线段树

一、线段树建树、单点修改、区间查询

#include <cstdio>
const int MAXN = 10005;
int arr[MAXN] = {1, 3, 5, 7, 9, 11}, tree[MAXN];//arr表示原数组，tree表示线段树数组 
void build_tree(int node, int start, int end) {//建树，node表示当前节点，[start，end]表示node在arr数组内的区间 
    if (start == end) {
        tree[node] = arr[start];
        return;
    }
    int mid = (start + end) / 2;
    int left_node = node * 2 + 1;//左儿子节点编号 
    int right_node = node * 2 + 2;//有儿子节点编号 
    build_tree(left_node, start, mid);//构建node节点的左子树 
    build_tree(right_node, mid + 1, end);//构建node节点的右子树 
    tree[node] = tree[left_node] + tree[right_node];     
}
void update_tree(int node, int start, int end, int idx, int val) {//修改线段树上的值，idx表示修改的下标，val表示修改的值 
    if (start == end) {
        tree[node] = arr[idx] = val;
        return;
    }
    int mid = (start + end) / 2;
    int left_node = node * 2 + 1;
    int right_node = node * 2 + 2;
    if (idx <= mid) {//判断idx是在左子树上还是右子树上 
        update_tree(left_node, start, mid, idx, val);
    } else {
        update_tree(right_node, mid + 1, end, idx, val);
    }
    tree[node] = tree[left_node] + tree[right_node];
}
int query_tree(int node, int start, int end, int L, int R) {//查询[L, R]区间上的值 
    //printf("%d %d", start, end);
    if (end < L || start > R) {//当前节点表示的区间不在节点范围内 
        return 0;
    } else if (start == end || (L <= start && end <= R)) {//剪枝 
        return tree[node];
    }
    int mid = (start + end) / 2;
    int left_node = node * 2 + 1; 
    int right_node = node * 2 + 2;
    int left_sum = query_tree(left_node, start, mid, L, R);//左子树和 
    int right_sum = query_tree(right_node, mid + 1, end, L, R);//右子树和 
    //printf("%d %d %d\n", start, end, left_sum + right_sum);
    return left_sum + right_sum;
}
int main() {
    build_tree(0, 0, 5);
    for (int i = 0; i < 15; i++) {
        printf("%d ", tree[i]);
    }
    printf("\n");
    /*update_tree(arr, tree, 0, 0, 5, 1, 2);
    for (int i = 0; i < 15; i++) {
        printf("%d ", tree[i]);
    }*/
    printf("%d", query_tree(0, 0, 5, 0, 0));
    return 0;
}

二、线段树建树、区间修改、区间查询

#include <cstdio>
typedef long long ll;
const int MAXN = 1e6 + 5;
ll tree[MAXN << 2], tag[MAXN << 2], a[MAXN], tot;
void pushUp(ll k) {  //向上传递左子树和右子树数字之和
    tree[k] = tree[k << 1] + tree[k << 1 | 1];
}
void buildTree(ll left, ll right, ll k) {  //建立线段树
    if (left == right) {
        tree[k] = a[++tot];
        return;
    }
    ll mid = (left + right) >> 1;
    buildTree(left, mid, k << 1);
    buildTree(mid + 1, right, k << 1 | 1);
    pushUp(k);
}
void pushDown(ll left, ll right, ll k) {  //向下传递延迟标记
    if (tag[k] != 0) {
        ll mid = (left + right) >> 1;
        tree[k << 1] += (mid - left + 1) * tag[k];
        tree[k << 1 | 1] += (right - mid) * tag[k];
        tag[k << 1] += tag[k];
        tag[k << 1 | 1] += tag[k];
        tag[k] = 0;
        pushUp(k);
    }
}
void upData(ll left, ll right, ll L, ll R, ll k, ll val) {
    if (L <= left && right <= R) {
        tree[k] += (right - left + 1) * val;
        tag[k] += val;
        return;
    }
    ll mid = (left + right) >> 1;
    pushDown(left, right, k);
    if (mid >= L) {
        upData(left, mid, L, R, k << 1, val);
    }
    if (mid < R) {
        upData(mid + 1, right, L, R, k << 1 | 1, val);
    }
    pushUp(k);
}
ll query(ll left, ll right, ll L, ll R, ll k) {
    if (L <= left && right <= R) {
        return tree[k];
    }
    pushDown(left, right, k);
    ll mid = (left + right) >> 1, sum = 0;
    if (mid >= L) {
        sum += query(left, mid, L, R, k << 1);
    }
    if (mid < R) {
        sum += query(mid + 1, right, L, R, k << 1 | 1);
    }
    pushUp(k);
    return sum;
}
int main() {
    ll n, q, l, r, x, flag;
    scanf("%lld %lld", &n, &q);
    for (int i = 1; i <= n; i++) {
        scanf("%lld", &a[i]);
    }
    buildTree(1, n, 1);
    for (int i = 1; i <= q; i++) {
        scanf("%lld", &flag);
        if (flag == 1) {
            scanf("%lld %lld %lld", &l, &r, &x);
            upData(1, n, l, r, 1, x);
        } else {
            scanf("%lld %lld", &l, &r);
            printf("%lld\n", query(1, n, l, r, 1));
        }
    }
    return 0;
}