hdu 3648 Median Filter

http://acm.hdu.edu.cn/showproblem.php?pid=3648

　　题意相当简单，就是要找出所有给定大小的r*r的矩阵的中位数。

　　这题理论上可以用各种各样的数据结构完成，可以用线段树（或线段树的退化版，点树），treap，AVL树，或者树状数组等。不过，由于数据规模的限制，这题就只能用树状数组来过了。因为其他以上提到的数据结构都是因为常数太大，所以会超时。另外，这题还要模拟矩阵移动的过程，要蛇形移动，否则元素进出树状数组的次数过多也会超时！

AC精简版：

#include <cstdio>
#include <cassert>
#include <cstring>
#include <algorithm>
#include <cmath>

using namespace std;

#define lson l, m, rt << 1
#define rson m + 1, r, rt << 1 | 1

const int maxn = 1000005;
int mp[501][501], out[500][500];

void scan(int &a){
    char ch;

    while ((ch = getchar()) < '0' || ch > '9');
    a = ch - '0';
    while ((ch = getchar()) >= '0' && ch <= '9')
        a = a * 10 + ch - '0';
}
int C[maxn], Max;

void add(int p){
    p++;
    while (p <= Max){
        C[p]++;
        p += p & (-p);
    }
}

void sub(int p){
    p++;
    while (p <= Max){
        C[p]--;
        p += p & (-p);
    }
}

int find(int k){
    int pos = 0, cnt = 0;

    k++;
    for(int i = 20; i >= 0; i--){
        pos += (1 << i);
        if (pos >= Max || cnt + C[pos] >= k) pos -= (1 << i);
        else cnt += C[pos];
    }
    return pos;
}

void deal(int n, int r){
    int len = r << 1 | 1;
    int end = n - len + 1;
    int pos = (len * len + 1) >> 1;

    Max = 0;
    for (int i = 0; i < n; i++){
        for (int j = 0; j < n; j++){
            scan(mp[i][j]);
            Max = max(Max, mp[i][j]);
        }
    }
    Max++;
    fill(C, C + Max + 1, 0);

    for (int i = 0, endi = len - 1; i < endi; i++){
        for (int j = 0; j < len; j++){
            add(mp[i][j]);
        }
    }
    for (int i = 0; i < end; i++){
        if (i & 1){
            for (int j = 0; j < len; j++){
                add(mp[i + len - 1][j + end - 1]);
            }
            out[i][end - 1] = find(pos - 1);
            for (int j = end - 2; j >= 0; j--){
                for (int k = 0; k < len; k++){
                    sub(mp[i + k][j + len]);
                    add(mp[i + k][j]);
                }
                out[i][j] = find(pos - 1);
            }
            for (int j = 0; j < len; j++){
                sub(mp[i][j]);
            }
        }
        else{
            for (int j = 0; j < len; j++){
                add(mp[i + len - 1][j]);
            }
            out[i][0] = find(pos - 1);
            for (int j = 1; j < end; j++){
                for (int k = 0; k < len; k++){
                    sub(mp[i + k][j - 1]);
                    add(mp[i + k][j + len - 1]);
                }
                out[i][j] = find(pos - 1);
            }
            for (int j = 0; j < len; j++){
                sub(mp[i][end + j - 1]);
            }
        }
    }
    for (int i = 0; i < end; i++){
        for (int j = 0; j < end; j++){
            printf("%d ", out[i][j]);
        }
        puts("");
    }
}

int main(){
    int n, m;

    while (~scanf("%d%d", &n, &m) && (n || m)){
        deal(n, m);
    }

    return 0;
}

原始版本（把线段树和树状数组都写进去了。。。。囧）：

#include <cstdio>
#include <cassert>
#include <cstring>
#include <algorithm>
#include <cmath>

using namespace std;

#define lson l, m, rt << 1
#define rson m + 1, r, rt << 1 | 1

int mp[501][501], out[500][500];

/*
const int maxn = 1000005;
int sum[maxn << 2];

void up(int rt){
    sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
}

void update(int pos, int val, int l, int r, int rt){
    if (l == r){
        assert(l == pos);
        sum[rt] += val;
        return ;
    }
    if (!sum[rt] && (sum[rt << 1] || sum[rt << 1 | 1])) sum[rt << 1] = sum[rt << 1 | 1] = 0;

    int m = (l + r) >> 1;

    if (pos <= m) update(pos, val, lson);
    else update(pos, val, rson);
    up(rt);
}

int query(int k, int l, int r, int rt){
    if (l == r){
        return l;
    }
    int m = (l + r) >> 1;

    if (sum[rt << 1] >= k) return query(k, lson);
    else return query(k - sum[rt << 1], rson);
}
*/

void scan(int &a){
    char ch;

    while ((ch = getchar()) < '0' || ch > '9');
    a = ch - '0';
    while ((ch = getchar()) >= '0' && ch <= '9')
        a = a * 10 + ch - '0';
}


