C - Social Distance CodeForces - 1367C
C - Social Distance
CodeForces - 1367C
题目大意
有t组测试案例 ，输入n和k，n是桌子的数量，k是餐厅规定的每两个人之间的桌子数量，以字符串为例，n=8，k=2，字符串“10010000” 那么在满足餐厅规定的前提下可以占用一张桌子使其变成“10010010”，现在目的是找到满足餐厅规定下最多可以占用桌子的数量是多少？
思路
首先我们可以思考每两个1之间需要有k个0，那么我们可以从数组1的位置开始遍历，如果这个数是‘1’，那么它后面至少应该有k个‘0’，要在满足后面k个位置都是0的基础上，然后再继续从这个数组的位置加上k在加上1的位置开始遍历，如果这个位置的数为‘0’，那么可以把‘0’，换成‘1’，然后继续上面的操作。
代码如下
#include
using namespace std;
const int N=2e5+5;
char a[N];
int main()
{
int t,n,k;
scanf("%d\n",&t);
while(t--)
{
scanf("%d%d\n",&n,&k);
gets(a); //输入字符串
int c=0,d,j;
for(int i=0; i 原题内容
Polycarp and his friends want to visit a new restaurant. The restaurant has n tables arranged along a straight line. People are already sitting at some tables. The tables are numbered from 1 to n in the order from left to right. The state of the restaurant is described by a string of length n which contains characters “1” (the table is occupied) and “0” (the table is empty).
Restaurant rules prohibit people to sit at a distance of k or less from each other. That is, if a person sits at the table number i, then all tables with numbers from i−k to i+k (except for the i-th) should be free. In other words, the absolute difference of the numbers of any two occupied tables must be strictly greater than k.
For example, if n=8 and k=2, then:
strings “10010001”, “10000010”, “00000000”, “00100000” satisfy the rules of the restaurant;
strings “10100100”, “10011001”, “11111111” do not satisfy to the rules of the restaurant, since each of them has a pair of “1” with a distance less than or equal to k=2.
In particular, if the state of the restaurant is described by a string without “1” or a string with one “1”, then the requirement of the restaurant is satisfied.
You are given a binary string s that describes the current state of the restaurant. It is guaranteed that the rules of the restaurant are satisfied for the string s.
Find the maximum number of free tables that you can occupy so as not to violate the rules of the restaurant. Formally, what is the maximum number of “0” that can be replaced by “1” such that the requirement will still be satisfied?
For example, if n=6, k=1, s= “100010”, then the answer to the problem will be 1, since only the table at position 3 can be occupied such that the rules are still satisfied.
Input
The first line contains a single integer t (1≤t≤104) — the number of test cases in the test. Then t test cases follow.
Each test case starts with a line containing two integers n and k (1≤k≤n≤2⋅105) — the number of tables in the restaurant and the minimum allowed distance between two people.
The second line of each test case contains a binary string s of length n consisting of “0” and “1” — a description of the free and occupied tables in the restaurant. The given string satisfy to the rules of the restaurant — the difference between indices of any two “1” is more than k.
The sum of n for all test cases in one test does not exceed 2⋅105.
Output
For each test case output one integer — the number of tables that you can occupy so as not to violate the rules of the restaurant. If additional tables cannot be taken, then, obviously, you need to output 0.
Example
Input
6
6 1
100010
6 2
000000
5 1
10101
3 1
001
2 2
00
1 1
0
Output
1
2
0
1
1
1
Note
The first test case is explained in the statement.
In the second test case, the answer is 2, since you can choose the first and the sixth table.
In the third test case, you cannot take any free table without violating the rules of the restaurant.