洛谷 P1393 P3157 动态逆序对

嘛，好久没碰CDQ分治了，做道题练练手。

时间倒流——把删数改为加数。

对于每个被删的，我的想法是拆成询问和add，后来发现一个足矣。

我本来准备对每个删的数都求一遍整体逆序对，后来发现无论如何都不可做。

然后发现是只求改的逆序对，做两次CDQ，一次统计在前面大的，一次统计在后面小的。

注意：这两次的区别是id那一维的顺序不同，而time顺序是相同的。

记得离散化。

然后我打完 + 静态差错之后，一发过样例AC，稳！！！

顺手切了一模一样的3157，WA了两个点。发现输出负数......换成longlong之后AC。

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

 typedef long long LL;

 const LL N = ;

 LL x[N], a[N], n;

 struct TreeArray {
     LL tr[N];
     inline void clear() {
         memset(tr, , sizeof(tr));
         return;
     }
     inline void add(LL x, LL a) {
         for(; x < N; x += x & (-x)) {
             tr[x] += a;
         }
         return;
     }
     inline LL getsum(LL x) {
         LL ans = ;
         for(; x; x -= x & (-x)) {
             ans += tr[x];
         }
         return ans;
     }
     inline LL ask(LL l, LL r) {
         if(l == ) {
             return getsum(r);
         }
         return getsum(r) - getsum(l - );
     }
 }ta;

 struct Node {
     LL val, ans, time, type, id;
 }node[N], temp[N];

 inline bool cmp_t(Node d, Node e) {
     return d.time < e.time;
 }
 inline bool cmp__t(Node d, Node e) {
     return d.time > e.time;
 }

 void CDQ1(LL l, LL r) {
     if(l == r) {
         return;
     }
     LL mid = (l + r) >> ;
     CDQ1(l, mid);
     CDQ1(mid + , r);

     LL i = l, j = mid + , t = ;
     while(i <= mid || j <= r) {
         if(j > r || (i <= mid && node[i].id < node[j].id)) {
             ta.add(node[i].val, );
             temp[++t] = node[i++];
         }
         else {
             if(node[j].type == ) {
                 node[j].ans += ta.ask(node[j].val + , n);
             }
             temp[++t] = node[j++];
         }
     }
     for(i = l; i <= mid; i++) {
         ta.add(node[i].val, -);
     }
     t = ;
     for(LL i = l; i <= r; i++) {
         node[i] = temp[++t];
     }
     return;
 }

 void CDQ2(LL l, LL r) {
     if(l == r) {
         return;
     }
     LL mid = (l + r) >> ;
     CDQ2(l, mid);
     CDQ2(mid + , r);

     LL i = l, j = mid + , t = ;
     while(i <= mid || j <= r) {
         if(j > r || (i <= mid && node[i].id > node[j].id)) { /// error : id < id
             ta.add(node[i].val, 1);/// error : if(type == 1)
             temp[++t] = node[i++];
         }
         else {
             if(node[j].type == ) {
                 node[j].ans += ta.getsum(node[j].val - );
             }
             temp[++t] = node[j++];
         }
     }
     for(i = l; i <= mid; i++) {
         ta.add(node[i].val, -);/// error : if(type == 1)
     }
     t = ;
     for(i = l; i <= r; i++) {
         node[i] = temp[++t];
     }
     return;
 }

 LL pos[N];

 int main() {
     LL m;
     scanf("%lld%lld", &n, &m);
     for(LL i = ; i <= n; i++) {
         scanf("%lld", &a[i]);
         x[i] = a[i];
         node[i].id = i;
         node[i].type = ; /// normal
     }
     std::sort(x + , x + n + );
     LL xx = std::unique(x + , x + n + ) - x - ;
     for(LL i = ; i <= n; i++) {
         LL p = std::lower_bound(x + , x + xx + , a[i]) - x;
         node[i].val = p;
         pos[p] = i;
     }
     /// li san hua wan bi

     LL nn = n, p;
     for(LL i = ; i <= m; i++) {
         scanf("%lld", &p);
         p = std::lower_bound(x + , x + xx + , p) - x;
         p = pos[p];
         node[p].type = ; /// add
         node[p].time = nn--;
     }
     for(LL i = ; i <= n; i++) {
         if(node[i].type == ) {
             node[i].time = nn--;
         }
     }
     LL ans = ;
     for(LL i = ; i <= n; i++) {
         if(node[i].type == ) {
             ans += ta.ask(node[i].val + , n);
             ta.add(node[i].val, );
         }
     }
     ta.clear();
     std::sort(node + , node + n + , cmp_t);
     CDQ1(, n);
     std::sort(node + , node + n + , cmp_t); /// error : cmp__t -> cmp_t
     CDQ2(, n);
     std::sort(node + , node + n + , cmp__t);
     for(LL i = ; i <= m; i++) {
         ans += node[i].ans;
     }
     for(LL i = ; i <= m; i++) {
         printf("%lld\n", ans);
         ans -= node[i].ans;
     }
     return ;
 }

