RMQ 区间最大值最小值 最频繁次数

Posted 2020-10-10 Aragaki

区间的最大值和最小值

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
using namespace std;
const int MAXN = 100117;
int n,query;
int num[MAXN];

int F_Min[MAXN][20],F_Max[MAXN][20];

void Init()
{
    for(int i = 1; i <= n; i++)
    {
        F_Min[i][0] = F_Max[i][0] = num[i];
    }

    for(int i = 1; (1<<i) <= n; i++)  //按区间长度递增顺序递推
    {
        for(int j = 1; j+(1<<i)-1 <= n; j++)  //区间起点
        {
            F_Max[j][i] = max(F_Max[j][i-1],F_Max[j+(1<<(i-1))][i-1]);
            F_Min[j][i] = min(F_Min[j][i-1],F_Min[j+(1<<(i-1))][i-1]);
        }
    }
}

int Query_max(int l,int r)
{
    int k = (int)(log(double(r-l+1))/log((double)2));
    return max(F_Max[l][k], F_Max[r-(1<<k)+1][k]);
}

int Query_min(int l,int r)
{
    int k = (int)(log(double(r-l+1))/log((double)2));
    return min(F_Min[l][k], F_Min[r-(1<<k)+1][k]);
}

int main()
{
    int a,b;
    scanf("%d %d",&n,&query);
    for(int i = 1; i <= n; i++)
        scanf("%d",&num[i]);
    Init();
    while(query--)
    {
        scanf("%d %d",&a,&b);
        printf("区间%d到%d的最大值为：%d\n",a,b,Query_max(a,b));
        printf("区间%d到%d的最小值为：%d\n",a,b,Query_min(a,b));
        printf("区间%d到%d的最大值和最小值只差为：%d\n",a,b,Query_max(a,b)-Query_min(a,b));
    }
    return 0;
}

区间内出现次数最多的数字出现的次数

#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;

const int maxn = 100017;
int num[maxn], f[maxn], MAX[maxn][20];
int n;
int max(int a,int b)
{
    return a>b ? a:b;
}
int rmq_max(int l,int r)
{
    if(l > r)
        return 0;
    int k = log((double)(r-l+1))/log(2.0);
    return max(MAX[l][k],MAX[r-(1<<k)+1][k]);
}
void init()
{
    for(int i = 1; i <= n; i++)
    {
        MAX[i][0] = f[i];
    }
    int k = log((double)(n+1))/log(2.0);
    for(int i = 1; i <= k; i++)
    {
        for(int j = 1; j+(1<<i)-1 <= n; j++)
        {
            MAX[j][i] = max(MAX[j][i-1],MAX[j+(1<<(i-1))][i-1]);
        }
    }
}
int main()
{
    int a, b, q;
    while(scanf("%d",&n) && n)
    {
        scanf("%d",&q);
        for(int i = 1; i <= n; i++)
        {
            scanf("%d",&num[i]);
        }
        sort(num+1,num+n+1);
        for(int i = 1; i <= n; i++)
        {
            if(i == 1)
            {
                f[i] = 1;
                continue;
            }
            if(num[i] == num[i-1])
            {
                f[i] = f[i-1]+1;
            }
            else
            {
                f[i] = 1;
            }

        }

        init();

        for(int i = 1; i <= q; i++)
        {
            scanf("%d%d",&a,&b);
            int t = a;
            while(t<=b && num[t]==num[t-1])
            {
                t++;
            }
            int cnt = rmq_max(t,b);
            int ans = max(t-a,cnt);
            printf("%d\n",ans);
        }
    }
    return 0;
}
/*
10 3
-1 -1 1 2 1 1 1 10 10 10
2 3
1 10
5 10
*/