【CF1774C】Ice and Fire (Construction, DP)

[Title description]
There are $n$ person, the$i$ person's temperature is$i$ .
Environment type is$0$ or$1$ , if the environment is$0$ , the person with the lower temperature wins, if the condition is$1$ , the person with the highest temperature wins,$n-1$ environment type forms a length$n-$The binary string ssof$1$$s$ .
If$x$ people participate in the game, then there are$x-1$ battle, environment type isssthe first x of$s$$x-1$ element. where there are not less than$When\; there\; are\; 2$ people, choose$2$ people fight, of which$The\; environment\; type\; of\; the\; i$ battle is$s_i$.
For any one from $2$ to$n$ of$x$ , if all temperatures do not exceed$All\; x$ people participate in the competition, how many people have a chance to win (survive to the end)?

[Input format]
An integer t in the first line $t(1\le t\le 10^3)$, indicating the number of test samples. Enter an integer n ( 2 ≤ n ≤ 2 × 1 0 5 ) n(2\le n\le 2\times 10^5)
for the first line of each test sample$n(2\le n\le 2\times 10^5)$, indicating the number of players.
The second line enters a length$n-1$ for the string$s$ . Data guarantees nn
in each set of test cases$The\; sum\; of\; n$ does not exceed$3\times 10^5$。

[Output format]
For each set of test cases, output a line with a total of $n-1$ integer, i.e. for 2 from$2$ tonneveryxx$of\; n$$x$ , how many people have a chance to win.

【Input sample】

2
4
001
4
101

【Example of output】

1 1 3
1 2 3

【Explanation/Tip】
In the first test case, for $x=2$ and $x=3$, only the player whose temperature value is $1$ can be the winner. For $x=4$ , the player whose temperature value is $2,3,4$ can be the winner.

【analyze】

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Suppose the environment of the last game is $1$ , that is, the person with the highest temperature wins, then the temperature is$People\; with\; 1$ will lose even if they live to the last game.

Similarly, if the last $The\; environment\; of\; field\; k$ is$1$ , then there are$k(1\sim k)$ Individuals must have no chance to win, the other$x-All\; k$ players have a chance to win, because only the temperature is greater than or equal to$k+1$ person may continuously beat the temperature of$1\sim k$ 's people live to the end.

So how to ensure $k+1\sim x$ contestants have a chance to live to the end$What\; about\; k$ field? Suppose you want to make player$i(k+1\le i\le x)$ live to the end$k$ field, just let the rest be in$k+1\sim$The players in$x$$k-1$ field environment must be$0$ , then let the remaining player$j$ and$1\sim$Players in$k$$i$ lived till the end$k$ field.

Conversely, if the last $The\; environment\; of\; field\; k$ is all$0$ can also prove that the number of people who have a chance to win is$x-k$。

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【Code】

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

int main()
{
    
    
    int T, n;
    string s;
    cin >> T;
    while (T--)
    {
    
    
        cin >> n >> s;
        cout << 1 << ' ';
        for (int i = 1, k = 1; i < s.size(); i++)  // k表示最长相同后缀的长度
        {
    
    
            if (s[i] == s[i - 1]) k++;
            else k = 1;
            cout << i + 2 - k << ' ';  // 第1 ~ i + 2名选手参赛
        }
        cout << endl;
    }
    return 0;
}