P3157

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

 const int N = ;

 int x[N], a[N], n;

 struct TreeArray {
     int tr[N];
     inline void clear() {
         memset(tr, , sizeof(tr));
         return;
     }
     inline void add(int x, int a) {
         for(; x < N; x += x & (-x)) {
             tr[x] += a;
         }
         return;
     }
     inline int getsum(int x) {
         int ans = ;
         for(; x; x -= x & (-x)) {
             ans += tr[x];
         }
         return ans;
     }
     inline int ask(int l, int r) {
         if(l == ) {
             return getsum(r);
         }
         return getsum(r) - getsum(l - );
     }
 }ta;

 struct Node {
     int val, ans, time, type, id;
 }node[N], temp[N];

 inline bool cmp_t(Node d, Node e) {
     return d.time < e.time;
 }
 inline bool cmp__t(Node d, Node e) {
     return d.time > e.time;
 }

 void CDQ1(int l, int r) {
     if(l == r) {
         return;
     }
     int mid = (l + r) >> ;
     CDQ1(l, mid);
     CDQ1(mid + , r);

     int i = l, j = mid + , t = ;
     while(i <= mid || j <= r) {
         if(j > r || (i <= mid && node[i].id < node[j].id)) {
             ta.add(node[i].val, );
             temp[++t] = node[i++];
         }
         else {
             if(node[j].type == ) {
                 node[j].ans += ta.ask(node[j].val + , n);
             }
             temp[++t] = node[j++];
         }
     }
     for(i = l; i <= mid; i++) {
         ta.add(node[i].val, -);
     }
     t = ;
     for(int i = l; i <= r; i++) {
         node[i] = temp[++t];
     }
     return;
 }

 void CDQ2(int l, int r) {
     if(l == r) {
         return;
     }
     int mid = (l + r) >> ;
     CDQ2(l, mid);
     CDQ2(mid + , r);

     int i = l, j = mid + , t = ;
     while(i <= mid || j <= r) {
         if(j > r || (i <= mid && node[i].id > node[j].id)) {
             ta.add(node[i].val, );
             temp[++t] = node[i++];
         }
         else {
             if(node[j].type == ) {
                 node[j].ans += ta.getsum(node[j].val - );
             }
             temp[++t] = node[j++];
         }
     }
     for(i = l; i <= mid; i++) {
         ta.add(node[i].val, -);
     }
     t = ;
     for(i = l; i <= r; i++) {
         node[i] = temp[++t];
     }
     return;
 }

 int main() {
     int m;
     scanf("%d%d", &n, &m);
     for(int i = ; i <= n; i++) {
         scanf("%d", &a[i]);
         x[i] = a[i];
         node[i].id = i;
         node[i].type = ; /// normal
     }
     std::sort(x + , x + n + );
     int xx = std::unique(x + , x + n + ) - x - ;
     for(int i = ; i <= n; i++) {
         int p = std::lower_bound(x + , x + xx + , a[i]) - x;
         node[i].val = p;
     }
     /// li san hua wan bi

     int nn = n;
     for(int i = ; i <= m; i++) {
         scanf("%d", &xx);
         node[xx].type = ; /// add
         node[xx].time = nn--;
     }
     for(int i = ; i <= n; i++) {
         if(node[i].type == ) {
             node[i].time = nn--;
         }
     }
     int ans = ;
     for(int i = ; i <= n; i++) {
         if(node[i].type == ) {
             ans += ta.ask(node[i].val + , n);
             ta.add(node[i].val, );
         }
     }
     ta.clear();
     std::sort(node + , node + n + , cmp_t);
     CDQ1(, n);
     std::sort(node + , node + n + , cmp_t);
     CDQ2(, n);
     std::sort(node + , node + n + , cmp__t);
     for(int i = ; i <= m; i++) {
         ans += node[i].ans;
     }
     for(int i = ; i <= m + ; i++) {
         printf("%d ", ans);
         ans -= node[i].ans;
     }
     return ;
 }

P1393

CDQ大法好！