# Word Ladder (Length of shortest chain to reach a target word)

Given a dictionary, and two words ‘start’ and ‘target’ (both of same length). Find length of the smallest chain from ‘start’ to ‘target’ if it exists, such that adjacent words in the chain only differ by one character and each word in the chain is a valid word i.e., it exists in the dictionary. It may be assumed that the ‘target’ word exists in dictionary and length of all dictionary words is same.

Example:

Input: Dictionary = {POON, PLEE, SAME, POIE, PLEA, PLIE, POIN} start = TOON target = PLEA Output: 7 Explanation: TOON - POON - POIN - POIE - PLIE - PLEE - PLEA

The idea is to use BFS. We start from the given start word, traverse all words that adjacent (differ by one character) to it and keep doing so until we find the target word or we have traversed all words.

Below is C++ implementation of above idea.

## C++

`// C++ program to find length of the shortest chain ` `// transformation from source to target ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// To check if strings differ by exactly one character ` `bool` `isadjacent(string& a, string& b) ` `{ ` ` ` `int` `count = 0; ` `// to store count of differences ` ` ` `int` `n = a.length(); ` ` ` ` ` `// Iterate through all characters and return false ` ` ` `// if there are more than one mismatching characters ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` `if` `(a[i] != b[i]) count++; ` ` ` `if` `(count > 1) ` `return` `false` `; ` ` ` `} ` ` ` `return` `count == 1 ? ` `true` `: ` `false` `; ` `} ` ` ` `// A queue item to store word and minimum chain length ` `// to reach the word. ` `struct` `QItem ` `{ ` ` ` `string word; ` ` ` `int` `len; ` `}; ` ` ` `// Returns length of shortest chain to reach 'target' from 'start' ` `// using minimum number of adjacent moves. D is dictionary ` `int` `shortestChainLen(string& start, string& target, set<string> &D) ` `{ ` ` ` `// Create a queue for BFS and insert 'start' as source vertex ` ` ` `queue<QItem> Q; ` ` ` `QItem item = {start, 1}; ` `// Chain length for start word is 1 ` ` ` `Q.push(item); ` ` ` ` ` `// While queue is not empty ` ` ` `while` `(!Q.empty()) ` ` ` `{ ` ` ` `// Take the front word ` ` ` `QItem curr = Q.front(); ` ` ` `Q.pop(); ` ` ` ` ` `// Go through all words of dictionary ` ` ` `for` `(set<string>::iterator it = D.begin(); it != D.end(); it++) ` ` ` `{ ` ` ` `// Process a dictionary word if it is adjacent to current ` ` ` `// word (or vertex) of BFS ` ` ` `string temp = *it; ` ` ` `if` `(isadjacent(curr.word, temp)) ` ` ` `{ ` ` ` `// Add the dictionary word to Q ` ` ` `item.word = temp; ` ` ` `item.len = curr.len + 1; ` ` ` `Q.push(item); ` ` ` ` ` `// Remove from dictionary so that this word is not ` ` ` `// processed again. This is like marking visited ` ` ` `D.erase(temp); ` ` ` ` ` `// If we reached target ` ` ` `if` `(temp == target) ` ` ` `return` `item.len; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `return` `0; ` `} ` ` ` `// Driver program ` `int` `main() ` `{ ` ` ` `// make dictionary ` ` ` `set<string> D; ` ` ` `D.insert(` `"poon"` `); ` ` ` `D.insert(` `"plee"` `); ` ` ` `D.insert(` `"same"` `); ` ` ` `D.insert(` `"poie"` `); ` ` ` `D.insert(` `"plie"` `); ` ` ` `D.insert(` `"poin"` `); ` ` ` `D.insert(` `"plea"` `); ` ` ` `string start = ` `"toon"` `; ` ` ` `string target = ` `"plea"` `; ` ` ` `cout << ` `"Length of shortest chain is: "` ` ` `<< shortestChainLen(start, target, D); ` ` ` `return` `0; ` `}` |