/*

const int maxn = 1 << 20;
int sum[maxn << 1], Max;

void add(int n){
    int i = Max + n;

    for (++sum[i]; i > 1; i >>= 1){
        if (~i & 1){
            sum[i >> 1]++;
        }
    }
}

void sub(int n){
    if (!sum[n += Max]) return ;
    for (--sum[n]; n > 1; n >>= 1){
        if (~n & 1){
            --sum[n >> 1];
        }
    }
}

int find(int n){
    int i = 1;

    while (i < Max){
        if (n < sum[i]) i <<= 1;
        else n -= sum[i], i = i << 1 | 1;
    }

    return i - Max;
}
*/

const int maxn = 1000005;
int C[maxn], Max;

void add(int p){
    p++;
    while (p <= Max){
        C[p]++;
        p += p & (-p);
    }
}

void sub(int p){
    p++;
    while (p <= Max){
        C[p]--;
        p += p & (-p);
    }
}

int find(int k){
    int pos = 0, cnt = 0;

    k++;
    for(int i = 20; i >= 0; i--){
        pos += (1 << i);
        if (pos >= Max || cnt + C[pos] >= k) pos -= (1 << i);
        else cnt += C[pos];
    }
    return pos;
}


void deal(int n, int r){
    int len = r << 1 | 1;
    int end = n - len + 1;
    int pos = (len * len + 1) >> 1;
    //int maxSize = -1, minSize = maxn;

    Max = 0;
    //printf("len %d end %d pos %d\n", len, end, pos);
    for (int i = 0; i < n; i++){
        for (int j = 0; j < n; j++){
            scan(mp[i][j]);
            //scanf("%d", &mp[i][j]);
            Max = max(Max, mp[i][j]);
            //maxSize = max(mp[i][j], maxSize);
            //minSize = min(mp[i][j], minSize);
        }
    }
    Max++;
    fill(C, C + Max + 1, 0);
    /*
    if (Max){
        Max = 1 << (int)(log((double)Max) / log(2.0) + 1);
    }
    */

    //sum[1] = 0;
    for (int i = 0, endi = len - 1; i < endi; i++){
        for (int j = 0; j < len; j++){
            //printf("push %d %d\n", i, j);
            add(mp[i][j]);
            //update(mp[i][j], 1, minSize, maxSize, 1);
        }
    }
    for (int i = 0; i < end; i++){
        if (i & 1){
            for (int j = 0; j < len; j++){
                //printf("push %d %d\n", i + len - 1, j + end - 1);
                add(mp[i + len - 1][j + end - 1]);
                //update(mp[i + len - 1][j + end - 1], 1, minSize, maxSize, 1);
            }
            out[i][end - 1] = find(pos - 1);
            //out[i][end - 1] = query(pos, minSize, maxSize, 1);
            for (int j = end - 2; j >= 0; j--){
                for (int k = 0; k < len; k++){
                    //printf("pop %d %d\n", i + k, j + len);
                    sub(mp[i + k][j + len]);
                    //update(mp[i + k][j + len], -1, minSize, maxSize, 1);
                    //printf("push %d %d\n", i + k, j);
                    add(mp[i + k][j]);
                    //update(mp[i + k][j], 1, minSize, maxSize, 1);
                }
                out[i][j] = find(pos - 1);
                //out[i][j] = query(pos, minSize, maxSize, 1);
            }
            for (int j = 0; j < len; j++){
                //printf("pop %d %d\n", i, j);
                sub(mp[i][j]);
                //update(mp[i][j], -1, minSize, maxSize, 1);
            }
        }
        else{
            for (int j = 0; j < len; j++){
                //printf("push %d %d\n", i + len - 1, j);
                add(mp[i + len - 1][j]);
                //update(mp[i + len - 1][j], 1, minSize, maxSize, 1);
            }
            out[i][0] = find(pos - 1);
            //out[i][0] = query(pos, minSize, maxSize, 1);
            for (int j = 1; j < end; j++){
                for (int k = 0; k < len; k++){
                    //printf("pop %d %d\n", i + k, j - 1);
                    sub(mp[i + k][j - 1]);
                    //update(mp[i + k][j - 1], -1, minSize, maxSize, 1);
                    //printf("push %d %d\n", i + k, j + len - 1);
                    add(mp[i + k][j + len - 1]);
                    //update(mp[i + k][j + len - 1], 1, minSize, maxSize, 1);
                }
                out[i][j] = find(pos - 1);
                //out[i][j] = query(pos, minSize, maxSize, 1);
            }
            for (int j = 0; j < len; j++){
                //printf("pop %d %d\n", i, end + j - 1);
                sub(mp[i][end + j - 1]);
                //update(mp[i][end + j - 1], -1, minSize, maxSize, 1);
            }
        }
    }
    for (int i = 0; i < end; i++){
        for (int j = 0; j < end; j++){
            //if (j) putchar(' ');
            printf("%d ", out[i][j]);
        }
        puts("");
    }
}

int main(){
    int n, m;

    while (~scanf("%d%d", &n, &m) && (n || m)){
        deal(n, m);
    }

    return 0;
}

——written by Lyon