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leetCode-282:Expression Add Operators

问题描述

给定一个数字字符串和一个整数,在数字字符串中间插入 +-* 符号构成一个表达式,要求找出所有表达式的值等于目标数字的表达式。题目链接:**点我**

样例输入输出

输入:num = “123”, target = 6

输出:[“1*2*3”, “1+2+3”]

输入:num = “3456237490”, target = 9191

输出:[]

问题解法

题目要求找出所有的结果,故只能用搜索进行求解。需要注意的是将字符串转成数字时以及运算过程中不要超过整形范围的边界,同时注意数字不能有前置0,但是数字0是允许出现的。代码如下

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class Solution {
private String maxValue = String.valueOf(Integer.MAX_VALUE);

public List<String> addOperators(String num, int target) {
List<String> result = new ArrayList<>();
List<Integer> nums = new ArrayList<>();
for (int i = 0; i < num.length(); i++) {
String left = num.substring(0, i + 1);
if (!isValid(left)) {
break;
}
Integer leftNum = Integer.parseInt(left, 10);
nums.add(leftNum);
search(result, num, i + 1, nums, new ArrayList<>(), target);
nums.remove(nums.size() - 1);
}
return result;
}

private void search(List<String> result, String num, int start, List<Integer> nums, List<Character> ops, int target) {
if (start == num.length()) {
if (isEqual(nums, ops, target)) {
String item = convert(nums, ops);
result.add(item);
}

return;
}

for (int i = start; i < num.length(); i++) {
String left = num.substring(start, i + 1);
if (!isValid(left)) {
break;
}
Integer leftNum = Integer.parseInt(left, 10);
nums.add(leftNum);
ops.add('+');
search(result, num, i + 1, nums, ops, target);
ops.set(ops.size() - 1, '-');
search(result, num, i + 1, nums, ops, target);
ops.set(ops.size() - 1, '*');
search(result, num, i + 1, nums, ops, target);

nums.remove(nums.size() - 1);
ops.remove(ops.size() - 1);
}
}

private String convert(List<Integer> nums, List<Character> ops) {
StringBuilder sb = new StringBuilder();
sb.append(nums.get(0));
for (int i = 0; i < ops.size(); i++) {
sb.append(ops.get(i)).append(nums.get(i + 1));
}
return sb.toString();
}

private boolean isEqual(List<Integer> nums, List<Character> ops, int target) {
Deque<Integer> numQueue = new LinkedList<>();
Deque<Character> opQueue = new LinkedList<>();
numQueue.addLast(nums.get(0));
int i = 1;
int j = 0;
while (i < nums.size()) {
numQueue.addLast(nums.get(i));
if (ops.get(j) == '*') {
int first = numQueue.pollLast();
int second = numQueue.pollLast();
// 避免溢出
if (first != 0 && Integer.MAX_VALUE / first < second) {
return false;
}
int temp = first * second;
numQueue.addLast(temp);
} else {
opQueue.addLast(ops.get(j));
}
i++;
j++;
}

while (!opQueue.isEmpty()) {
int first = numQueue.pollFirst();
int second = numQueue.pollFirst();
int temp;
if (opQueue.pollFirst() == '+') {
temp = first + second;
} else {
temp = first - second;
}

numQueue.addFirst(temp);
}

return numQueue.pollFirst() == target;
}

private boolean isValid(String num) {
if (num.length() == 1) {
return true;
}

if (num.charAt(0) == '0') {
return false;
}

return num.length() < maxValue.length() || num.compareTo(maxValue) < 1;
}
}