# Check if all bits can be made same by single flip

Given a binary string, find if it is possible to make all its digits equal (either all 0’s or all 1’s) by flipping exactly one bit.

Input: 101 Output: Yes Explanation: In 101, the 0 can be flipped to make it all 1 Input: 11 Output: No Explanation: No matter whichever digit you flip, you will not get the desired string. Input: 1 Output: Yes Explanation: We can flip 1, to make all 0's

**Method 1 (Counting 0’s and 1’s)**

If all digits of a string can be made identical by doing exactly one flip, that means the string has all its digits equal to one another except this digit which has to be flipped, and this digit must be different than all other digits of the string. The value of this digit could be either zero or one. Hence, this string will either have exactly one digit equal to zero, and all other digits equal to one, or exactly one digit equal to one, and all other digit equal to zero.

Therefore, we only need to check whether the string has exactly one digit equal to zero/one, and if so, the answer is yes; otherwise the answer is no.

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Below is the implementation of above idea.

## C++

`// C++ program to check if a single bit can` `// be flipped tp make all ones` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// This function returns true if we can` `// bits same in given binary string str.` `bool` `canMakeAllSame(string str)` `{` ` ` `int` `zeros = 0, ones = 0;` ` ` `// Traverse through given string and` ` ` `// count numbers of 0's and 1's` ` ` `for` `(` `char` `ch : str)` ` ` `(ch == ` `'0'` `) ? ++zeros : ++ones;` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(zeros == 1 || ones == 1);` `}` `// Driver code` `int` `main()` `{` ` ` `canMakeAllSame(` `"101"` `) ? ` `printf` `(` `"Yes\n"` `) : ` `printf` `(` `"No\n"` `);` ` ` `return` `0;` `}` |

## Java

`// Java program to check if a single bit can` `// be flipped to make all ones` `public` `class` `GFG {` ` ` `// This function returns true if we can` ` ` `// bits same in given binary string str.` ` ` `static` `boolean` `canMakeAllSame(String str)` ` ` `{` ` ` `int` `zeros = ` `0` `, ones = ` `0` `;` ` ` `// Traverse through given string and` ` ` `// count numbers of 0's and 1's` ` ` `for` `(` `int` `i = ` `0` `; i < str.length(); i++) {` ` ` `char` `ch = str.charAt(i);` ` ` `if` `(ch == ` `'0'` `)` ` ` `++zeros;` ` ` `else` ` ` `++ones;` ` ` `}` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(zeros == ` `1` `|| ones == ` `1` `);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `System.out.println(canMakeAllSame(` `"101"` `) ? ` `"Yes"` `: ` `"No"` `);` ` ` `}` `}` `// This code is contributed by Sumit Ghosh` |

## Python3

`# python program to check if a single` `# bit can be flipped tp make all ones` `# This function returns true if we can` `# bits same in given binary string str.` `def` `canMakeAllSame(` `str` `):` ` ` `zeros ` `=` `0` ` ` `ones ` `=` `0` ` ` `# Traverse through given string and` ` ` `# count numbers of 0's and 1's` ` ` `for` `i ` `in` `range` `(` `0` `, ` `len` `(` `str` `)):` ` ` `ch ` `=` `str` `[i];` ` ` `if` `(ch ` `=` `=` `'0'` `):` ` ` `zeros ` `=` `zeros ` `+` `1` ` ` `else` `:` ` ` `ones ` `=` `ones ` `+` `1` ` ` `# Return true if any of the two` ` ` `# counts is 1` ` ` `return` `(zeros ` `=` `=` `1` `or` `ones ` `=` `=` `1` `);` `# Driver code` `if` `(canMakeAllSame(` `"101"` `)):` ` ` `print` `(` `"Yes\n"` `)` `else` `:` ` ` `print` `(` `"No\n"` `)` `# This code is contributed by Sam007.` |

## C#

`// C# program to check if a single bit can` `// be flipped to make all ones` `using` `System;` `class` `GFG {` ` ` ` ` `// This function returns true if we can` ` ` `// bits same in given binary string str.` ` ` `static` `bool` `canMakeAllSame(` `string` `str)` ` ` `{` ` ` `int` `zeros = 0, ones = 0;` ` ` `// Traverse through given string and` ` ` `// count numbers of 0's and 1's` ` ` `for` `(` `int` `i = 0; i < str.Length; i++) {` ` ` `char` `ch = str[i];` ` ` `if` `(ch == ` `'0'` `)` ` ` `++zeros;` ` ` `else` ` ` `++ones;` ` ` `}` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(zeros == 1 || ones == 1);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `Console.WriteLine(canMakeAllSame(` `"101"` `) ? ` `"Yes"` `: ` `"No"` `);` ` ` `}` `}` `// This code is contributed by Sam007` |

