
Problem Statement
The task is to evaluate a string expression
that represents nested ternary expressions. A ternary expression is generally of the form "condition ? trueResult : falseResult". In this problem:
- The conditions can be either
'T'
(true) or'F'
(false). - The results can be either digits (
0
to9
) or other ternary expressions. - The expressions nest in a right-to-left fashion, meaning you solve the most deeply nested or rightmost expression first.
The input ensures that all ternary expressions are correctly formatted and use only the specified characters. The expressions evaluate to either a single digit, 'T'
, or 'F'
. The nesting can be arbitrarily complex, but the structure is always correct and the operations are defined to roll out from the most nested (rightmost) to the least.
Examples
Example 1
Input:
expression = "T?2:3"
Output:
"2"
Explanation:
If true, then result is 2; otherwise result is 3.
Example 2
Input:
expression = "F?1:T?4:5"
Output:
"4"
Explanation:
The conditional expressions group right-to-left. Using parenthesis, it is read/evaluated as: "(F ? 1 : (T ? 4 : 5))" --> "(F ? 1 : 4)" --> "4" or "(F ? 1 : (T ? 4 : 5))" --> "(T ? 4 : 5)" --> "4"
Example 3
Input:
expression = "T?T?F:5:3"
Output:
"F"
Explanation:
The conditional expressions group right-to-left. Using parenthesis, it is read/evaluated as: "(T ? (T ? F : 5) : 3)" --> "(T ? F : 3)" --> "F" "(T ? (T ? F : 5) : 3)" --> "(T ? F : 5)" --> "F"
Constraints
5 <= expression.length <= 104
expression
consists of digits,'T'
,'F'
,'?'
, and':'
.- It is guaranteed that
expression
is a valid ternary expression and that each number is a one-digit number.
Approach and Intuition
To solve the problem efficiently, follow the insights provided by the examples and constraints:
Right-to-Left Parsing: Since the expressions are evaluated from right to left, begin parsing the string from the end to the start. This allows us to handle the most deeply nested expression first, simplifying the larger expression step-by-step.
Stack Utilization: Use a stack to manage and resolve nested ternary expressions. Every time you encounter a decision point (
'?'
), the previously encountered results determined by':'
and the conditions ('T'
or'F'
) can be resolved.- Push characters onto the stack until you encounter a
'?'
. - Determine the true or false branches based on the condition immediately before
'?'
. - Evaluate and replace the ternary expression with its result, pushing the result back to the stack.
- Push characters onto the stack until you encounter a
Scenarios Based on Examples:
- For single ternary like
T?2:3
, push when encountering numbers or results and evaluate upon hitting a condition. - For nested ternary like
F?1:T?4:5
, resolve the innermostT?4:5
first creating a simpler ternaryF?1:4
, which can be further resolved based on the outer condition.
- For single ternary like
Using this approach, even deeper or more complex ternary structures can be unraveled from the inside out, leading to a stack that eventually contains the singular resolved value of the entire expression.
Solutions
- C++
- Java
- C
- JavaScript
- Python
class Solution {
public:
string ternaryParser(string expr) {
int index = 0;
for ( ; index < expr.size(); ) {
if (expr[index] != 'T' && expr[index] != 'F'
|| index == expr.size() - 1 || expr[index + 1] == ':') {
break;
}
if (expr[index] == 'T') {
index += 2;
} else {
int nestDepth;
for (nestDepth = 1, index += 2; nestDepth != 0; index++) {
if (expr[index] == ':') {
nestDepth--;
} else if (expr[index] == '?') {
nestDepth++;
}
}
}
}
return expr.substr(index, 1);
}
};
This solution tackles the problem of parsing a given ternary expression string and identifying the result based on traditional ternary operation logic. The procedure utilizes a simple yet effective evaluation approach, enabling it to navigate through nested expressions seamlessly. Below is a concise summary of the solution's methodology in C++:
- Initiate
index
to 0, which is used to traverse through the string character by character. - Iterate through the characters of
expr
until the end of the string is reached or a character ':' or the last character is encountered directly after 'T' or 'F'. - If the current character indicates 'T', the algorithm skips to the expression part following the '?'; thus,
index
increments by 2. - For a 'F', it becomes necessary to handle nested ternary operations. This is achieved by:
- Initializing
nestDepth
to 1 and starting from the character after 'F'. - Incrementing
index
and adjustingnestDepth
based on occurrences of '?' (which increases depth) and ':' (which decreases depth). The loop exits whennestDepth
returns to zero, indicating the end of this nested section.
