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线段树的实现是解决区间查询和点更新问题的高效数据结构。以下是对问题的详细解答和代码实现。
我们需要处理两个主要操作:区间查询最高分和点更新分数。线段树能够在O(logN)的时间复杂度内完成这些操作,适用于大量数据的情况。
#include#include using namespace std;int arr[200005];int tree[400002]; // 线段树大小为4*nvoid build_tree(int arr[], int tree[], int node, int start, int end) { if (start == end) { tree[node] = arr[start]; } else { int mid = (start + end) / 2; int left_node = 2 * node + 1; int right_node = 2 * node + 2; build_tree(arr, tree, left_node, start, mid); build_tree(arr, tree, right_node, mid + 1, end); tree[node] = max(tree[left_node], tree[right_node]); }}void update_tree(int arr[], int tree[], int node, int start, int end, int idx, int val) { if (start == end) { arr[idx] = val; tree[node] = val; } else { int mid = (start + end) / 2; int left_node = 2 * node + 1; int right_node = 2 * node + 2; if (idx <= mid) { update_tree(arr, tree, left_node, start, mid, idx, val); } else { update_tree(arr, tree, right_node, mid + 1, end, idx, val); } tree[node] = max(tree[left_node], tree[right_node]); }}int query_tree(int arr[], int tree[], int node, int start, int end, int L, int R) { if (R < start || L > end) { return 0; } else if (L <= start && end <= R) { return tree[node]; } else { if (start == end) { return tree[node]; } else { int mid = (start + end) / 2; int left_node = 2 * node + 1; int right_node = 2 * node + 2; int max_left = query_tree(arr, tree, left_node, start, mid, L, R); int max_right = query_tree(arr, tree, right_node, mid + 1, end, L, R); return max(max_left, max_right); } }}int main() { int n, m; while (scanf("%d %d", &n, &m) != EOF) { for (int i = 0; i < n; ++i) { scanf("%d", &arr[i]); } build_tree(arr, tree, 0, 0, n - 1); for (int i = 0; i < m; ++i) { char op; int a, b; scanf("%c %d %d", &op, &a, &b); if (op == 'U') { update_tree(arr, tree, 0, 0, n - 1, a - 1, b); } else if (op == 'Q') { int res = query_tree(arr, tree, 0, 0, n - 1, a - 1, b - 1); cout << res << endl; } } }}
build_tree函数递归地构建线段树,每个节点存储其区间内的最大值。update_tree函数递归地更新某个位置的值,并更新路径上的所有相关节点。query_tree函数递归地查询区间内的最大值,返回结果。这种实现能够高效处理大量的区间查询和点更新操作,适用于大规模数据处理。
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