -= 4;
                printf("%d\n", sum[num1][t1] ^ sum[num1][s1] ^ sum[num2][t2] ^ sum[num2][s2]);
            }
        }
    }
    return 0;
}

M题

题面

题意

给你一个字符串\(S\)，然后\(q\)次查询，每次查询\(T\)串是否在\(S\)的子序列中出现过。

思路

由于这题数据比较水，因此我们可以用二分过，但是正解是序列自动机或者\(dp\)预处理。

二分代码实现如下

#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 1e5 + 7;
char s[maxn], t[1010];
vector<int>v[30];
vector<int>::iterator it;
int main() {
    scanf ( "%s", s + 1 );
    int len = strlen ( s + 1 ), q, x, flag, len1, cnt, i;
    for (  i = 1 ; i <= len ; i++ ) {
        int x = s[i] - 'a';
        v[x].push_back ( i );
    }
    scanf ( "%d", &q );
    while ( q-- ) {
        scanf ( "%s", t + 1 );
        flag = 0;
        len1 = strlen ( t + 1 );
        if ( len1 > len ) {
            printf ( "NO\n" );
            continue;
        }
        x = t[1] - 'a';
        if ( v[x].size() != 0 ) cnt = v[x][0];
        else {
            printf ( "NO\n" );
            continue;
        }
        for (  i = 2 ; i <= len1 ; i++ ) {
            x = t[i] - 'a';
            if ( v[x].size() == 0 || v[x].back() <= cnt ) {
                flag = 1;
                break;
            }
            it = upper_bound ( v[x].begin(), v[x].end(), cnt );
            if ( it == v[x].end() ) {
                flag = 1;
                break;
            }
            cnt = ( *it );
        }
        if ( flag ) printf ( "NO\n" );
        else printf ( "YES\n" );
    }
    return 0;
}