关于线段树的原理在此不赘述，可参考：https://www.cnblogs.com/AC-King/p/7789013.html
此处用结构体的线段树
一、建树模板：
#define MID(l, r) ((l) + ((r) - (l)) / 2)
#define lson(o) ((o)<<1)
#define rson(o) ((o)<<1|1)
1 int a[maxn]; 2 struct node 3 { 4 int l, r, mmax, mmin, sum; 5 }tree[maxn]; 6 void build(int o, int l, int r) 7 { 8 tree[o].l = l, tree[o].r = r; 9 if(l == r) 10 { 11 tree[o].mmax = tree[o].mmin = tree[o].sum = a[l]; 12 return; 13 } 14 int m = MID(l, r); 15 int lc = lson(o), rc = rson(o); 16 build(lc, l, m); 17 build(rc, m + 1, r); 18 tree[o].mmax = max(tree[lc].mmax, tree[rc].mmax); 19 tree[o].mmin = min(tree[lc].mmin, tree[rc].mmin); 20 tree[o].sum = tree[lc].sum + tree[rc].sum; 21 }
二、查询区间[ql, qr]中的max,min,sum
1 int ql, qr;//查询区间[ql, qr]中的max,min,sum 2 int ans_max, ans_min, ans_sum; 3 void query_init()//查询前，将全局变量初始化 4 { 5 ans_max = -INF; 6 ans_min = INF; 7 ans_sum = 0; 8 } 9 void query(int o) 10 { 11 if(ql <= tree[o].l && qr >= tree[o].r)//[L, R]包含在[ql, qr]区间内，直接用该节点的信息，达到线段树查询快的操作 12 { 13 ans_max = max(ans_max, tree[o].mmax); 14 ans_min = min(ans_min, tree[o].mmin); 15 ans_sum += tree[o].sum; 16 return; 17 } 18 int m = MID(tree[o].l, tree[o].r); 19 if(ql <= m)query(lson(o)); 20 if(qr > m)query(rson(o)); 21 }
三、单点更新，a[p] += v
如果需要更新成a[p] = v，把下面的+=换成=即可
1 //单点更新，a[p] += v; 2 int p, v; 3 void update(int o) 4 { 5 if(tree[o].l == tree[o].r) 6 { 7 tree[o].mmax += v; 8 tree[o].mmin += v; 9 tree[o].sum += v; 10 return; 11 } 12 int m = MID(tree[o].l, tree[o].r); 13 int lc = lson(o), rc = rson(o); 14 if(p <= m)update(lc); 15 else update(rc); 16 tree[o].mmax = max(tree[lc].mmax, tree[rc].mmax); 17 tree[o].mmin = min(tree[lc].mmin, tree[rc].mmin); 18 tree[o].sum = tree[lc].sum + tree[rc].sum; 19 }
四、综上所述
注意开4倍区间
#define MID(l, r) ((l) + ((r) - (l)) / 2)
#define lson(o) ((o)<<1)
#define rson(o) ((o)<<1|1)
1 int a[maxn]; 2 struct node 3 { 4 int l, r, mmax, mmin, sum; 5 }tree[maxn]; 6 void build(int o, int l, int r) 7 { 8 tree[o].l = l, tree[o].r = r; 9 if(l == r) 10 { 11 tree[o].mmax = tree[o].mmin = tree[o].sum = a[l]; 12 return; 13 } 14 int m = MID(l, r); 15 int lc = lson(o), rc = rson(o); 16 build(lc, l, m); 17 build(rc, m + 1, r); 18 tree[o].mmax = max(tree[lc].mmax, tree[rc].mmax); 19 tree[o].mmin = min(tree[lc].mmin, tree[rc].mmin); 20 tree[o].sum = tree[lc].sum + tree[rc].sum; 21 } 22 int ql, qr;//查询区间[ql, qr]中的max,min,sum 23 int ans_max, ans_min, ans_sum; 24 void query_init()//查询前，将全局变量初始化 25 { 26 ans_max = -INF; 27 ans_min = INF; 28 ans_sum = 0; 29 } 30 void query(int o) 31 { 32 if(ql <= tree[o].l && qr >= tree[o].r)//[L, R]包含在[ql, qr]区间内，直接用该节点的信息，达到线段树查询快的操作 33 { 34 ans_max = max(ans_max, tree[o].mmax); 35 ans_min = min(ans_min, tree[o].mmin); 36 ans_sum += tree[o].sum; 37 return; 38 } 39 int m = MID(tree[o].l, tree[o].r); 40 if(ql <= m)query(lson(o)); 41 if(qr > m)query(rson(o)); 42 } 43 //单点更新，a[p] += v; 44 int p, v; 45 void update(int o) 46 { 47 if(tree[o].l == tree[o].r) 48 { 49 tree[o].mmax += v; 50 tree[o].mmin += v; 51 tree[o].sum += v; 52 return; 53 } 54 int m = MID(tree[o].l, tree[o].r); 55 int lc = lson(o), rc = rson(o); 56 if(p <= m)update(lc); 57 else update(rc); 58 tree[o].mmax = max(tree[lc].mmax, tree[rc].mmax); 59 tree[o].mmin = min(tree[lc].mmin, tree[rc].mmin); 60 tree[o].sum = tree[lc].sum + tree[rc].sum; 61 }