CS Academy Switch the Lights

题目链接：https://csacademy.com/contest/archive/task/switch-the-lights/statement/

题目大意：有N盏灯，0表示灯是灭的，1表示灯亮。每盏灯i操作一次可以更改第i到r[i]盏灯的状态，每个灯的操作花费为C[i].问最小花费。

解题思路：首先我们很快就会发现实际上由于第i盏灯不会影响到之前的灯，因此我们只需要从头到尾判断每盏灯的状态，但是问题在于如何计算一盏灯之前有多少盏灯会影响到这盏灯（editorial里面有solution的）。

朴素的想法就是O(n²)，但是仔细思考一下：我们设置一个全局计数器cnt，每次更改灯 i 的状态时cnt++，到达这个灯i的 r[i] 的时候cnt--，那么就可以保证对于一盏灯来说，能够影响它的即是全局计数器的值。那么我们可以用一个数组sum[i]记录这个灯之前，以i为结束的灯的个数。那么对于灯i：

如果 cnt 为奇数并且 a[i] == 0 或者 cnt 为偶数并且 a[i] == 1，那么需要更新这个灯，cnt++，sum[r[i]]++

然后cnt -= sum[i] ，表示有sum[i]个灯到这个点不再对后续灯产生影响

代码：

 1 const int maxn = 1e5 + 10;
 2 int n;
 3 int a[maxn];
 4 int r[maxn], c[maxn];
 5 int sum[maxn];
 6 
 7 void solve(){
 8     memset(sum, 0, sizeof(sum)); 
 9     ll ans = 0;
10     int v = 0;
11     for(int i = 1; i <= n; i++){
12         if((v & 1) && (a[i]) == 0 || !(v & 1) && (a[i] == 1)){
13             ans += c[i];
14             v++;
15             sum[r[i]]++;
16         }
17         v -= sum[i];
18     }
19     printf("%lld\n", ans);
20 }
21 int main(){
22     scanf("%d", &n);
23     for(int i = 1; i <= n; i++){
24         char ch;
25         scanf(" %c", &ch);
26         a[i] = ch == '0'? 0: 1;
27     }
28     for(int i = 1; i <= n; i++) scanf("%d", &r[i]);
29     for(int i = 1; i <= n; i++) scanf("%d", &c[i]);
30     solve();
31 }

题目：

Switch the Lights

Time limit: 1000 ms
Memory limit: 128 MB

There are

There are also $i^{th}ith switch toggles the state of all the lightbulbs between ii and R_iRi, and it costs C_iCi to use it.$

Find the minimum total cost of switching off all the lightbulbs.

Standard input

The first line contains a single integer

The second line contains a string of length $i^{th}ith character of the string is 0 if initially the i^{th}ith lightbulb is turned off, and 1 if it's turned on.$

The third line contains

The fourth line contains

Standard output

If there is no solution output

Otherwise, print the answer on the first line.

Constraints and notes

$\leq N \leq 10^51≤N≤105$
$\leq R_i \leq Ni≤Ri≤N$
$\leq C_i \leq 10^91≤Ci≤109$

Input	Output	Explanation
4 1010 2 3 3 4 3 1 2 3	4	`1010` Initial state of the lightbulbs `1100` After toggling the $2\text{ and }32 and 3 (cost 11)$ `0000` After toggling the $1\text{ and }21 and 2 (cost 33)$
5 01100 1 2 3 4 5 1 5 5 2 3	10	`01100` Initial state of the lightbulbs `00100` After toggling the `00000` After toggling the
4 0101 3 4 3 4 1 1 1 1	2	`0101` Initial state of the lightbulbs `0111` After toggling the `0000` After toggling the $2\text{, }3\text{ and } 42, 3 and 4 (cost 11)$

posted @ 2017-09-02 22:03 EricJeffrey 阅读(324) 评论(0) 编辑收藏举报

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EricJeffrey

CS Academy Switch the Lights

Switch the Lights

Standard input

Standard output

Constraints and notes

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