# Array Queries for multiply, replacements and product

This is Range query question in which we have been provided with and array of size N. Given are 3 types of queries and you have to answer M number of specified queries.

Type 1 query :You will be given 3 values in the form of L R X and in this type of query to have to multiply x to the array elements inclusive in the range L to R.

Type 2 query :In this query also you will be given 3 values in the form of L R Y and after executing this type of query you will replace the array elements in the form that the first element is replaced by Y, the second element is replaced by 2*Y and as follows inclusive in the range L to R.

Type 3 query : In this you will be given 2 value L and R and in this you have to
find the product of all numbers in the range. As this number could be very large, you have to just find the number of trailing zeros of this number when represented in decimal notation.

Examples:

```Input : arr[] = {2, 4, 3, 5, 5|
queries[] = {{3 2 4}, {3 2 5}, {2 2 4 1},
{1 3 3 10}, {3 1 5}}
Output : 5
Explanation :
Since the first query is of type 3 so we multiply
the elements 4 * 3 * 5 = 60.
Since the second query is of type 3 so we multiply
the elements 4 * 3 * 5 * 5 = 300.
Since the third query is of type 2 and the value of
Y is 1 so after execution of this query the array
becomes [2, 1, 2, 3, 5].
Since the fourth query is of type 1 and the value of
x is 10 so after execution of this query the array
becomes [2, 1, 20, 3, 5].
Now the last query is of type 3 then we simply multiply
all the elements inclusive in the given range i.e.
2 * 1 * 20 * 3 * 5 = 600.
Now our task is to calculate the trailing zeros obtained
in the type 3 query i.e. 60 has 1 trailing zero, 300 has
2 trailing zeros and 600 has 2 trailing zeros so the
answer of this given input is 5.
```

Method 1:
In this we can simply apply the Brute force method. In the brute force method we will apply all the operation in the array elements and for every type 3 query we will store the obtained result in a new array then we will calculate the number of trailing zeros for every result thus obtained and then calculate the desired sum.
The complexity of this method will be O(m*n) as we will operate the entire array m times for the given m queries and an extra space of size m will be required to save the results obtained in the type 3 queries for calculating the number of trailing zeros after execution of m queries.
So, time complexity is O(m*n) and space complexity is O(m).

Method 2:
In this method we have 2 vectors because a number with trailing zero can be multiple of 10 and 10 is a multiple of 2 and 5 so two separate vectors have been maintained for this purpose. And the rest has been explained below.

 `// CPP program to solve three types of queries. ` `#include ` `using` `namespace` `std; ` ` `  `//vector of 1000 elements,  ` `//all set to 0 ` `vector<``int``> twos(1000,0); ` ` `  `//vector of 1000 elements,  ` `//all set to 0  ` `vector<``int``> fives(1000,0); ` ` `  `int` `sum = 0; ` ` `  `// Function to check number of ` `// trailing zeros in multiple of 2 ` `int` `returnTwos(``int` `val) ` `{ ` `    ``int` `count = 0; ` `    ``while` `(val % 2 == 0 && val != 0) { ` ` `  `        ``val = val / 2; ` `        ``count++; ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Function to check number of ` `// trailing zeros in multiple of 5 ` `int` `returnFives(``int` `val) ` `{ ` `    ``int` `count = 0; ` `    ``while` `(val % 5 == 0 && val != 0) { ` ` `  `        ``val = val / 5; ` `        ``count++; ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Function to solve the queries received ` `void` `solve_queries(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `type, ql, qr, x, y; ` ` `  `    ``cin >> type; ` ` `  `    ``// If the query is of type 1. ` `    ``if` `(type == 1) { ` ` `  `        ``cin >> ql >> qr >> x; ` ` `  `        ``// Counting the number of ` `        ``// zeros in the given value of x ` `        ``int` `temp = returnTwos(x); ` `        ``int` `temp1 = returnFives(x); ` ` `  `        ``for` `(``int` `i = ql - 1; i < qr; i++) { ` ` `  `            ``// The value x has been multiplied ` `            ``// to their respective indices ` `            ``arr[i] = arr[i] * x; ` ` `  `            ``// The value obtained above has been ` `            ``// added to their respective vectors ` `            ``twos[i] += temp; ` `            ``fives[i] += temp1; ` `        ``} ` `    ``} ` ` `  `    ``// If the query is of type 2. ` `    ``if` `(type == 2) { ` ` `  `        ``cin >> ql >> qr >> y; ` ` `  `        ``// Counting the number of ` `        ``// zero in the given value of x ` `        ``int` `temp = returnTwos(y); ` `        ``int` `temp1 = returnFives(y); ` ` `  `        ``for` `(``int` `i = ql - 1; i < qr; i++) { ` ` `  `            ``// The value y has been replaced ` `            ``// to their respective indices ` `            ``arr[i] = (i - ql + 2) * y; ` ` `  `            ``// The value obtained above has been ` `            ``// added to their respective vectors ` `            ``twos[i] = returnTwos(i - ql + 2) + temp; ` `            ``fives[i] = returnFives(i - ql + 2) + temp1; ` `        ``} ` `    ``} ` ` `  `    ``// If the query is of type 2 ` `    ``if` `(type == 3) { ` ` `  `        ``cin >> ql >> qr; ` `        ``int` `sumtwos = 0; ` `        ``int` `sumfives = 0; ` ` `  `        ``for` `(``int` `i = ql - 1; i < qr; i++) { ` ` `  `            ``// as the number of trailing zeros for ` `            ``// each case has been found for each array  ` `            ``// element then we simply add those to ` `            ``// the respective index to a variable ` `            ``sumtwos += twos[i]; ` `            ``sumfives += fives[i]; ` `        ``} ` ` `  `        ``// Compare the number of zeros ` `        ``// obtained in the multiples of five and two ` `        ``// consider the minimum of them and add them ` `        ``sum += min(sumtwos, sumfives); ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n, m; ` ` `  `    ``// Input the Size of array ` `    ``// and number of queries ` `    ``cin >> n >> m; ` ` `  `    ``int` `arr[n]; ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``cin >> arr[i]; ` `        ``twos[i] = returnTwos(arr[i]); ` `        ``fives[i] = returnFives(arr[i]); ` `    ``} ` ` `  `    ``// Running the while loop ` `    ``// for m number of queries ` `    ``while` `(m--) { ` ` `  `        ``solve_queries(arr, n); ` `    ``} ` ` `  `    ``cout << sum << endl; ` `    ``return` `0; ` `} `

Input:

```5 5
2 4 3 5 5
3 2 4
3 2 5
2 2 4 1
1 3 3 10
3 1 5
```

Output:

```5
```

The complexity of this code is O(n).

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