Fast Matrix Operations
A Simple Problem with Integers
每次将区间向下更新，或是用之前的方法，统计当前节点到父节点处的覆盖数目。
#include <cstdio> #include <iostream> using namespace std; const int MAXN = 100005; typedef long long int64; int d[MAXN]; class SegNode { public: int L, R; int64 c, sum; int64 get_c() { return c * (R - L + 1); } void log(const char *info) { printf("%s: [%d %d]: %lld, %lld.\n", info, L, R, c, sum); } } node[MAXN * 4]; class SegTree { public: void log(const char *info) { printf("%s:\n", info); printf("{%d %d}, %lld, %lld.\n", node[3].L, node[3].R, node[3].c, node[3].sum); } void build(int r, int L, int R) { node[r].L = L; node[r].R = R; node[r].c = 0; if (L == R) { node[r].sum = d[L]; } else { int M = (L + R) / 2; build(2 * r, L, M); build(2 * r + 1, M + 1, R); node[r].sum = node[2 * r].sum + node[2 * r + 1].sum; } } int64 query(int r, int L, int R) { if (L <= node[r].L && node[r].R <= R) { return node[r].sum + node[r].get_c(); } else { node[2 * r].c += node[r].c; node[2 * r + 1].c += node[r].c; int64 res = 0; if (L <= node[2 * r].R) { res += query(2 * r, L, R); } if (R >= node[2 * r + 1].L) { res += query(2 * r + 1, L, R); } node[r].c = 0; node[r].sum = node[2 * r].sum + node[2 * r + 1].sum + node[2 * r].get_c() + node[2 * r + 1].get_c(); //node[r].log("query"); return res; } } void insert(int r, int L, int R, int c) { if (L <= node[r].L && node[r].R <= R) { node[r].c += c; } else { node[2 * r].c += node[r].c; node[2 * r + 1].c += node[r].c; if (L <= node[2 * r].R) { insert(2 * r, L, R, c); } if (R >= node[2 * r + 1].L) { insert(2 * r + 1, L, R, c); } node[r].c = 0; node[r].sum = node[2 * r].sum + node[2 * r + 1].sum + node[2 * r].get_c() + node[2 * r + 1].get_c(); } //log("tree"); //node[r].log("insert"); } /*{{{ insert2*/ void insert2(int r, int L, int R, int c) { if (L <= node[r].L && node[r].R <= R) { node[r].c += c; } else { if (L <= node[2 * r].R) { insert(2 * r, L, R, c); } if (R >= node[2 * r + 1].L) { insert(2 * r + 1, L, R, c); } node[r].sum = node[2 * r].sum + node[2 * r + 1].sum + node[2 * r].get_c() + node[2 * r + 1].get_c(); } } /*}}}*/ /*{{{ query2*/ int64 query2(int r, int L, int R, int dd) { dd += node[r].c; if (L <= node[r].L && node[r].R <= R) { return node[r].sum + (node[r].R - node[r].L + 1) * dd; } else { int res = 0; if (L <= node[2 * r].R) { res += query(2 * r, L, R); } if (R >= node[2 * r + 1].L) { res += query(2 * r + 1, L, R); } return res; } } /*}}}*/ }; int main() { int n, q; while (scanf("%d%d", &n, &q) != EOF) { SegTree tree; for (int i = 1; i <= n; i++) scanf("%d", &d[i]); tree.build(1, 1, n); while (q--) { char ch[2]; int a, b; scanf("%s%d%d", ch, &a, &b); if (ch[0] == 'C') { int c; scanf("%d", &c); tree.insert(1, a, b, c); //tree.insert2(1, a, b, c); } else if (ch[0] == 'Q') { printf("%lld\n", tree.query(1, a, b)); /* int dd = 0; printf("%lld\n", tree.query2(1, a, b, dd)); */ } } } }
需要注意的是：
1. 插入及查询在树上向下遍历时，不然是否有遍历，都应该将节点上的覆盖数目向下传递；
2. 树构建的时候，一些节点会构建不出来，这种类型的节点，在插入向孩子节点遍历的时候，之前判断失败的条件，可能会判断成功，从而导致错误；
3. 节点中的sum表示的是当前节点构成的树除了当前节点上的覆盖数以外的所有数的和。
#include <cstdio> #include <cstring> #include <iostream> #include <algorithm> using namespace std; typedef long long int64; class SegNode { public: int L, R, B, T; int64 v, m_min, m_max, m_sum; bool is_clear; SegNode* sons[4]; SegNode() { v = m_min = m_max = m_sum = 0; is_clear = false; memset(sons, NULL, sizeof(sons)); } int area() { return (R - L + 1) * (T - B + 1); } }; class SegTree { public: void free(SegNode *node) { for (int i = 0; i < 4; i++) { if (node->sons[i] != NULL) { free(node->sons[i]); } } if (node != NULL) { delete node; node = NULL; } } void