GATE CS 2017 Set 1 Q.55 (CS Q.55): Functions, Recursion, Scope and Storage Classes

The output of executing the following C program is ______.

#include <stdio.h>

int total(int v) {
    static int count = 0;
    while (v) {
        count += v & 1;
        v >>= 1;
    }
    return count;
}

void main() {
    static int x = 0;
    int i = 5;
    for (; i > 0; i--) {
        x = x + total(i);
    }
    printf("%d\n", x);
}

Your answer

Official answer and solution

Official answer: 23
From: Official GATE 2017 answer key

Solution

Trace the execution of total() noting that the static variable count retains its value across successive loop calls.

In function total(v):

int total(int v) {
    static int count = 0;
    while (v) {
        count += v & 1;
        v >>= 1;
    }
    return count;
}

Because count is declared static, it is initialized to 0 once and preserves its accumulated value across successive calls. The loop counts the number of 1s in the binary representation of $v$ (Hamming weight) and adds it to count.

The function main() runs a loop for $i = 5, 4, 3, 2, 1$ :

$i = 5$ (binary 101, weight = 2):
count becomes $0 + 2 = 2$ . total(5) returns 2.
$x = 0 + 2 = 2$ .
$i = 4$ (binary 100, weight = 1):
count becomes $2 + 1 = 3$ . total(4) returns 3.
$x = 2 + 3 = 5$ .
$i = 3$ (binary 011, weight = 2):
count becomes $3 + 2 = 5$ . total(3) returns 5.
$x = 5 + 5 = 10$ .
$i = 2$ (binary 010, weight = 1):
count becomes $5 + 1 = 6$ . total(2) returns 6.
$x = 10 + 6 = 16$ .
$i = 1$ (binary 001, weight = 1):
count becomes $6 + 1 = 7$ . total(1) returns 7.
$x = 16 + 7 = 23$ .

The loop finishes when $i = 0$ . printf outputs $x = 23$ .

Final answer

23.0

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2017 Computer Science and Information Technology (CS) Session 1
Question: 55 of 65, printed as CS Q.55
Section: Computer Science and Information Technology

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