E - Addition and Subtraction Hard AtCoder - 2273 思维观察题
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http://arc066.contest.atcoder.jp/tasks/arc066_c?lang=en
这类题目是我最怕的,没有什么算法,但是却很难想,
这题的题解是这样的,观察到,在+号里面添加括号是没用的,
那么看看减号,任意两个相邻减号,
比如1 - 20 + 8 - 13 - 5 + 6 + 7 - 8
可以变成1 - (20 + 8 - 13) + 5 + 6 + 7 + 8
为什么后面的可以全部都变成正数呢?
因为可以这样变,1 - (20 + 8 - 13 - (5 + 6 + 7) - 8)
所以,观察到,这个观察到,到底需要多大的脑洞呢?
暴力枚举任意一对相邻的减号,只有其里面包括的数字全部变成负数为代价,使得后面的数字全部变正。
暴力枚举即可。
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <assert.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;
#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
#include <bitset>
const int maxn = 1e5 + 20;
LL perfixSum[maxn], absSum[maxn];
vector<int>pos;
void cut(LL &val, int pos1, int pos2) {
if (pos1 > pos2) return;
val -= absSum[pos2] - absSum[pos1 - 1];
}
void work() {
int n;
scanf("%d", &n);
int val;
scanf("%d", &val);
perfixSum[1] = val;
absSum[1] = val;
for (int i = 2; i <= n; ++i) {
int val;
char op;
cin >> op;
scanf("%d", &val);
if (op == '+') {
perfixSum[i] = perfixSum[i - 1] + val;
} else {
perfixSum[i] = perfixSum[i - 1] - val;
pos.push_back(i);
}
absSum[i] = absSum[i - 1] + val;
}
LL ans = perfixSum[n];
for (int i = 0; i <= (int)pos.size() - 2; ++i) {
int p1 = pos[i], p2 = pos[i + 1];
LL tans = absSum[n] - absSum[p2 - 1];
tans += perfixSum[p1];
cut(tans, p1 + 1, p2 - 1);
ans = max(ans, tans);
}
cout << ans << endl;
}
int main() {
#ifdef local
freopen("data.txt", "r", stdin);
// freopen("data.txt", "w", stdout);
#endif
// int val;
// scanf("%d", &val);
// cout << val << endl;
work();
return 0;
}
View Code