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题目链接:http://poj.org/problem?id=3067
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题意:
左边N个点,右边M个点,分别南北方向排列,1对应1,2对应2,给出
K条记录,每条记录表示左边的A点和右边的B点相连,两条相连的先会有一
个交点,现在保证任意三个线不会交与一点,问一共多少个交点。
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题解:
树状数组
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思路:
题目求的是交点的数目,仔细观察就可以发现,如果有以下四个点,A1
,B1属于左边,A2,B2属于右边,当且仅当 A1和A2的大小关系 和 B1与B2
的大小关系 相反,于是可以联想到求一个数列的逆序数的时候用到的树状数
组的成段求和。
我们只要将读入的整数对按左边的点递增排序,如果左边点大小相同则按
右边点递增排序,每次在树状数组中统计比当前右边的点大的数的数目,然后
再将这个点插入树状数组,这就实现了一个逆序统计。
这里需要注意的是,统计的时候需要采用__int64,因为总的交点数可能
会超过int。最大的情况是左右两边都是1000个点,并且两两有边,那么最大
的交点数量就是:
1 * (1 + 2 + + 999)
+
2 * (1 + 2 + + 998)
+
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998 * (1 + 2)
+
999 * 1
+
1000 * 0
可以写个程序统计一下,发现这个数字是超过int的。
ll ans = 0;
for(i = 1; i <= 1000; i++) {
ans += i * (1001 - i) * (1000 - i) / 2;
}
*/
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#include <iostream>
#include <algorithm>
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using namespace std;
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 struct Double {
int l, r;
}dt[1000100];
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int N, M, K;
#define ll __int64
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 int cmp(Double a, Double b) {
if(a.l == b.l)
return a.r < b.r;
return a.l < b.l;
}
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 int lowbit(int x) {
return x & (-x);
}
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ll c[1010];
 void add(int pos) {
 while(pos <= M) {
c[pos] ++;
pos += lowbit(pos);
}
}
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 ll sum(int pos) {
ll s = 0;
 while(pos > 0) {
s += c[pos];
pos -= lowbit(pos);
}
return s;
}
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 int main() {
int t;
int i;
int Case = 1;
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scanf("%d", &t);
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 while(t--) {
memset(c, 0, sizeof(c));
scanf("%d %d %d", &N, &M, &K);
 for(i = 0; i < K; i++) {
scanf("%d %d", &dt[i].l, &dt[i].r);
}
sort(dt, dt + K, cmp);
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ll ans = 0;
 for(i = 0; i < K; i++) {
ans += sum(M) - sum(dt[i].r);
add(dt[i].r);
}
printf("Test case %d: %I64d\n", Case++, ans);
}
return 0;
}
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