題意：

給出一個矩陣，初始每個位置上的值都為0，然後有兩種操作

• 一種是更改某個位置上的值
• 另一種是求某個位置附近曼哈頓距離不大於K的所有位置的值的總和

技巧：

• 坐標旋轉，使得操作之後菱形變成方方正正的矩形，（即“曼哈頓距離”轉化為“切比雪夫距離”）方便使用樹狀數組進行計算。

• 利用哈希進行離散，節約空間，即不開不必要的空間。

坐標旋轉：

• X=x-y
• Y=x+y

這個結果顯示，A’B’C’D’（X，Y）是ABCD（x，y）繞原點（0，0）左旋轉45°後的結果，同時長度變為原來的sqrt(2)倍。

由於菱形範圍為對角線OA的距離，正方形為一半邊長OM的距離，相等，所以無需對距離進行操作。

坐標離散：

1,離線離散

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 4000005;
const int maxm = 80005;

#define lowbit(x) ((x)&(-x))
int N, M, W, E, H[maxn+5], fenw[maxn + 5];
int
 
 O[maxm], X[maxm], Y[maxm], Z[maxm];

inline int find (int x) {
    return lower_bound(H + 1, H + E, x) - H;
}

void hashPoint (int x, int y) {
    for (int i = x; i <= W; i += lowbit(i)) {
        for (int j = y; j <= W; j += lowbit(j))
            H[E++] = i * W + j;
    }
}

void
 
 add(int x, int y, int d) {
    for (int i = x; i <= W; i += lowbit(i)) {
        for (int j = y; j <= W; j += lowbit(j)) {
            int pos = find(i * W + j);
            fenw[pos] += d;
        }
    }
}

int sum (int x, int y) {
    int ret = 0;
    for (int i = x; i; i -= lowbit(i)) {
        for (int j = y; j; j -= lowbit(j)) {
            int pos = find(i * W + j);
            if (H[pos] == i * W + j)
                ret += fenw[pos];
        }
    }
    return ret;
}

void init () {
    E = 1;
    W = 2 * N;
    scanf("%d", &M);
    memset(fenw, 0, sizeof(fenw));
    for (int i = 1; i <= M; i++) {
        scanf("%d%d%d%d", &O[i], &X[i], &Y[i], &Z[i]);
        int x = X[i] - Y[i] + N;
        int y = X[i] + Y[i];
        if (O[i] == 1)
            hashPoint(x, y);
    }
    sort(H + 1, H + E);
    E = unique(H + 1, H + E) - H;
}

void solve() {
    for (int i = 1; i <= M; i++) {
        int x = X[i] - Y[i] + N;
        int y = X[i] + Y[i];

        if (O[i] == 1)
            add(x, y, Z[i]);
        else {
            int a = max(1, x - Z[i]);
            int b = max(1, y - Z[i]);
            int c = min(W, x + Z[i]);
            int d = min(W, y + Z[i]);
            printf("%d\n", sum(c, d) - sum(c, b-1) - sum(a-1, d) + sum(a-1, b-1));
        }
    }
}

int main () {
    while (scanf("%d", &N) == 1 && N) {
        init();
        solve();
    }
    return 0;
}

2，線性探測再散列。以前再kbrdhash時用到過，大同小異吧http://www.cnblogs.com/hua-dong/p/7714475.html。

但是不知道為什麽炸內存了（別人的代碼）

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define MAXN 4001003
#define MAXM 88888
using namespace std;
int n, m;
int W;
int h[MAXN];
int a[MAXN];
int hash(int x)
{
    int pos = x % MAXN;
    while(true)
    {
        if(h[pos] == 0 || h[pos] == x)
        {
            h[pos] = x;
            return pos;
        }
        pos++;
        if(pos == MAXN) pos = 0;
    }
}
int gethash(int x)
{
    int pos = x % MAXN;
    while(true)
    {
        if(h[pos] == 0 || h[pos] == x) return pos;
        pos++;
        if(pos == MAXN) pos = 0;
    }
}
inline int lowbit(int x)
{
    return x & -x;
}
void add(int x, int y, int val)
{
    for(int i = x; i <= W; i += lowbit(i))
        for(int j = y; j <= W; j += lowbit(j))
            a[hash(i * W + j)] += val;
}
int getsum(int x, int y)
{
    int sum = 0;
    for(int i = x; i > 0; i -= lowbit(i))
        for(int j = y; j > 0; j -= lowbit(j))
            sum += a[gethash(i * W + j)];
    return sum;
}
int main()
{
    int p, x, y, z, xa, xb, ya, yb, newx, newy;
    while(scanf("%d", &n) != EOF && n)
    {
        scanf("%d", &m);
        W = n * 2;
        memset(a, 0, sizeof(a));
        memset(h, 0, sizeof(h));
        for(int i = 0; i < m; i++)
        {
            scanf("%d%d%d%d", &p, &x, &y, &z);
            newx = x - y + n;
            newy = x + y;
            if(p == 1) add(newx, newy, z);
            else
            {
                xa = max(1, newx - z);
                ya = max(1, newy - z);
                xb = min(W, newx + z);
                yb = min(W, newy + z);
                printf("%d\n", getsum(xb, yb) - getsum(xa - 1, yb) - getsum(xb, ya - 1) + getsum(xa - 1, ya - 1));
            }
        }
    }
    return 0;
}

（類似用到了坐標轉化的題：HDU4312）

HDU4456-Crowd （坐標旋轉處理+hash處理+二維樹狀數組）