Inserting m into n such that m starts at bit j and ends at bit i.

31 May, 2021
We are given two numbers n and m, and two-bit positions, i and j. Insert bits of m into n starting from j to i. We can assume that the bits j through i have enough space to fit all of m. That is, if m = 10011, you can assume that there are at least 5 bits between j and i. You would not, for example, have j = 3 and i = 2, because m could not fully fit between bit 3 and bit 2. Examples :  
Input : n = 1024
        m = 19
        i = 2
        j = 6;
Output : n = 1100
Binary representations of input numbers
m in binary is (10011)2
n in binary is (10000000000)2
Binary representations of output number
(10000000000)2

Input : n = 5
        m = 3
        i = 1
        j = 2
Output : 7
 
Algorithm :  
1. Clear the bits j through i in n 

2. Shift m so that it lines up with bits j through i 

3. Return Bitwise AND of m and n. 
The trickiest part is Step 1. How do we clear the bits in n? We can do this with a mask. This mask will have all 1s, except for 0s in the bits j through i. We create this mask by creating the left half of the mask first, and then the right half. Following is the implementation of the above approach. 
C++
Java
Python3
C#
PHP
Javascript
// C++ program for implementation of updateBits()#include <bits/stdc++.h>using namespace std; // Function to updateBits M insert to N.int updateBits(int n, int m, int i, int j){    /* Create a mask to clear bits i through j      in n. EXAMPLE: i = 2, j = 4. Result      should be 11100011. For simplicity, we'll      use just 8 bits for the example. */     int allOnes = ~0; // will equal sequence of all ls     // ls before position j, then 0s. left = 11100000    int left= allOnes << (j + 1);     // l's after position i. right = 00000011    int right = ((1 << i) - 1);     // All ls, except for 0s between i and j. mask 11100011    int mask = left | right;     /* Clear bits j through i then put min there */    int n_cleared = n & mask; // Clear bits j through i.    int m_shifted = m << i;   // Move m into correct position.     return (n_cleared | m_shifted); // OR them, and we're done!} // Driver Codeint main(){    int n = 1024; // in Binary N= 10000000000    int m = 19;   // in Binary M= 10011    int i = 2, j = 6;     cout << updateBits(n,m,i,j);     return 0;}
// Java program for implementation of updateBits() class UpdateBits{    // Function to updateBits M insert to N.    static int updateBits(int n, int m, int i, int j)    {        /* Create a mask to clear bits i through j          in n. EXAMPLE: i = 2, j = 4. Result          should be 11100011. For simplicity, we'll          use just 8 bits for the example. */              int allOnes = ~0; // will equal sequence of all ls              // ls before position j, then 0s. left = 11100000        int left= allOnes << (j + 1);              // l's after position i. right = 00000011        int right = ((1 << i) - 1);              // All ls, except for 0s between i and j. mask 11100011        int mask = left | right;              /* Clear bits j through i then put min there */        // Clear bits j through i.        int n_cleared = n & mask;        // Move m into correct position.        int m_shifted = m << i;                  // OR them, and we're done!        return (n_cleared | m_shifted);    }         public static void main (String[] args)    {        // in Binary N= 10000000000        int n = 1024;                 // in Binary M= 10011        int m = 19;                   int i = 2, j = 6;              System.out.println(updateBits(n,m,i,j));    }}
# Python3 program for implementation# of updateBits() # Function to updateBits M insert to N.def updateBits(n, m, i, j):     # Create a mask to clear bits i through    # j in n. EXAMPLE: i = 2, j = 4. Result    # should be 11100011. For simplicity,    # we'll use just 8 bits for the example.     # will equal sequence of all ls    allOnes = ~0     # ls before position j,    # then 0s. left = 11100000    left = allOnes << (j + 1)     # l's after position i. right = 00000011    right = ((1 << i) - 1)     # All ls, except for 0s between    # i and j. mask 11100011    mask = left | right     # Clear bits j through i then put min there    n_cleared = n & mask         # Move m into correct position.    m_shifted = m << i     return (n_cleared | m_shifted)  # Driver Coden = 1024 # in Binary N = 10000000000m = 19   # in Binary M = 10011i = 2; j = 6print(updateBits(n, m, i, j)) # This code is contributed by Anant Agarwal.
// C# program for implementation of// updateBits()using System; class GFG {         // Function to updateBits M    // insert to N.    static int updateBits(int n, int m,                           int i, int j)    {                 /* Create a mask to clear bits i          through j in n. EXAMPLE: i = 2,          j = 4. Result should be 11100011.          For simplicity, we'll use just 8          bits for the example. */               // will equal sequence of all ls        int allOnes = ~0;               // ls before position j, then 0s.        // left = 11100000        int left= allOnes << (j + 1);               // l's after position i.        // right = 00000011        int right = ((1 << i) - 1);               // All ls, except for 0s between i        // and j. mask 11100011        int mask = left | right;               /* Clear bits j through i then put        min there */        // Clear bits j through i.        int n_cleared = n & mask;                 // Move m into correct position.        int m_shifted = m << i;                   // OR them, and we're done!        return (n_cleared | m_shifted);    }          public static void Main()    {                 // in Binary N= 10000000000        int n = 1024;                  // in Binary M= 10011        int m = 19;          int i = 2, j = 6;               Console.WriteLine(updateBits(n, m, i, j));    }} //This code is contributed by Anant Agarwal.
<?php// PHP program for implementation// of updateBits() // Function to updateBits// M insert to N. function updateBits($n, $m, $i, $j){    // Create a mask to clear    // bits i through j in n.    // EXAMPLE: i = 2, j = 4.    // Result should be 11100011.    // For simplicity, we'll use    // just 8 bits for the example.     // will equal sequence of all ls    $allOnes = ~0;     // ls before position j, then    // 0s. left = 11100000    $left= $allOnes << ($j + 1);     // l's after position i.    // right = 00000011    $right = ((1 << $i) - 1);     // All ls, except for 0s between    // i and j. mask 11100011    $mask = $left | $right;     // Clear bits j through i    // then put min there         // Clear bits j through i.    $n_cleared = $n & $mask;         // Move m into correct position.    $m_shifted = $m << $i;     // OR them, and we're done!    return ($n_cleared | $m_shifted);} // Driver Code // in Binary N= 10000000000$n = 1024; // in Binary M= 10011$m = 19;$i = 2;$j = 6; echo updateBits($n, $m, $i, $j); // This code is contributed by Ajit?>
<script> // JavaScript program for implementation of updateBits()      // Function to updateBits M insert to N.    function updateBits(n,m,i,j)    {        /* Create a mask to clear bits i through j        in n. EXAMPLE: i = 2, j = 4. Result        should be 11100011. For simplicity, we'll        use just 8 bits for the example. */             let allOnes = ~0; // will equal sequence of all ls             // ls before position j, then 0s. left = 11100000        let left= allOnes << (j + 1);             // l's after position i. right = 00000011        let right = ((1 << i) - 1);             // All ls, except for 0s between i and j. mask 11100011        let mask = left | right;             /* Clear bits j through i then put min there */        // Clear bits j through i.        let n_cleared = n & mask;        // Move m into correct position.        let m_shifted = m << i;                 // OR them, and we're done!        return (n_cleared | m_shifted);    }                  // in Binary N= 10000000000        let n = 1024;                 // in Binary M= 10011        let m = 19;                 let i = 2, j = 6;             document.write(updateBits(n,m,i,j));      // This code is contributed by sravan </script>
Output:  
 1100  // in Binary (10001001100)2
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