Uva11992-Fast Matrix Operations (line segment tree interval modification)

Uva11992-Fast Matrix Operations (line segment tree interval modification)

Question Link

Give you a r * C matrix, initialized to 0.
Three operations are provided:
1x1, Y1, X2, Y2, and V add V to each element in the Child matrix consisting of X1, Y1, X2, and Y2.
2x1, Y1, X2, Y2, and V change each element of the Child matrix to v.
3x1, Y1, X2, Y2 queries the sum of the elements of the child matrix and the maximum and minimum values of these elements.

Solution: Because the matrix has a maximum of 20 rows, you can build a line segment tree with the elements of this matrix. Each node has three additional information: Sum, max_num, and min_num. then, when you modify the query, it will be done in each row. Note: during each set operation, the add of the node should be cleared, because the add operation is unnecessary. Then, each Pushdown operation must first process set and then add. Pushdown processes the subnode of the node, and then update the additional information of the node through pushup.

Code:

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;#define lson(x) ((x)<<1)#define rson(x) (((x)<<1) + 1)const int N = 1e6 + 5;const int INF = 0x3f3f3f3f;struct Item {    int sum, Max_num, Min_num;    Item (int sum = 0, int Max_num = -INF, int Min_num = INF) {        this->set(sum, Max_num, Min_num);    }    void set (int sum, int Max_num, int Min_num) {        this->sum = sum;        this->Max_num = Max_num;        this->Min_num  = Min_num;    }};struct Node {    Item v;    int l, r;    int addv, setv;    void set (int l, int r, int addv = 0, int setv = -1) {        this->l = l;        this->r = r;        this->addv = addv;        this->setv = setv;        }}node[4 * N];Item get_item (Item a, Item b) {    return Item(a.sum + b.sum, max(a.Max_num, b.Max_num), min(a.Min_num, b.Min_num));}void Node_add(int u, int addv) {    node[u].addv += addv;    node[u].v.sum += addv * (node[u].r - node[u].l + 1);    node[u].v.Max_num += addv;    node[u].v.Min_num += addv;}void Node_set(int u, int setv) {    node[u].setv = setv;    node[u].addv = 0;    node[u].v.sum = setv * (node[u].r - node[u].l + 1);    node[u].v.Max_num = node[u].v.Min_num = setv;}void pushup (int u) {    node[u].set(node[lson(u)].l, node[rson(u)].r);    node[u].v = get_item(node[lson(u)].v, node[rson(u)].v);}void pushdown(int u) {    if (node[u].setv >= 0) {        Node_set(lson(u), node[u].setv);        Node_set(rson(u), node[u].setv);        node[u].setv = -1;    }    if (node[u].addv) {        Node_add(lson(u), node[u].addv);        Node_add(rson(u), node[u].addv);        node[u].addv = 0;        }}void Build (int u, int l, int r) {    if (l == r) {         node[u].set(l, r);        node[u].v.set(0, 0, 0);    } else {        int m = (l + r) / 2;        Build(lson(u), l, m);        Build(rson(u), m + 1, r);        pushup(u);    }}void Add (int u, int l, int r, int addv) {    if (node[u].l >= l && node[u].r <= r)        Node_add(u, addv);    else {        pushdown(u);        int m = (node[u].l + node[u].r) / 2;        if (l <= m)            Add (lson(u), l, r, addv);        if (r > m)            Add (rson(u), l, r, addv);        pushup(u);    }}void Set (int u, int l, int r, int setv) {    if (node[u].l >= l && node[u].r <= r)        Node_set(u, setv);    else {        pushdown(u);        int m = (node[u].l + node[u].r) / 2;        if (l <= m)            Set (lson(u), l, r, setv);        if (r > m)            Set (rson(u), l, r, setv);        pushup(u);    }}Item Query (int u, int l, int r) {    if (node[u].l >= l && node[u].r <= r)         return node[u].v;    else {        Item ans;        pushdown(u);        int m = (node[u].l + node[u].r) / 2;        if (l <= m)            ans = get_item (ans, Query(lson(u), l, r));        if (r > m)            ans = get_item (ans, Query(rson(u), l, r));            pushup(u);        return ans;    }}int main () {    int r, c, m;    int type;    int x1, y1, x2, y2, v;    while (scanf ("%d%d%d", &r, &c, &m) != EOF) {        Build(1, 1, r * c);        while (m--) {            scanf ("%d", &type);            if (type == 1) {                scanf ("%d%d%d%d%d", &x1, &y1, &x2, &y2, &v);                for (int i = x1 - 1; i < x2; i++)                    Add(1, i * c + y1, i * c + y2, v);            } else if (type == 2) {                scanf ("%d%d%d%d%d", &x1, &y1, &x2, &y2, &v);                for (int i = x1 - 1; i < x2; i++)                    Set(1, i * c + y1, i * c + y2, v);            } else {                scanf ("%d%d%d%d", &x1, &y1, &x2, &y2);                Item ans;                for (int i = x1 - 1; i < x2; i++)                    ans = get_item(ans, Query(1, i * c + y1, i * c + y2));                printf ("%d %d %d\n", ans.sum, ans.Min_num, ans.Max_num);            }        }    }    return 0;}

Uva11992-Fast Matrix Operations (line segment tree interval modification)