## PHP

`<?php` `// PHP program to check if a single bit can` `// be flipped tp make all ones` ` ` `// This function returns true if we can` `// bits same in given binary string str.` `function` `canMakeAllSame(` `$str` `)` `{` ` ` `$zeros` `= 0;` ` ` `$ones` `= 0;` ` ` ` ` `// Traverse through given string and` ` ` `// count numbers of 0's and 1's` ` ` ` ` `for` `(` `$i` `=0;` `$i` `<` `strlen` `(` `$str` `);` `$i` `++)` ` ` `{` ` ` `$ch` `= ` `$str` `[` `$i` `];` ` ` `if` `(` `$ch` `== ` `'0'` `)` ` ` `++` `$zeros` `;` ` ` `else` ` ` `++` `$ones` `;` ` ` `}` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(` `$zeros` `== 1 || ` `$ones` `== 1);` `}` ` ` `// Driver code` ` ` `if` `(canMakeAllSame(` `"101"` `) )` ` ` `echo` `"Yes\n"` `;` ` ` `else` `echo` `"No\n"` `;` ` ` `return` `0;` `?>` |

## Javascript

`<script>` `// Javascript program to check if a single bit can` `// be flipped to make all ones` ` ` ` ` `// This function returns true if we can` ` ` `// bits same in given binary string str.` ` ` `function` `canMakeAllSame(str)` ` ` `{` ` ` `let zeros = 0, ones = 0;` ` ` ` ` `// Traverse through given string and` ` ` `// count numbers of 0's and 1's` ` ` `for` `(let i = 0; i < str.length; i++) {` ` ` `let ch = str[i];` ` ` `if` `(ch == ` `'0'` `)` ` ` `++zeros;` ` ` `else` ` ` `++ones;` ` ` `}` ` ` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(zeros == 1 || ones == 1);` ` ` `}` ` ` ` ` `// Driver code` ` ` `document.write(canMakeAllSame(` `"101"` `) ? ` `"Yes"` `: ` `"No"` `);` ` ` ` ` `// This code is contributed by rag2127` `</script>` |

**Output:**

Yes

**Time complexity :** O(n) where n is the length of the string.

**Method 2 (Counting 0’s and 1’s)**

The idea is to compute sum of all bits. If sum is n-1 or 1, then output is true, else false. This solution doesn’t require a comparison in a loop.

Below is the implementation of above idea.

## C++

`// Check if all bits can be made same by single flip` `// Idea is to add the integer value all the elements` `// in the given string.` `// If the sum is 1 it indicates that there is` `// only single '1' in the string.` `// If the sum is 0 it indicates that there is only` `// single '0' in the string.` `// It takes O(n) time.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `bool` `isOneFlip(string str)` `{` ` ` `int` `sum = 0;` ` ` `int` `n = str.length();` ` ` `// Traverse through given string and` ` ` `// count the total sum of numbers` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `sum += str[i] - ` `'0'` `;` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(sum == n - 1 || sum == 1);` `}` `// Main function` `int` `main()` `{` ` ` `isOneFlip(` `"101111111111"` `) ? ` `printf` `(` `"Yes\n"` `) : ` `printf` `(` `"No\n"` `);` ` ` `return` `0;` `}` |

## Java

`/*Check if all bits can be made same by single` `flip. Idea is to add the integer value all the` `elements in the given string.` `If the sum is 1 it indicates that there is` ` ` `only single '1' in the string.` `If the sum is 0 it indicates that there is only` ` ` `single '0' in the string.` `It takes O(n) time.*/` `public` `class` `GFG {` ` ` `static` `boolean` `isOneFlip(String str)` ` ` `{` ` ` `int` `sum = ` `0` `;` ` ` `int` `n = str.length();` ` ` `// Traverse through given string and` ` ` `// count the total sum of numbers` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `sum += str.charAt(i) - ` `'0'` `;` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(sum == n - ` `1` `|| sum == ` `1` `);` ` ` `}` ` ` `// Main function` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `System.out.println(isOneFlip(` `"101111111111"` `) ? ` `"Yes"` `: ` `"No"` `);` ` ` `}` `}` `// This code is contributed by Sumit Ghosh` |

