accumulate() and partial_sum() in C++ STL : Numeric header
The numeric header is part of the numeric library in C++ STL. This library consists of basic mathematical functions and types, as well as optimized numeric arrays and support for random number generation. Some of the functions in the numeric header:
- partial_sum etc.
This article explains accumulate() and partial_sum() in the numeric header which can be used during competitive programming to save time and effort.
1) accumulate(): This function returns the sum of all the values lying in a range between [first, last) with the variable sum. We usually find out the sum of elements in a particular range or a complete array using a linear operation which requires adding all the elements in the range one by one and storing it into some variable after each iteration.
accumulate(first, last, sum);
accumulate(first, last, sum, myfun);
- first, last: first and last elements of range whose elements are to be added
- sum: initial value of the sum
- myfun: a function for performing any specific task.
For example, we can find the product of elements between the first and last.
Result using accumulate: 31 Result using accumulate withuser-defined function: 750 Result using accumulate with pre-defined function: -29
Note: For adding larger values beyond the int range the sum should be initialized with 0ll or a user-defined sum with the suffix ll, else the sum will be overflown. (here ll refers to long long int)
See this Example Problem for more reference: Sum of all elements between k1’th and k2’th smallest elements
2) partial_sum( ): This function assigns a partial sum of the corresponding elements of an array to every position of the second array. It returns the partial sum of all the sets of values lying between [first, last) and stores it in another array b.
For example, if x represents an element in [first, last) and y represents an element in the result, the ys can be calculated as:
y0 = x0 y1 = x0 + x1 y2 = x0 + x1 + x2 y3 = x0 + x1 + x2 + x3 y4 = x0 + x1 + x2 + x3 + x4
partial_sum(first, last, b);
partial_sum(first, last, b, myfun);
- first, last: first and last element of the range whose elements are to be added
- b: index of array where corresponding partial sum will be stored
- myfun: a user-defined function for performing any specific task
Partial Sum - Using Default function: 1 3 6 10 15 Partial sum - Using user defined function: 1 5 11 19 29
Explanation of code :
simply, ith element of a array + i-1th element of array b makes equal to ith element of b
b =1+no ele=> 1
b =2+1=> 3
b= 3+3=> 6
b=6+4=10 and so on
in the same way :
means b= 1+2*0 => 1
b = 1+2*2=> 5
b= 5+3*2=> 11
b=11+4*2=> 19 and so on upto last.
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