Get the average value from a vector of Integers

Question

I have been unable to find a way of getting the average value from a vector of integers in C++.

I can't possibly start adding all of the values because I could exceed the maximum integer accepted value.

How can I calculate this efficiently and quickly ? Are there any standard libraries in the C++ language to do that ?

Answer 1

The go-to approach is just summing with a sufficiently wide integer type with std::accumulate:

double avg1(std::vector<int> const& v) {
    return 1.0 * std::accumulate(v.begin(), v.end(), 0LL) / v.size();
}

If this sum overflows (with 23 million ints, the average would have to be at least 4.01x10¹¹ - which is to say, it won't overflow since that won't even fit in an int32_t... so you're way good, but on the off chance you get several orders of magnitude more numbers, or have wider a int type), then you can instead use the common "online" algorithm for calculating the mean:

double avg2(std::vector<int> const& v) {
    int n = 0;
    double mean = 0.0;
    for (auto x : v) {
        double delta = x - mean;
        mean += delta/++n;
    }
    return mean;
}

This won't overflow, isn't very prone to loss of precision, but may be more expensive due to repeated extra divisions.

Answer 2

I have been unable to find a way of getting the average value from a vector of integers in C++. I can't possibly start adding all of the values because I could exceed the maximum integer accepted value. How can I calculate this efficiently and quickly ? Are there any standard libraries in the C++.

A lot of discussion of finding a sum that might be too big for even a uint64_t.

So follow this suggestion and stop worrying ...

I have used, can recommend, and am very impressed with the multi-precision C++ library called "gmpxx.h".

I have used it for several interesting efforts, including code to generate a big fibonacci with no apparent effort. It is easy to use, and surprisingly quick, and I have found on the web examples of how to use.

Code snippet:

mpz_class  n;   // a multi-precision integer, 
n = 1;          // easy initialize
size_t F = 1000; 
for (size_t i=1; i<=F; ++i)
   n = n * i;
// show
std::string Fstr = digiComma(n);  // inserts comma's
std::cout << "\n" << F << "! = " << Fstr
          << "\n" << digitCnt(Fstr) << " bytes " <<  std::endl;

My output is a 2568 character (>1900 digits), comma delimited, big int value in < 20 ms.

1000! = 402,387,260,077,093,773,543,702,433,923,003,985,719,374,864,210,714,632,543,799, 910,429,938,512,398,629,020,592,044,208,486,969,404,800,479,988,610,197,196,058, 631,666,872,994,808,558,901,323,829,669,944,590,997,424,504,087,073,759,918,823, 627,727,188,732,519,779,505,950,995,276,120,874,975,462,497,043,601,418,278,094, 646,496,291,056,393,887,437,886,487,337,119,181,045,825,783,647,849,977,012,476, 632,889,835,955,735,432,513,185,323,958,463,075,557,409,114,262,417,474,349,347, 553,428,646,576,611,667,797,396,668,820,291,207,379,143,853,719,588,249,808,126, 867,838,374,559,731,746,136,085,379,534,524,221,586,593,201,928,090,878,297,308, 431,392,844,403,281,231,558,611,036,976,801,357,304,216,168,747,609,675,871,348, 312,025,478,589,320,767,169,132,448,426,236,131,412,508,780,208,000,261,683,151, 027,341,827,977,704,784,635,868,170,164,365,024,153,691,398,281,264,810,213,092, 761,244,896,359,928,705,114,964,975,419,909,342,221,566,832,572,080,821,333,186, 116,811,553,615,836,546,984,046,708,975,602,900,950,537,616,475,847,728,421,889, 679,646,244,945,160,765,353,408,198,901,385,442,487,984,959,953,319,101,723,355, 556,602,139,450,399,736,280,750,137,837,615,307,127,761,926,849,034,352,625,200, 015,888,535,147,331,611,702,103,968,175,921,510,907,788,019,393,178,114,194,545, 257,223,865,541,461,062,892,187,960,223,838,971,476,088,506,276,862,967,146,674, 697,562,911,234,082,439,208,160,153,780,889,893,964,518,263,243,671,616,762,179, 168,909,779,911,903,754,031,274,622,289,988,005,195,444,414,282,012,187,361,745, 992,642,956,581,746,628,302,955,570,299,024,324,153,181,617,210,465,832,036,786, 906,117,260,158,783,520,751,516,284,225,540,265,170,483,304,226,143,974,286,933, 061,690,897,968,482,590,125,458,327,168,226,458,066,526,769,958,652,682,272,807, 075,781,391,858,178,889,652,208,164,348,344,825,993,266,043,367,660,176,999,612, 831,860,788,386,150,279,465,955,131,156,552,036,093,988,180,612,138,558,600,301, 435,694,527,224,206,344,631,797,460,594,682,573,103,790,084,024,432,438,465,657, 245,014,402,821,885,252,470,935,190,620,929,023,136,493,273,497,565,513,958,720, 559,654,228,749,774,011,413,346,962,715,422,845,862,377,387,538,230,483,865,688, 976,461,927,383,814,900,140,767,310,446,640,259,899,490,222,221,765,904,339,901, 886,018,566,526,485,061,799,702,356,193,897,017,860,040,811,889,729,918,311,021, 171,229,845,901,641,921,068,884,387,121,855,646,124,960,798,722,908,519,296,819, 372,388,642,614,839,657,382,291,123,125,024,186,649,353,143,970,137,428,531,926, 649,875,337,218,940,694,281,434,118,520,158,014,123,344,828,015,051,399,694,290, 153,483,077,644,569,099,073,152,433,278,288,269,864,602,789,864,321,139,083,506, 217,095,002,597,389,863,554,277,196,742,822,248,757,586,765,752,344,220,207,573, 630,569,498,825,087,968,928,162,753,848,863,396,909,959,826,280,956,121,450,994, 871,701,244,516,461,260,379,029,309,120,889,086,942,028,510,640,182,154,399,457, 156,805,941,872,748,998,094,254,742,173,582,401,063,677,404,595,741,785,160,829, 230,135,358,081,840,096,996,372,524,230,560,855,903,700,624,271,243,416,909,004, 153,690,105,933,983,835,777,939,410,970,027,753,472,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

2568 bytes

real 0m0.013s

user 0m0.004s

sys 0m0.000s

So how big is a uint64_t? I think the biggest Fib that fits in uint64_t is Fib(93).