## Python3

`# Check if all bits can be made same` `# by single flip Idea is to add the` `# integer value all the elements in` `# the given string. If the sum is 1` `# it indicates that there is only` `# single '1' in the string. If the` `# sum is 0 it indicates that there` `# is only single '0' in the string.` `# It takes O(n) time.` `def` `isOneFlip(` `str` `):` ` ` `sum` `=` `0` ` ` `n ` `=` `len` `(` `str` `)` ` ` `# Traverse through given string` ` ` `# and count the total sum of` ` ` `# numbers` ` ` `for` `i ` `in` `range` `( ` `0` `, n ):` ` ` `sum` `+` `=` `int` `(` `str` `[i]) ` `-` `int` `(` `'0'` `)` ` ` `# Return true if any of the two` ` ` `# counts is 1` ` ` `return` `(` `sum` `=` `=` `n ` `-` `1` `or` `sum` `=` `=` `1` `)` `# Main function` `(` `print` `(` `"Yes"` `) ` `if` `isOneFlip(` `"101111111111"` `)` ` ` `else` `print` `(` `"No"` `))` `# This code is contributed by Smitha` |

## C#

`/*Check if all bits can be made same by single` ` ` `flip. Idea is to add the integer value all the` ` ` `elements in the given string.` ` ` `If the sum is 1 it indicates that there is` ` ` `only single '1' in the string.` ` ` `If the sum is 0 it indicates that there is only` ` ` `single '0' in the string.` ` ` `It takes O(n) time.*/` `using` `System;` `class` `GFG {` ` ` ` ` `static` `bool` `isOneFlip(` `string` `str)` ` ` `{` ` ` `int` `sum = 0;` ` ` `int` `n = str.Length;` ` ` `// Traverse through given string and` ` ` `// count the total sum of numbers` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `sum += str[i] - ` `'0'` `;` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(sum == n - 1 || sum == 1);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `Console.WriteLine(isOneFlip(` `"101111111111"` `) ? ` `"Yes"` `: ` `"No"` `);` ` ` `}` `}` `// This code is contributed by Sam007` |

## PHP

`<?php` `// Check if all bits can be made same by` `// single flip Idea is to add the integer` `// value all the elements in the given` `// string. If the sum is 1 it indicates` `// that there is only single '1' in the` `// string. If the sum is 0 it indicates` `// that there is only single '0' in the` `// string. It takes O(n) time.` `function` `isOneFlip(` `$str` `)` `{` ` ` `$sum` `= 0;` ` ` `$n` `= ` `strlen` `(` `$str` `);` ` ` `// Traverse through given string and` ` ` `// count the total sum of numbers` ` ` `for` `( ` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `$sum` `+= ` `$str` `[` `$i` `] - ` `'0'` `;` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(` `$sum` `== ` `$n` `- 1 || ` `$sum` `== 1);` `}` `// Main function` ` ` `if` `(isOneFlip(` `"101111111111"` `) )` ` ` `echo` `"Yes\n"` `;` ` ` `else` ` ` `echo` `"No\n"` `;` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` `/*Check if all bits can be made same by single` `flip. Idea is to add the integer value all the` `elements in the given string.` `If the sum is 1 it indicates that there is` ` ` `only single '1' in the string.` `If the sum is 0 it indicates that there is only` ` ` `single '0' in the string.` `It takes O(n) time.*/` `function` `isOneFlip(str)` `{` ` ` `let sum = 0;` ` ` `let n = str.length;` ` ` `// Traverse through given string and` ` ` `// count the total sum of numbers` ` ` `for` `(let i = 0; i < n; i++)` ` ` `sum += str[i] - ` `'0'` `;` ` ` `// Return true if any of the two counts` ` ` `// is 1` ` ` `return` `(sum == n - 1 || sum == 1);` `}` `// Driver code` `document.write(isOneFlip(` `"101111111111"` `) ?` ` ` `"Yes"` `: ` `"No"` `);` `// This code is contributed by avanitrachhadiya2155` `</script>` |

**Output:**

Yes

**Time Complexity:** O(N)**Auxiliary Space: **O(1)

Thanks to **Sourabh Gavhale** for suggesting this solution

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