Geiz-Revive > 洛谷-P4513-小白逛公园

洛谷-P4513-小白逛公园

2019-06-19

线段树

$\Large\color{violet}{Describe}$

颓完文化课回来做水题能愉悦身心

题意就是单点修改，区间最大子段和，硬上线段树即可，维护是经典方法，如果换成区间修改也是可以做的。有兴趣可以去做一做$GSS$系列的题，最大子段和是个经典模型，尽量要掌握。

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node operator +(const node &a, const node &b) {
	node c;
	c.tot = a.tot + b.tot;
	c.lsum = max(a.lsum, b.lsum + a.tot);
	c.rsum = max(b.rsum, a.rsum + b.tot);
	c.sum = max({ a.sum,b.sum,a.rsum + b.lsum });
	return c;
}

其中$tot$代表原数列中的值的和，$sum$是最大子段和，$lsum$是最大前缀和，$rsum$是最大后缀和，维护想一想应该就很显然了。

$\large Code:$

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#pragma region revive
#include <set>
#include <map>
#include <cmath>
#include <queue>
#include <stack>
#include <bitset>
#include <cstdio>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define inl inline
#define re register int
#define fa(x) t[x].fa
#define son(x,y) t[x].child[y]
#define ls(x) t[x].child[0]
#define rs(x) t[x].child[1]
#define ll long long
const int inf = 0x3f3f3f3f;
#define lowbit(x) ((x) & (-x))
using namespace std;
#ifndef _DEBUG
#define getchar() (*(IOB.in.p++))
#define putchar(c) (*(IOB.out.p++)=(c))
#define io_eof() (IOB.in.p>=IOB.in.pend)
struct IOBUF { struct { char buff[1 << 26], *p, *pend; }in; struct { char buff[1 << 26], *p; }out; IOBUF() { in.p = in.buff; out.p = out.buff; in.pend = in.buff + fread(in.buff, 1, 1 << 26, stdin); }~IOBUF() { fwrite(out.buff, 1, out.p - out.buff, stdout); } }IOB;
#endif
template<typename IO>
inl void write(IO x) {
	if (x == 0) return (void)putchar('0');
	if (x < 0)putchar('-'), x = -x;
	static char buf[30];
	char* p = buf;
	while (x) {
		*(p++) = x % 10 + '0';
		x /= 10;
	}
	while (p > buf)putchar(*(--p));
}
inl void writestr(const char *s) { while (*s != 0)putchar(*(s++)); }
template<typename IO>inl void writeln(IO x) { write(x), putchar('\n'); }
template<typename IO>inl void writesp(IO x) { write(x), putchar(' '); }
inl int readstr(char *s) {
	char *begin = s, c = getchar();
	while (c < 33 || c>127) {
		c = getchar();
	}
	while (c >= 33 && c <= 127) {
		*(s++) = c;
		c = getchar();
	}
	*s = 0;
	return s - begin;
}
template<typename IO>
inl IO read() {
	IO x = 0;
	register bool w = 0;
	register char c = getchar();
	while (c > '9' || c < '0') {
		if (c == '-') w = 1;
		c = getchar();
	}
	while (c >= '0' && c <= '9') {
		x = (x << 3) + (x << 1) + (c ^ 48);
		c = getchar();
	}
	return w ? -x : x;
}
#pragma endregion
#undef ls
#undef rs
#define ls(x) ((x)<<1)
#define rs(x) (ls(x)|1)
struct node {
	int lsum, rsum, sum, tot;
}t[10000001];
node operator +(const node &a, const node &b) {
	node c;
	c.tot = a.tot + b.tot;
	c.lsum = max(a.lsum, b.lsum + a.tot);
	c.rsum = max(b.rsum, a.rsum + b.tot);
	c.sum = max({ a.sum,b.sum,a.rsum + b.lsum });
	return c;
}
int a[1000001];
inl void maintain(int x) {
	t[x] = t[ls(x)] + t[rs(x)];
}
inl void change(int k, int l, int r, int p, int w) {
	if (l == r) return (void)(t[k].tot = t[k].sum = t[k].lsum = t[k].rsum = w);
	re mid = l + r >> 1;
	if (p <= mid)change(ls(k), l, mid, p, w);
	else change(rs(k), mid + 1, r, p, w);
	maintain(k);
}
inl void build(int k, int l, int r) {
	if (l == r) return (void)(t[k].tot = t[k].sum = t[k].lsum = t[k].rsum = a[l]);
	re mid = l + r >> 1;
	build(ls(k), l, mid), build(rs(k), mid + 1, r);
	maintain(k);
}
inl node query(int k, int l, int r, int x, int y) {
	if (l >= x && r <= y)return t[k];
	re mid = l + r >> 1;
	node ans = { 0,0,0,0 };
	if (x <= mid) {
		ans = query(ls(k), l, mid, x, y);
		if (y > mid)ans = ans + query(rs(k), mid + 1, r, x, y);
	}
	else if (y > mid)ans = query(rs(k), mid + 1, r, x, y);
	return ans;
}
signed main() {
	re n = read<int>(), m = read<int>(), op, x, y;
	for (re i = 1; i <= n; i++)a[i] = read<int>();
	build(1, 1, n);
	while (m--) {
		op = read<int>(), x = read<int>(), y = read<int>();
		if (op == 1) { if (x > y)swap(x, y); writeln(query(1, 1, n, x, y).sum); }
		else change(1, 1, n, x, y);
	}
}