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Positive Array CodeChef Solution

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Positive Array CodeChef Solution

Positive Array CodeChef Solution

A¬†1-indexed array is called¬†positive¬†if every element of the array is greater than or equal to the index on which it lies. Formally, an array¬†BB¬†of size¬†MM¬†is called positive if¬†Bi‚Č•iBi‚Č•i¬†for each¬†1‚ȧi‚ȧM1‚ȧi‚ȧM.

For example, the arrays [1],[2,2],[3,2,4,4][1],[2,2],[3,2,4,4] are positive while the arrays [2,1],[3,1,2][2,1],[3,1,2] are not positive.

You are given an array AA containing NN integers. You want to distribute all elements of the array into some positive arrays. The elements of a positive array might not occur in the order they appear in the array AA.

Find the minimum number of positive arrays that the elements of the array AA can be divided into.

Please see the sample cases below for more clarity.

Input Format

  • The first line of input will contain a single integer¬†TT, denoting the number of test cases.
  • Each test case consists of two lines of input.
    • The first line of each test case contains an integer¬†NN¬†‚ÄĒ the number of elements in the array¬†AA.
    • The next line contains¬†NN¬†space-separated integers¬†A1,A2,‚Ķ,ANA1,A2,‚Ķ,AN¬†‚ÄĒ the elements of array¬†AA.

Positive Array CodeChef Solution

Output Format

For each test case, output on a new line the minimum number of positive arrays that the elements of the array¬†AA¬†can be divided into.‚Äč

Constraints

  • 1‚ȧT‚ȧ1041‚ȧT‚ȧ104
  • 1‚ȧN‚ȧ1051‚ȧN‚ȧ105
  • 1‚ȧAi‚ȧN1‚ȧAi‚ȧN
  • The sum of¬†NN¬†over all test cases won’t exceed¬†2‚čÖ1052‚čÖ105.

Sample Input 1 

5
3
2 3 3
4
3 1 1 2
3
1 1 1
5
1 2 2 4 5
6
3 2 1 2 2 1

Sample Output 1 

1
2
3
2
3

Explanation

Positive Array CodeChef Solution

Test case 11: The given array is already positive. So the optimal division is [2,3,3][2,3,3].

Test case 22: One possible division is [1,2],[1,3][1,2],[1,3].

Test case 33: The only possible division is [1],[1],[1][1],[1],[1].

Test case 44: One possible division is [1,2,5],[2,4][1,2,5],[2,4].

Test case 55: One possible division is [1,2,3],[1],[2,2][1,2,3],[1],[2,2].

SOLUTION

Positive Array CodeChef Solution

SOLUTION

Positive Array CodeChef Solution

SOLUTION

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