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CyC2018
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@ -2327,15 +2327,17 @@ Note that different sequences are counted as different combinations.
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Therefore the output is 7.
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```
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完全背包。
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```java
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public int combinationSum4(int[] nums, int target) {
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if (nums == null || nums.length == 0) return 0;
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int[] dp = new int[target + 1];
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dp[0] = 1;
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for (int i = 1; i <= target; i++) {
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for (int j = 0; j < nums.length; j++) {
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if (nums[j] <= i) {
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dp[i] += dp[i - nums[j]];
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for (int num : nums) {
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if (num <= i) {
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dp[i] += dp[i - num];
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}
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}
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}
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@ -2343,30 +2345,13 @@ public int combinationSum4(int[] nums, int target) {
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}
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```
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**只能进行两次的股票交易**
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[Leetcode : 123. Best Time to Buy and Sell Stock III (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/description/)
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```java
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public int maxProfit(int[] prices) {
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int firstBuy = Integer.MIN_VALUE, firstSell = 0;
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int secondBuy = Integer.MIN_VALUE, secondSell = 0;
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for (int curPrice : prices) {
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if (firstBuy < -curPrice) firstBuy = -curPrice;
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if (firstSell < firstBuy + curPrice) firstSell = firstBuy + curPrice;
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if (secondBuy < firstSell - curPrice) secondBuy = firstSell - curPrice;
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if (secondSell < secondBuy + curPrice) secondSell = secondBuy + curPrice;
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}
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return secondSell;
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}
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```
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**只能进行 k 次的股票交易**
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[Leetcode : 188. Best Time to Buy and Sell Stock IV (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/description/)
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```html
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dp[i, j] = max(dp[i, j-1], prices[j] - prices[jj] + dp[i-1, jj]) { jj in range of [0, j-1] } = max(dp[i, j-1], prices[j] + max(dp[i-1, jj] - prices[jj]))
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dp[i, j] = max(dp[i, j-1], prices[j] - prices[jj] + dp[i-1, jj]) { jj in range of [0, j-1] }
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= max(dp[i, j-1], prices[j] + max(dp[i-1, jj] - prices[jj]))
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```
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```java
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@ -2392,6 +2377,24 @@ public int maxProfit(int k, int[] prices) {
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}
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```
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**只能进行两次的股票交易**
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[Leetcode : 123. Best Time to Buy and Sell Stock III (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/description/)
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```java
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public int maxProfit(int[] prices) {
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int firstBuy = Integer.MIN_VALUE, firstSell = 0;
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int secondBuy = Integer.MIN_VALUE, secondSell = 0;
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for (int curPrice : prices) {
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if (firstBuy < -curPrice) firstBuy = -curPrice;
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if (firstSell < firstBuy + curPrice) firstSell = firstBuy + curPrice;
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if (secondBuy < firstSell - curPrice) secondBuy = firstSell - curPrice;
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if (secondSell < secondBuy + curPrice) secondSell = secondBuy + curPrice;
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}
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return secondSell;
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}
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```
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### 数组区间
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**数组区间和**
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@ -2824,8 +2827,7 @@ public int countPrimes(int n) {
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```java
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int gcd(int a, int b) {
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if (b == 0) return a;
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return gcd(b, a % b);
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return b == 0 ? a : gcd(b, a% b);
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}
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```
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@ -2841,47 +2843,80 @@ int lcm(int a, int b){
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对于 a 和 b 的最大公约数 f(a, b)，有：
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1\. 如果 a 和 b 均为偶数，f(a, b) = 2\*f(a/2, b/2);
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2\. 如果 a 是偶数 b 是奇数，f(a, b) = f(a/2, b);
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3\. 如果 b 是偶数 a 是奇数，f(a, b) = f(a, b/2);
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4\. 如果 a 和 b 均为奇数，f(a, b) = f(a, a-b);
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- 如果 a 和 b 均为偶数，f(a, b) = 2\*f(a/2, b/2);
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- 如果 a 是偶数 b 是奇数，f(a, b) = f(a/2, b);
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- 如果 b 是偶数 a 是奇数，f(a, b) = f(a, b/2);
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- 如果 a 和 b 均为奇数，f(a, b) = f(a, a-b);
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乘 2 和除 2 都可以转换为移位操作。
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### 进制转换
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Java 中 static String toString(int num, int radix) 可以将一个整数装换为 redix 进制表示的字符串。
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**7 进制**
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[Leetcode : 504. Base 7 (Easy)](https://leetcode.com/problems/base-7/description/)
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```java
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public String convertToBase7(int num) {
