11/8
16:25
线段树(Segment Tree)是一种数据结构,它支持区间最大值、最小值以及区间和的查询的修改操作,时间复杂度O(nlogn)。
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#include <cstdio> #include <iostream> #include <cstring> #include <algorithm> using namespace std; typedef long long LL; const int maxn = 100005; int n, m, x, y, opt = 0; LL z; LL a[maxn]; struct Segment_Tree { LL l, r, sum, max_val, min_val, tag; } tree[maxn << 4]; inline int getint() { int r = 0, k = 1; char c = getchar(); for(; c < '0' || c > '9'; c = getchar()) if(c == '-') k = -1; for(; c >= '0' && c <= '9'; c = getchar()) r = r * 10 + c - '0'; return r * k; } inline LL getll() { LL r = 0, k = 1; char c = getchar(); for(; c < '0' || c > '9'; c = getchar()) if(c == '-') k = -1; for(; c >= '0' && c <= '9'; c = getchar()) r = r * 10 + c - '0'; return r * k; } void push_up(int now) { tree[now].sum = tree[now << 1].sum + tree[now << 1 | 1].sum; tree[now].max_val = max(tree[now << 1].max_val, tree[now << 1 | 1].max_val); tree[now].min_val = min(tree[now << 1].min_val, tree[now << 1 | 1].min_val); return; } void push_down(int now) { tree[now << 1].tag += tree[now].tag; tree[now << 1].sum += tree[now].tag * (tree[now << 1].r - tree[now << 1].l + 1); tree[now << 1].max_val += tree[now].tag; tree[now << 1].min_val += tree[now].tag; tree[now << 1 | 1].tag += tree[now].tag; tree[now << 1 | 1].sum += tree[now].tag * (tree[now << 1 | 1].r - tree[now << 1 | 1].l + 1); tree[now << 1 | 1].max_val += tree[now].tag; tree[now << 1 | 1].min_val += tree[now].tag; tree[now].tag = 0; return; } void build(int now, int l, int r) { tree[now].l = l; tree[now].r = r; tree[now].tag = 0; if(l == r) { tree[now].sum = tree[now].max_val = tree[now].min_val = a[l]; return; } int mid = (tree[now].l + tree[now].r) >> 1; build(now << 1, l, mid); build(now << 1 | 1, mid + 1, r); push_up(now); return; } void update(int now, int ll, int rr, LL x) { if(ll <= tree[now].l && tree[now].r <= rr) { tree[now].tag += x; tree[now].sum += x * (tree[now].r - tree[now].l + 1); tree[now].max_val += x; tree[now].min_val += x; return; } push_down(now); int mid = (tree[now].l + tree[now].r) >> 1; if(rr <= mid) update(now << 1, ll, rr, x); else if(ll > mid) update(now << 1 | 1, ll, rr, x); else { update(now << 1, ll, mid, x); update(now << 1 | 1, mid + 1, rr, x); } push_up(now); return; } LL query_sum(int now, int ll, int rr) { if(ll <= tree[now].l && tree[now].r <= rr) return tree[now].sum; push_down(now); int mid = (tree[now].l + tree[now].r) >> 1; if(rr <= mid) return query_sum(now << 1, ll, rr); else if(ll > mid) return query_sum(now << 1 | 1, ll, rr); else return (query_sum(now << 1, ll, mid) + query_sum(now << 1 | 1, mid + 1, rr)); } LL query_max(int now, int ll, int rr) { if(ll <= tree[now].l && tree[now].r <= rr) return tree[now].max_val; push_down(now); int mid = (tree[now].l + tree[now].r) >> 1; if(rr <= mid) return query_max(now << 1, ll, rr); else if(ll > mid) return query_max(now << 1 | 1, ll, rr); else return max(query_max(now << 1, ll, mid), query_max(now << 1 | 1, mid + 1, rr)); } LL query_min(int now, int ll, int rr) { if(ll <= tree[now].l && tree[now].r <= rr) return tree[now].max_val; push_down(now); int mid = (tree[now].l + tree[now].r) >> 1; if(rr <= mid) return query_min(now << 1, ll, rr); else if(ll > mid) return query_min(now << 1 | 1, ll, rr); else return min(query_min(now << 1, ll, mid), query_min(now << 1 | 1, mid + 1, rr)); } int main(int argc, char const * argv[]) { ios :: sync_with_stdio(false); n = getint(); m = getint(); for(int i = 1; i <= n; i++) a[i] = getll(); build(1, 1, n); while(m--) { opt = getint(); x = getint(); y = getint(); if(opt == 1) { z = getll(); update(1, x, y, z); } else if(opt == 2) { printf("%lld\n", query_sum(1, x, y)); } } return 0; } |
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