- Initializing
- Return the current character of the expression, which is the result of the ternary operation at the initial segment of the string up to this point.
The solution is efficient with its linear traversal strategy, managing complexities introduced by nested ternary structures straightforwardly. This parser provides direct access to the result of the evaluated expression without executing redundant iterations or recursions.
class Solution {
public String computeTernary(String expr) {
int pos = 0;
while (pos < expr.length()) {
char current = expr.charAt(pos);
boolean breakConditions = (current != 'T' && current != 'F') || pos == expr.length() - 1 || expr.charAt(pos + 1) == ':';
if (breakConditions) {
break;
}
if (current == 'T') {
pos += 2;
} else {
int depth;
for (depth = 1, pos += 2; depth != 0; pos++) {
if (expr.charAt(pos) == ':') {
depth--;
} else if (expr.charAt(pos) == '?') {
depth++;
}
}
}
}
return expr.substring(pos, pos + 1);
}
}
This Java solution interprets a ternary expression string and returns the result of the expression. The computeTernary
method processes the ternary expression by iterating through it character by character, starting by initializing pos
to 0. The loop continues as long as pos
is less than the length of the expression string.
Each iteration checks the current character:
- The program first determines whether to break out of the loop using
breakConditions
. This happens if the current character is neither 'T' (True) nor 'F' (False), it's the last character in the string, or the next character is ':'. - If the character is 'T' (indicating true for the ternary condition), the position
pos
is moved by 2, directly pointing to the result part of this ternary section. - If the character is 'F', it means the condition is false, so the code skips to the next relevant section of the ternary expression. This is achieved by adjusting
pos
while maintaining a countdepth
to correctly manage multiple nested ternary expressions. The depth increments on encountering '?' and decrements on encountering ':'; whendepth
equals 0, the correct position is found.
Finally, the function returns the substring of expr
starting from pos
to pos + 1
, effectively extracting the character that results from evaluating the ternary expression. This solution essentially navigates through the ternary expression, effectively ignoring entire branches based on the condition results, and directly points to the resulting character for the evaluated expression.
char * evaluateTernary(char * expr) {
int idx = 0;
while (idx < strlen(expr)) {
if ((expr[idx] != 'T' && expr[idx] != 'F') || idx == strlen(expr) - 1 || expr[idx + 1] == ':') {
break;
}
if (expr[idx] == 'T') {
idx += 2;
} else {
int depth;
for (depth = 1, idx += 2; depth != 0; idx++) {
if (expr[idx] == ':') {
depth--;
} else if (expr[idx] == '?') {
depth++;
}
}
}
}
char *output = malloc(2);
output[0] = expr[idx];
output[1] = '\0';
return output;
}
The provided code is designed to parse and evaluate a string expression representing a ternary operation in C. Ternary operations in this context follow the format condition ? trueValue : falseValue
, where condition
can be 'T' (true) or 'F' (false). This function evaluateTernary
accepts a ternary expression as an input and returns the result of the evaluation as a string.
Here's a breakdown of how the code functions:
- Initialize an index variable (
idx
) to traverse through the given expression. - Use a loop to iterate through the expression until an end condition is met. The end condition is either reaching the end of the string or finding a character that does not need further parsing (
F
,T
followed by:
or being at the last character). - Inside the loop:
- If the current character is
T
and is not near the end or followed by:
, move to the expression part after?
(true part) by incrementingidx
by 2. - If the character is
F
, skip to the corresponding false part after the current question mark?