*chevron_right*

*filter_none*

## Python

`# To check if strings differ by ` `# exactly one character ` ` ` `def` `isadjacent(a, b): ` ` ` `count ` `=` `0` ` ` `n ` `=` `len` `(a) ` ` ` ` ` `# Iterate through all characters and return false ` ` ` `# if there are more than one mismatching characters ` ` ` `for` `i ` `in` `range` `(n): ` ` ` `if` `a[i] !` `=` `b[i]: ` ` ` `count ` `+` `=` `1` ` ` `if` `count > ` `1` `: ` ` ` `break` ` ` ` ` `return` `True` `if` `count ` `=` `=` `1` `else` `False` ` ` `# A queue item to store word and minimum chain length ` `# to reach the word. ` `class` `QItem(): ` ` ` ` ` `def` `__init__(` `self` `, word, ` `len` `): ` ` ` `self` `.word ` `=` `word ` ` ` `self` `.` `len` `=` `len` ` ` `# Returns length of shortest chain to reach ` `# 'target' from 'start' using minimum number ` `# of adjacent moves. D is dictionary ` `def` `shortestChainLen(start, target, D): ` ` ` ` ` `# Create a queue for BFS and insert ` ` ` `# 'start' as source vertex ` ` ` `Q ` `=` `[] ` ` ` `item ` `=` `QItem(start, ` `1` `) ` ` ` `Q.append(item) ` ` ` ` ` `while` `( ` `len` `(Q) > ` `0` `): ` ` ` ` ` `curr ` `=` `Q.pop() ` ` ` ` ` `# Go through all words of dictionary ` ` ` `for` `it ` `in` `D: ` ` ` ` ` `# Process a dictionary word if it is ` ` ` `# adjacent to current word (or vertex) of BFS ` ` ` `temp ` `=` `it ` ` ` `if` `isadjacent(curr.word, temp) ` `=` `=` `True` `: ` ` ` ` ` `# Add the dictionary word to Q ` ` ` `item.word ` `=` `temp ` ` ` `item.` `len` `=` `curr.` `len` `+` `1` ` ` `Q.append(item) ` ` ` ` ` `# Remove from dictionary so that this ` ` ` `# word is not processed again. This is ` ` ` `# like marking visited ` ` ` `D.remove(temp) ` ` ` ` ` `# If we reached target ` ` ` `if` `temp ` `=` `=` `target: ` ` ` `return` `item.` `len` ` ` `D ` `=` `[] ` `D.append(` `"poon"` `) ` `D.append(` `"plee"` `) ` `D.append(` `"same"` `) ` `D.append(` `"poie"` `) ` `D.append(` `"plie"` `) ` `D.append(` `"poin"` `) ` `D.append(` `"plea"` `) ` `start ` `=` `"toon"` `target ` `=` `"plea"` `print` `"Length of shortest chain is: %d"` `\ ` ` ` `%` `shortestChainLen(start, target, D) ` ` ` `# This code is contributed by Divyanshu Mehta ` |

*chevron_right*

*filter_none*

Output:

Length of shortest chain is: 7

Time Complexity of the above code is O(n²m) where n is the number of entries originally in the dictionary and m is the size of the string

Thanks to Gaurav Ahirwar and Rajnish Kumar Jha for above solution.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Minimum steps to reach target by a Knight | Set 1
- Shortest path to reach one prime to other by changing single digit at a time
- Check if it is possible to reach a number by making jumps of two given length
- Snake and Ladder Problem
- Find the probability of a state at a given time in a Markov chain | Set 1
- Finding the probability of a state at a given time in a Markov chain | Set 2
- Burn the binary tree starting from the target node
- Shortest paths from all vertices to a destination
- Shortest Path using Meet In The Middle
- Shortest path in an unweighted graph
- Some interesting shortest path questions | Set 1
- Shortest path in a Binary Maze
- Dijkstra’s shortest path algorithm using set in STL
- Multistage Graph (Shortest Path)
- Dijkstra's shortest path with minimum edges