本专题总结了线段树的各种应用，参考了胡浩大佬的文章，把代码全部改成了自己的风格。
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功能:单点增减，区间求和
参考例题为HDU1166 敌兵布阵
https://vjudge.net/problem/HDU-1166
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <queue>
#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
const int maxn = 54321;
int sum[maxn << 2];
void pushUp(int root) {
sum[root] = sum[root << 1] + sum[root << 1 | 1];
}
void build(int left, int right, int root) {
if (left == right) {
cin >> sum[root];
return;
}
int mid = (left + right) >> 1;
build(left, mid, root << 1);
build(mid + 1, right, root << 1 | 1);
pushUp(root);
}
void update(int pos, int add, int left, int right, int root) {
if (left == right) {
sum[root] += add;
return;
}
int mid = (left + right) >> 1;
if (pos <= mid) update(pos, add, left, mid, root << 1);
else update(pos, add, mid+1, right, root << 1 | 1);
pushUp(root);
}
int query(int L, int R, int left, int right, int root) {
if (L <= left && right <= R) {
return sum[root];
}
int mid = (left + right) >> 1;
int res = 0;
if(L<=mid) res += query(L, R, left, mid, root << 1);
if(R > mid) res += query(L, R, mid + 1, right, root << 1 | 1);
return res;
}
int main() {
int T, n;
scanf("%d", &T);
for (int cas = 1; cas <= T; cas++) {
printf("Case %d:\n", cas);
scanf("%d", &n);
build(1, n, 1);
char op[10];
while (scanf("%s", op)) {
if (op[0] == 'E') break;
int a, b;
scanf("%d%d", &a, &b);
if (op[0] == 'Q') printf("%d\n", query(a, b, 1, n, 1));
else if (op[0] == 'S') update(a, -b, 1, n, 1);
else update(a, b, 1, n, 1);
}
}
return 0;
}
-
功能：单点替换，求区间最值
题目为HDU1754
https://vjudge.net/problem/HDU-1754
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
const int maxn = 224321;
int Max[maxn << 2];
void pushUp(int root) {
Max[root] = max(Max[root << 1] , Max[root << 1 | 1]);
}
void build(int left, int right, int root) {
if (left == right) {
cin >> Max[root];
return;
}
int mid = (left + right) >> 1;
build(left, mid, root << 1);
build(mid + 1, right, root << 1 | 1);
pushUp(root);
}
void update(int pos, int change, int left, int right, int root) {
if (left == right) {
Max[root] = change;
return;
}
int mid = (left + right) / 2;
if (pos <= mid) update(pos, change, left, mid, root << 1);
else update(pos, change, mid + 1, right, root << 1 | 1);
pushUp(root);
}
int query(int L,int R,int left,int right,int root) {
if (L <= left && right <= R) {
return Max[root];
}
int mid = (left + right) / 2;
int res = 0;
if (L <= mid) res = max(res, query(L, R, left, mid, root << 1));
if (R > mid) res = max(res, query(L, R, mid + 1, right, root << 1 | 1));
return res;
}
int main() {
int n, m;
while (~scanf("%d%d", &n, &m)) {
build(1, n, 1);
while (m--) {
char op[2];
int a, b;
scanf("%s%d%d", op, &a, &b);
if (op[0] == 'Q') printf("%d\n", query(a, b, 1, n, 1));
else update(a, b, 1, n, 1);
}
}
return 0;
}
- 例题HDU2795(注意输入要用c语言才不会超时）
https://vjudge.net/problem/HDU-2795
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
const int maxn = 224321;
int Max[maxn << 2];
int h, w, n;
void pushUp(int root) {
Max[root] = max(Max[root << 1] , Max[root << 1 | 1]);
}
void build(int left, int right, int root) {
Max[root] = w;
if (left == right) return;
int mid = (left + right) >> 1;
build(left, mid, root << 1);
build(mid + 1, right, root << 1 | 1);
}
int query(int x, int l, int r, int root) {
if (l == r) {
Max[root] -= x;
return l;
}
int mid = (l + r) >> 1;
int ret = (Max[root << 1] >= x) ? query(x, l,mid,root<<1) : query(x, mid+1, r, root<<1|1);
pushUp(root);
return ret;
}
int main() {
while (~scanf("%d%d%d", &h, &w, &n)) {
if (h > n) h = n;
build(1, h, 1);
while (n--) {
int x;
scanf("%d", &x);
if (Max[1] < x) puts("-1");
else printf("%d\n", query(x, 1, h, 1));
}
}
return 0;
}