build(SegNode* &node, int L, int R, int B, int T) { node = new SegNode(); node->L = L; node->R = R; node->B = B; node->T = T; if (L == R && B == T) { // leaf } else { // non leaf int M1 = (L + R) / 2; int M2 = (B + T) / 2; if (L <= M1 && M2 + 1 <= T) build(node->sons[0], L, M1, M2 + 1, T); if (M1 + 1 <= R && M2 + 1 <= T) build(node->sons[1], M1 + 1, R, M2 + 1, T); if (L <= M1 && B <= M2) build(node->sons[2], L, M1, B, M2); if (M1 + 1 <= R && B <= M2) build(node->sons[3], M1 + 1, R, B, M2); } } void insert(SegNode *node, int L, int R, int B, int T, int v, int k) { //node->log(); if (L <= node->L && node->R <= R && B <= node->B && node->T <= T) { if (k == 1) node->v += v; else if (k == 2) { node->v = v; node->m_min = node->m_max = node->m_sum = 0; node->is_clear = true; } } else { int M1 = (node->L + node->R) / 2; int M2 = (node->B + node->T) / 2; for (int i = 0; i < 4; i++) { if (node->sons[i] != NULL) { down(node, node->sons[i]); } } if (L <= M1 && T >= M2 + 1) { if (node->sons[0] != NULL) insert(node->sons[0], L, R, B, T, v, k); } if (R >= M1 + 1 && T >= M2 + 1) { if (node->sons[1] != NULL) insert(node->sons[1], L, R, B, T, v, k); } if (L <= M1 && B <= M2) { if (node->sons[2] != NULL) insert(node->sons[2], L, R, B, T, v, k); } if (R >= M1 + 1 && B <= M2) { if (node->sons[3] != NULL) insert(node->sons[3], L, R, B, T, v, k); } // clear node[r] node->is_clear = false; node->v = 0; update(node); } } void down(SegNode *r, SegNode *t) { r->is_clear; if (r->is_clear) { t->is_clear = true; t->v = r->v; // t->m_min = t->m_max = t->m_sum = 0; } else { t->v += r->v; } } void update(SegNode *r) { bool need = true; for (int i = 0; i < 4; i++) { if (r->sons[i] != NULL) { if (need) { need = false; r->m_min = r->sons[i]->m_min + r->sons[i]->v; r->m_max = r->sons[i]->m_max + r->sons[i]->v; r->m_sum = r->sons[i]->m_sum + r->sons[i]->v * r->sons[i]->area(); } else { r->m_min = min(r->m_min, r->sons[i]->m_min + r->sons[i]->v); r->m_max = max(r->m_max, r->sons[i]->m_max + r->sons[i]->v); r->m_sum += r->sons[i]->m_sum + r->sons[i]->v * r->sons[i]->area(); } } } } void query(SegNode *node, int L, int R, int B, int T, int64& mmin, int64& mmax, int64& msum) { //node->log(); if (L <= node->L && node->R <= R && B <= node->B && node->T <= T) { mmin = min(mmin, node->m_min + node->v); mmax = max(mmax, node->m_max + node->v); msum += node->m_sum + node->v * node->area(); } else { int M1 = (node->L + node->R) / 2; int M2 = (node->B + node->T) / 2; for (int i = 0; i < 4; i++) { if (node->sons[i] != NULL) { down(node, node->sons[i]); } } if (L <= M1 && T >= M2 + 1) { if (node->sons[0] != NULL) query(node->sons[0], L, R, B, T, mmin, mmax, msum); } if (R >= M1 + 1 && T >= M2 + 1) { if (node->sons[1] != NULL) query(node->sons[1], L, R, B, T, mmin, mmax, msum); } if (L <= M1 && B <= M2) { if (node->sons[2] != NULL) query(node->sons[2], L, R, B, T, mmin, mmax, msum); } if (R >= M1 + 1 && B <= M2) { if (node->sons[3] != NULL) query(node->sons[3], L, R, B, T, mmin, mmax, msum); } // clear node[r] node->is_clear = false; node->v = 0; update(node); } } }; int main() { //freopen("fast.in", "r", stdin); int r, c, m; while (scanf("%d%d%d", &r, &c, &m) != EOF) { SegTree tree; SegNode *root = NULL; tree.build(root, 1, r, 1, c); for (int i = 0; i < m; i++) { int k, x1, y1, x2, y2, v; scanf("%d%d%d%d%d", &k, &x1, &y1, &x2, &y2); if (k == 3) { int64 mmin = 1e9, mmax = -1e9, msum = 0; tree.query(root, x1, x2, y1, y2, mmin, mmax, msum); printf("%lld %lld %lld\n", msum, mmin, mmax); } else { scanf("%d", &v); tree.insert(root, x1, x2, y1, y2, v, k); } } tree.free(root); } }