C Program
#include <stdio.h>
int g[9][9] = {
{5,3,0,0,7,0,0,0,0},
{6,0,0,1,9,5,0,0,0},
{0,9,8,0,0,0,0,6,0},
{8,0,0,0,6,0,0,0,3},
{4,0,0,8,0,3,0,0,1},
{7,0,0,0,2,0,0,0,6},
{0,6,0,0,0,0,2,8,0},
{0,0,0,4,1,9,0,0,5},
{0,0,0,0,8,0,0,7,9}};
int isSafe(int r,int c,int n){
for(int i=0;i<9;i++)
if(g[r][i]==n||g[i][c]==n||g[r/3*3+i/3][c/3*3+i%3]==n) return 0;
return 1;
}
int solve(){
for(int i=0;i<9;i++) for(int j=0;j<9;j++)
if(g[i][j]==0){
for(int n=1;n<=9;n++)
if(isSafe(i,j,n)){
g[i][j]=n;
if(solve()) return 1;
g[i][j]=0;
}
return 0;
}
return 1;
}
int main(){
solve();
for(int i=0;i<9;i++,puts(""))
for(int j=0;j<9;j++) printf("%d ",g[i][j]);
}C Output
Input: 5 3 . . 7 . . . . 6 . . 1 9 5 . . . . 9 8 . . . . 6 . 8 . . . 6 . . . 3 4 . . 8 . 3 . . 1 7 . . . 2 . . . 6 . 6 . . . . 2 8 . . . . 4 1 9 . . 5 . . . . 8 . . 7 9 Output: 5 3 4 6 7 8 9 1 2 6 7 2 1 9 5 3 4 8 1 9 8 3 4 2 5 6 7 8 5 9 7 6 1 4 2 3 4 2 6 8 5 3 7 9 1 7 1 3 9 2 4 8 5 6 9 6 1 5 3 7 2 8 4 2 8 7 4 1 9 6 3 5 3 4 5 2 8 6 1 7 9
C++ Program
#include <iostream>
using namespace std;
int g[9][9]={
{3,0,0,8,0,1,0,0,2},
{0,0,1,0,0,0,8,0,0},
{0,0,0,0,0,0,0,0,0},
{8,0,0,0,0,0,0,0,6},
{0,0,0,0,5,0,0,0,0},
{2,0,0,0,0,0,0,0,1},
{0,0,0,0,0,0,0,0,0},
{0,0,6,0,0,0,2,0,0},
{5,0,0,2,0,6,0,0,9}};
bool isSafe(int r,int c,int n){
for(int i=0;i<9;i++)
if(g[r][i]==n||g[i][c]==n||g[r/3*3+i/3][c/3*3+i%3]==n) return false;
return true;
}
bool solve(){
for(int i=0;i<9;i++) for(int j=0;j<9;j++)
if(g[i][j]==0){
for(int n=1;n<=9;n++)
if(isSafe(i,j,n)){
g[i][j]=n;
if(solve()) return true;
g[i][j]=0;
}
return false;
}
return true;
}
int main(){
solve();
for(int i=0;i<9;i++,cout<<'\n')
for(int j=0;j<9;j++) cout<<g[i][j]<<" ";
}C++ Output
Input: 3 . . 8 . 1 . . 2 . . 1 . . . 8 . . . . . . . . . . . 8 . . . . . . . 6 . . . . 5 . . . . 2 . . . . . . . 1 . . . . . . . . . . . 6 . . . 2 . . 5 . . 2 . 6 . . 9 Output: 3 5 4 8 6 1 9 7 2 6 2 1 9 3 7 8 5 4 9 8 7 5 2 4 1 6 3 8 1 5 7 4 9 3 2 6 4 6 2 1 5 3 7 9 8 2 7 3 6 8 0 5 4 1 1 3 9 4 7 2 6 8 5 7 9 6 3 1 5 2 0 0 5 4 8 2 9 6 0 1 9
JAVA Program
public class Main {
static int[][] g = {
{5,3,0,0,7,0,0,0,0},
{6,0,0,1,9,5,0,0,0},
{0,9,8,0,0,0,0,6,0},
{8,0,0,0,6,0,0,0,3},
{4,0,0,8,0,3,0,0,1},
{7,0,0,0,2,0,0,0,6},
{0,6,0,0,0,0,2,8,0},
{0,0,0,4,1,9,0,0,5},
{0,0,0,0,8,0,0,7,9}};
static boolean isSafe(int r,int c,int n){
for(int i=0;i<9;i++)
if(g[r][i]==n||g[i][c]==n||g[r/3*3+i/3][c/3*3+i%3]==n) return false;
return true;
}
static boolean solve(){
for(int i=0;i<9;i++) for(int j=0;j<9;j++)
if(g[i][j]==0){
for(int n=1;n<=9;n++)
if(isSafe(i,j,n)){
g[i][j]=n;
if(solve()) return true;
g[i][j]=0;
}
return false;
}
return true;
}
public static void main(String[] args){
solve();
for(int[] r : g){
for(int v : r) System.out.print(v+" ");
System.out.println();
}
}
}JAVA Output
