题目描述

之前提到过，线段树之所以更新查询快，是因为区间更新有lazy标记使得不需要每次都操作到叶子节点。

但是如果要操作一个节点时，其父节点上的lazy标记应当被释放，否则该节点无法得到最新的正确结果。

因而lazy标记下放的策略是在需要操作某个节点的子节点时，将该节点的lazy标记全部下放。见第69行。

同时应当注意，给某个节点增加lazy标记时，不要忘了修改该节点的相关统计值。因为更新完该节点后还要马上修改其父节点的统计值。见第80行。

代码如下：

#include <stdio.h>#define N 100005
#define MODE_ADD 0
#define MODE_SET 1typedef
struct _seg_tree_ {int left, right;int add;int setv;int val;_seg_tree_ *lson = NULL, *rson = NULL;_seg_tree_(int left_idx, int right_idx, int value): left(left_idx), right(right_idx), add(0), setv(-1), val(value) {}
} seg_tree, *pseg_tree;pseg_tree construct_seg_tree(int left, int right) {if (left == right) {int val;scanf("%d", &val);return new seg_tree(left, right, val);}int mid = left + (right - left) / 2;pseg_tree lson = construct_seg_tree(left, mid);pseg_tree rson = construct_seg_tree(mid + 1, right);pseg_tree ans = new seg_tree(left, right, lson->val + rson->val);ans->lson = lson;ans->rson = rson;return ans;
}void lazy_down(pseg_tree proot) {if (proot->setv != -1) {if (proot->lson != NULL) {proot->lson->setv = proot->setv;proot->lson->add = 0;proot->lson->val = proot->setv * (proot->lson->right - proot->lson->left + 1);proot->rson->setv = proot->setv;proot->rson->add = 0;proot->rson->val = proot->setv * (proot->rson->right - proot->rson->left + 1);}proot->setv = -1;}if (proot->add != 0) {if (proot->lson != NULL) {proot->lson->add += proot->add;proot->rson->add += proot->add;proot->lson->val += proot->add * (proot->lson->right - proot->lson->left + 1);proot->rson->val += proot->add * (proot->rson->right - proot->rson->left + 1);}proot->add = 0;}
}void modify_seg_tree(pseg_tree proot, int left, int right, int val, int type) {if (left == proot->left && right == proot->right) {if (type == MODE_ADD) {proot->add += val;proot->val += val * (right - left + 1);} else {proot->setv = val;proot->val = val * (right - left + 1);proot->add = 0;}return;}int mid = proot->left + (proot->right - proot->left) / 2;lazy_down(proot);if (left > mid) {modify_seg_tree(proot->rson, left, right, val, type);}else if (right <= mid) {modify_seg_tree(proot->lson, left, right, val, type);}else {modify_seg_tree(proot->rson, mid + 1, right, val, type);modify_seg_tree(proot->lson, left, mid, val, type);}proot->val = proot->lson->val + proot->rson->val;
}int main(){int n, m;scanf("%d%d", &n, &m);pseg_tree proot = construct_seg_tree(0, n);int type, left, right, val;for (int i = 0; i < m; i++) {scanf("%d%d%d%d", &type, &left, &right, &val);modify_seg_tree(proot, left, right, val, type);printf("%d\n", proot->val);}return 0;
}