. This involves skipping nested expressions correctly by increasing or decreasing a depth counter based on encountering additional?
and:
characters.
- If the current character is
- After identifying which part of the ternary will be returned (either directly after a
T
or after skipping parts following aF
), allocate memory for a result string and set its value to the directly referenced single character result (expr[idx]
). - Return the dynamically allocated string containing the result, ensuring to end the string properly with a null character (
\0
).
Use this function to evaluate simple, flat ternary expressions efficiently with a proper handling of nested or chained ternary operations. Note, though, that the function assumes the input to be properly formatted and free of errors.
var evaluateTernary = function(expr) {
let position = 0;
for (; position < expr.length;) {
if (expr[position] != 'T' && expr[position] != 'F'
|| position == expr.length - 1 || expr[position + 1] == ':') {
break;
}
if (expr[position] == 'T') {
position += 2;
} else {
let nestedDepth;
for (nestedDepth = 1, position += 2; nestedDepth != 0; position++) {
if (expr[position] == ':') {
nestedDepth--;
} else if (expr[position] == '?') {
nestedDepth++;
}
}
}
}
return expr.substring(position, position + 1);
};
The Ternary Expression Parser in JavaScript is designed to evaluate a simple ternary expression string to return the result. This implementation follows these primary steps:
Initialize
position
to track the current index within the string expression.Iterate through each character of the input string using a
for
loop. This loop continues as long as theposition
is less than the length of the string.The loop breaks under two conditions:
- If the current character is not 'T' (true) or 'F' (false).
- If it's the last character, or the next character is ':' which denotes the separation of values in the ternary operation.
Inside the loop, if the current character is 'T':
- Move
position
forward by two places to skip the true condition evaluation as the true part will be directly considered.
- Move
If the character at the current position is 'F' (false):
- Initiate a nested depth counter starting from 1 and increment
position
by two to begin parsing the false condition. - Increase the nested depth each time a '?' is encountered and decrease it when ':' is encountered.
- The inner loop continues until the nested depth returns to zero, which means the end of the current ternary expression has been reached.
- Initiate a nested depth counter starting from 1 and increment
Finally, the function returns a substring from the current
position
to the next character, which holds the evaluated result of the ternary expression.
This function effectively parses and evaluates a structured ternary expression through controlled iteration and depth tracking, making it a straightforward and efficient solution.
class Solution:
def getTernaryValue(self, expr: str) -> str:
index = 0
while True:
if expr[index] not in 'TF' or index == len(expr) - 1\
or expr[index + 1] == ':':
return expr[index]
if expr[index] == 'T':
index += 2
else:
layer_depth = 1
index += 2
while layer_depth != 0:
if expr[index] == ':':
layer_depth -= 1
elif expr[index] == '?':
layer_depth += 1
index += 1
The provided Python code defines a solution for parsing and evaluating ternary expressions. The code facilitates interpreting an expression where decisions are made based on the operators '?' and ':'. Given a ternary expression string, the code determines its result using a method named getTernaryValue
.
- The method starts by initializing
index
to track the current position in the expression string. - It contains a loop that runs until a decision is made, breaking when a value ('T' for true or 'F' for false, representing 'True' and 'False' respectively) is directly encountered without subsequent operators.
- For every character at the current index:
- If the character is 'T' and followed by a '?', it means the result depends on the expression following the '?'. The index is moved forward by 2 to evaluate the next relevant part of the expression.
- If the character is not 'T' (i.e., 'F') and followed by '?', the code needs to skip the next expression portion and move to the part after the corresponding ':'. This requires handling nested '?' and ':' characters to ensure correct skipping, achieved by maintaining a
layer_depth
count. When encountering a '?', the layer is considered deeper, and encountering ':' decreases the layer depth. - The loop breaks when the required part of the expression is processed, either providing 'T' or 'F' based on the evaluated condition.
This structure ensures that the ternary expression is evaluated correctly, considering the precedence and order dictated by its structure. The parser is efficient in handling nested and complex ternary operations by jumping over irrelevant parts based on the condition evaluations.
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