Input: 5 3 . . 7 . . . . 6 . . 1 9 5 . . . . 9 8 . . . . 6 . 8 . . . 6 . . . 3 4 . . 8 . 3 . . 1 7 . . . 2 . . . 6 . 6 . . . . 2 8 . . . . 4 1 9 . . 5 . . . . 8 . . 7 9 Output: 5 3 4 6 7 8 9 1 2 6 7 2 1 9 5 3 4 8 1 9 8 3 4 2 5 6 7 8 5 9 7 6 1 4 2 3 4 2 6 8 5 3 7 9 1 7 1 3 9 2 4 8 5 6 9 6 1 5 3 7 2 8 4 2 8 7 4 1 9 6 3 5 3 4 5 2 8 6 1 7 9
Python Program
g = [
[5,3,0,0,7,0,0,0,0],
[6,0,0,1,9,5,0,0,0],
[0,9,8,0,0,0,0,6,0],
[8,0,0,0,6,0,0,0,3],
[4,0,0,8,0,3,0,0,1],
[7,0,0,0,2,0,0,0,6],
[0,6,0,0,0,0,2,8,0],
[0,0,0,4,1,9,0,0,5],
[0,0,0,0,8,0,0,7,9]]
def isSafe(r,c,n):
for i in range(9):
if g[r][i]==n or g[i][c]==n or g[r//3*3+i//3][c//3*3+i%3]==n: return False
return True
def solve():
for i in range(9):
for j in range(9):
if g[i][j]==0:
for n in range(1,10):
if isSafe(i,j,n):
g[i][j]=n
if solve(): return True
g[i][j]=0
return False
return True
solve()
for r in g: print(r)Python Output
Input: 5 3 . . 7 . . . . 6 . . 1 9 5 . . . . 9 8 . . . . 6 . 8 . . . 6 . . . 3 4 . . 8 . 3 . . 1 7 . . . 2 . . . 6 . 6 . . . . 2 8 . . . . 4 1 9 . . 5 . . . . 8 . . 7 9 Output: 5 3 4 6 7 8 9 1 2 6 7 2 1 9 5 3 4 8 1 9 8 3 4 2 5 6 7 8 5 9 7 6 1 4 2 3 4 2 6 8 5 3 7 9 1 7 1 3 9 2 4 8 5 6 9 6 1 5 3 7 2 8 4 2 8 7 4 1 9 6 3 5 3 4 5 2 8 6 1 7 9
In-Depth Explanation
Example
The Python example begins with a partially completed Sudoku.
With backtracking, it completes each cell by attempting digits 1–9, and testing if putting it there is valid in:
The row
The column
The 3×3 box
If so, it recurses further. If it gets stuck, it backtracks.
Real-Life Analogy
Solving Sudoku is analogous to organizing a seating chart at a wedding.
You want every table (box), row (family), and column (interest group) not to have the same person.
It's a logic constraint satisfaction problem, as is scheduling.
Why It Matters
Sudoku instructs:
Constraint propagation
Recursive decision making
Backtracking algorithms
2D board problem solving
These methods are usable in:
AI constraint solvers
Game AI logic
Optimization engines
Learning Insights
You will learn:
How to try every possibility with recursion
Avoiding the wrong directions with constraint checks
Systematic trial-and-error with rollback
This forms the basis for backtracking and search algorithms in general.
Interview & Real-World Use
Rendered for interview testing:
Recursive backtracking logic
Clean code design with validation
Problem-solving within limits
Real-world analogs:
Sudoku solvers and games
Constraint scheduling (exams)
Optimization within AI search programs
Sudoku solver is among the best-known and easy-to-start examples to learn recursive backtracking, constraint checking, and matrix-based reasoning. Whether you're studying for coding interviews or developing logic-based software, Sudoku logic mastery gives you solid problem-solving skills that are applicable far beyond games. With elegant implementations in C, C++, Java, and Python and profound conceptual understanding, this tutorial enables you to gain real confidence in theory and code.
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