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if (num < 0) {
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return '-' + convertToBase7(-num);
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}
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if (num < 7) {
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return num + "";
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}
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if (num < 0) return '-' + convertToBase7(-num);
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if (num < 7) return num + "";
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return convertToBase7(num / 7) + num % 7;
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}
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```
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```java
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public String convertToBase7(int num) {
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if (num == 0) return "0";
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StringBuilder sb = new StringBuilder();
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boolean isNegative = num < 0;
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if (isNegative) num = -num;
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while (num > 0) {
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sb.append(num % 7);
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num /= 7;
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}
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String ret = sb.reverse().toString();
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return isNegative ? "-" + ret : ret;
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}
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```
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Java 中 static String toString(int num, int radix) 可以将一个整数转换为 redix 进制表示的字符串。
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```java
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public String convertToBase7(int num) {
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return Integer.toString(num, 7);
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}
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```
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**16 进制**
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[Leetcode : 405. Convert a Number to Hexadecimal (Easy)](https://leetcode.com/problems/convert-a-number-to-hexadecimal/description/)
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负数要用它的补码形式。
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```html
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Input:
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26
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Output:
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"1a"
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Input:
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-1
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Output:
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"ffffffff"
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```
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```java
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public String toHex(int num) {
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char[] map = {'0','1','2','3','4','5','6','7','8','9','a','b','c','d','e','f'};
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if(num == 0) return "0";
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String ret = "";
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StringBuilder sb = new StringBuilder();
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while(num != 0){
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ret = map[(num & 0b1111)] + ret;
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num >>>= 4;
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sb.append(map[num & 0b1111]);
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num >>>= 4; // 无符号右移，左边填 0
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}
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return ret;
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return sb.reverse().toString();
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}
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```
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@ -2918,15 +2953,14 @@ Return "100".
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```java
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public String addBinary(String a, String b) {
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int i = a.length() - 1, j = b.length() - 1, carry = 0;
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String str = "";
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while(i >= 0 || j >= 0){
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StringBuilder str = new StringBuilder();
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while (carry == 1 || i >= 0 || j >= 0) {
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if (i >= 0 && a.charAt(i--) == '1') carry++;
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if (j >= 0 && b.charAt(j--) == '1') carry++;
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str = (carry % 2) + str;
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str.append(carry % 2);
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carry /= 2;
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}
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if(carry == 1) str = "1" + str;
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return str;
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return str.reverse().toString();
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}
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```
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@ -2938,15 +2972,15 @@ public String addBinary(String a, String b) {
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```java
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public String addStrings(String num1, String num2) {
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StringBuilder sb = new StringBuilder();
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int carry = 0;
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for(int i = num1.length() - 1, j = num2.length() - 1; i >= 0 || j >= 0 || carry == 1; i--, j--){
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int x = i < 0 ? 0 : num1.charAt(i) - '0';
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int y = j < 0 ? 0 : num2.charAt(j) - '0';
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sb.append((x + y + carry) % 10);
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StringBuilder str = new StringBuilder();
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int carry = 0, i = num1.length() - 1, j = num2.length() - 1;
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while (carry == 1 || i >= 0 || j >= 0) {
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int x = i < 0 ? 0 : num1.charAt(i--) - '0';
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int y = j < 0 ? 0 : num2.charAt(j--) - '0';
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str.append((x + y + carry) % 10);
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carry = (x + y + carry) / 10;
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}
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return sb.reverse().toString();
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return str.reverse().toString();
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}
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```
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