Codeforces Round #305 Div1 B. Mike and Feet

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1

How do I do this question?

Click here for problem statement

Not able to understand the editorial.
Thanks in advance.

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2

For any position i in the array, for what length “window” can that number act as strength ?
for example, the array is
3 1 4 2 3 0

Clearly, the 2 at 3rd position (0th based indexing) will act as strength for the windows of length 1,2 and 3 only. This is because,if you expand the window on either side, we have the number 1 ( <2 ) and number 0 ( <2) .

So, for each index i we need to find the largest index j < i such that a[j] < a[i]. Let’s store it in l[i].
For each index i, we need to find the largest index j > i such that a[j] < a[i]. Let’s store it in r[i].
Clearly, the maximum window which you can get is from l[i] + 1 to r[i] - 1, which has a length of r[i] - l[i] - 1. Therefore, each element can act as strength for window size from 1 to r[i] - l[i] - 1.

You can calculate arrays l and r using a stack and then solve the problem.

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3

There is one very simple method. You can easily find the answer for x = 1. Initialize the array, a[200005][200005]. Therefore, a[1][1] = a1, a[1][2] = a2, …, a[1][i] = ai, …, a[1][n] = an. In the loop you can store maximum strength in tempmax while assigning values to the array. print - tempmax

tempmax = 0
Now for x = 2. a[2][2] = min(a[1][1], a[1][2]), a[2][3] = min(a[1][2], a[1][3]), …, a[2][i] = min(a[1][i-1], a[1][i]), …, a[2][n] = min(a[1][n-1], a[1][n]). print - tempmax

…

tempmax = 0
For x = i. a[x][x] = min(a[x-1][x-1], a[x-1][x]), a[x][x+1] = min(a[x-1][x], a[x-1][x+1]), …, a[x][x+i] = min(a[x-1][x+i-1], a[x-1][x+i]), …, a[x][n] = min(a[x-1][n-1], a[x-1][n]). print - tempmax

…

tempmax = 0
For x = n a[n][n] = min(a[n-1][n-1], a[n-1][n]) if(a[n][n] > tempmax) tempmax = a[n][n]. printf - tempmax

Now comes the question that logic is perfectly fine, but we can’t declare such a huge array. Again, there is a simple solution for that. The method to implement it using 1D array is as follows:

declare array a[200005]

tempmax = 0;
x = 1:
for(i=n to 1){
a[i] = ai;
if(a[i]>tempmax) tempmax = a[i];
}
printf("%d ", tempmax);

tempmax = 0;
x = 2:
for(i=n to 2){
a[i] = min(a[i], a[i-1]);
if(a[i]>tempmax) tempmax = a[i];
}
printf("%d ", tempmax);

…

tempmax = 0;
x = j:
for(i=n to j){
a[i] = min(a[i], a[i-1]);
if(a[i]>tempmax) tempmax = a[i];
}
printf("%d ", tempmax);

…

tempmax = 0;
x = n:
for(i=n to n){
a[i] = min(a[i], a[i-1]);
if(a[i]>tempmax) tempmax = a[i];
}
printf("%d ", tempmax);

Now I guess you got the notion about how to approach the question. The final code which you can implement is as follows:

//min function

int n, a[200005], tempmax, i, j;

//read the inputs

tempmax = 0;

for(i=1;i<=n;i++){

a[i] = ai;

if(a[i] > tempmax)

    tempmax = a[i];

}

printf("%d ", tempmax);

for(j=2;j<=n;j++){

tempmax=0;

for(i=n;i>=j;i--){

    a[i] = min(a[i-1], a[i]);


    if(a[i] > tempmax)

        tempmax = a[i];

}

printf("tempmax ");

}

But this method isn’t sufficient as it will give TLE. Please implement it using BIT.

4

A pretty simple approch :ok_hand: